research article experimental investigation of wave-induced ship hydroelastic vibrations by...

Research ArticleExperimental Investigation of Wave-Induced Ship HydroelasticVibrations by Large-Scale Model Measurement in Coastal Waves

Jialong Jiao Huilong Ren Shuzheng Sun and Christiaan Adika Adenya

College of Shipbuilding Engineering Harbin Engineering University Harbin 150001 China

Correspondence should be addressed to Huilong Ren renhuilong263net

Received 8 October 2015 Accepted 31 January 2016

Academic Editor Jorg Wallaschek

Copyright copy 2016 Jialong Jiao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Ship hydroelastic vibration is an issue involving mutual interactions among inertial hydrodynamic and elastic forces Theconventional laboratory tests for wave-induced hydroelastic vibrations of ships are performed in tank conditions An alternativeapproach to the conventional laboratory basin measurement proposed in this paper is to perform tests by large-scale modelmeasurement in real sea waves In order to perform this kind of novel experimental measurement a large-scale free runningmodeland the experiment scheme are proposed and introduced The proposed testing methodology is quite general and applicable to awide range of ship hydrodynamic experimental research The testing procedure is presented by illustrating a 5-hour voyage trial ofthe large-scale model carried out at Huludao harbor of China in August 2015 Hammer tests were performed to identify the naturalfrequencies of the ship model at the beginning of the tests Then a series of tests under different sailing conditions were carriedout to investigate the vibrational characteristics of the model As a postvoyage analysis load pressure acceleration and motionresponses of the model are studied with respect to different time durations based on the measured data

1 Introduction

In the recent decades ships have become larger and fasterdue to the world globalization and the development require-ments As a result the natural frequencies of large ships havebecome lower and may often fall into the range of waveencounter frequencies even in a common sea state [1]There-fore simulations of hydroelastic vibrations of large shipsshould be performed to accurately predict the wave-inducedloads of ships [2]

Hydroelastic mechanics is a branch of ship structuralmechanics which considers both ship hydrodynamic forceand hull structural elastic force [3] Since ship hydroelasticvibration problemsmdashinvolving the mutual interaction of acomplex shaped elastic hull with fluid and free surfacemdashare quite complex and cannot be satisfactorily processedby numerical and analytical approaches physical simulationtests constitute an indispensable approach in the investigationof ship hydroelasticity [4] Generally speaking there are twodifferent kinds ofmodels for performing tests for hydroelasticvibrational responses monoblock model and segmentedmodel [5 6] In the formermodel a material of proper Young

modulus which is much smaller than steel and of the samePoisson ratio as steel is used to build themodel hull in order tomake the stiffness of model similar to ship prototype [7] Thelatter model that is segmentedmodel is connected by a con-tinuous compliant backbone from which the sectional loadsand vibrations responses of the model hull can be measured[8] On the other hand the rare material in the first model isquite expensive and is not easy to be operated at model man-ufacture process Therefore the latter testing approach is amore popular choice compared with the former

The conventional laboratory segmented models forhydroelastic vibration responses are towed in the tank [9ndash11]Usually themodels are relatively small and the waves are gen-erated by wave makers It is known that the scale effects andboundary wall effects must be considered while designingand performing tank testsThewaves generated bywavemak-ers are unidirectional artificial and pseudo-random Fur-thermore the six degrees of freedom motions of the modelin the tank are usually measured by mechanical seakeepinginstrument which connects the model using its heave sticksHowever the heave sticks fixed on the model may restrict

Hindawi Publishing CorporationShock and VibrationVolume 2016 Article ID 9296783 14 pageshttpdxdoiorg10115520169296783

2 Shock and Vibration

the modelrsquos freedom of motions in some sense In summarythe above statements reflect some of the challenges of theconventional tank model tests

In fact the real sea conditions where ships sail are quitedifferent from those simulated in the tank In the sea thereexist wave diffraction refraction and breaking as well as theassociated effects caused by winds and currents Sea wavesspread along a dominant direction with components fromdifferent directions superimposed onto one another whilethe tank waves are usually unidirectional Although a fewnovel tank facilities allow for the generation of two directionscrossed irregular waves [12] the waves generated are stillmore or less different from the actual sea waves It is consid-ered that full-scale ship sea trial measurement reflects whatreally happens on the ship However the data acquisition isquite difficult since the weather and wave states are uncon-trollable Moreover the extreme high sea states desired forinvestigation are rarely suffered by a full-scale large ship

A new alternative approach to the laboratory basin mea-surement and full-scale sea measurement introduced in thispaper is to perform tests by large-scalemodels in real sea con-ditions [13ndash15] The measurements are carried out in short-crested directional spreading andwind-generated seawavesThe scale effects can be reduced by testing relatively largerscale models The large-scale models can be tested with theequipment of superstructures and appendages thus the windand current associated effects are taken into accountThe testscan be carried out at any arbitrary heading angle In a wordthis testing condition can be regarded as more realistic com-pared with the laboratory basin condition However therealso exist disadvantages regarding the proposed approachsuch as the fact that the sea wave conditions cannot be con-trolled and thus the trial procedure lasts a long time waitingfor the expected wave conditions

The characteristics of hydroelastic vibrations and bow-flare slamming of a small-scale model in regular waves havealready been studied through laboratory tank tests which canbe found in the authorsrsquo previous work [16] In the presentwork a large-scale model corresponding to the same pro-totype as that of the small-scale model was designed andmanufactured to allow for themeasurement of wave-inducedhydroelastic vibrations and slamming experienced in coastalwaves

In this paper the large-scale model structural design andexperimental system are introduced first Then a 5-hourvoyage trial performed at Huludao harbor of China in August26 2015 is presented Finally the hydroelastic vibrationaland bow impact characteristics of the large-scale model aredescribed and analyzed from different terms based on theexperimental results

2 Experimental Design

21 Hull Structural Design To investigate the hydroelasticvibrational behavior of a large ship a large-scale segmentedmodel hull was designed and built The principal parametersof the prototype and model are listed in Table 1 whereVCG denotes vertical center of gravity (COG) LCG denotes

Table 1 Principal parameters

Description Ship prototype Model hullScale 11 125Length overall (m) 313 1252Length waterline (m) 292 1168Moulded breadth (m) 395 158Depth (m) 255 102Draft (m) 10 040Displacement (t) 71875 46VCG from BL (m) 16 064LCG from AP (m) 1405 562

longitudinal COG BL denotes baseline and AP denotes aftperpendicular

The model hull was constructed by fiberglass reinforcedplastic (FRP) material A continuous backbone beam wasinstalled at the mean neutral axis height of the segmentedmodel to connect the segmentsThe shipmodel was designedto have 20 stations in total with station 0 at bow area and sta-tion 20 at aft areaThemodel hull was divided into seven inde-pendent segments by using the 2nd 4th 12th divisions atthe manufacture stage Sectional loads at the six cut divisionsare measured by using unidirectional strain sensors mountedon the backbone surfaces The monolithic large space fromthe 12th station to 20th station at aft area is used for housingpropulsion system General arrangements of the ship modelstructure and the onboard experimental apparatus are shownschematically in Figure 1

The pressure response behaviors of flare impact and bot-tom impact at bow area are studied in particular [17] Threepressure gauges intended to measure the bow-flare impactpressure and one intended to measure the bottom fluctuatingpressure are disposed at the center line of bow area whosepositions can be seen in Figure 2 The pressure gauges havea range of 100 kPa and an accuracy of 10 Pa for measure-ment The sampling frequency of pressure gauges was set at100Hz during the measurements

Photographs of the large-scale model are illustrated inFigure 3 Figure 3(a) shows the large-scale model onshorebefore the experimental activities at Huludao harborFigure 3(b) shows the backbone beam and its fixing instru-ments after model assembly in the laboratory of the Instituteof Naval Architecture and Ocean Engineering Mechanics(INOM) of Harbin Engineering University (HEU) where themodel was assembled and debugged

22 Backbone System Steel backbone beam with rectangulartubular structure was designed for the model to allow forthe measurement of ship wave loads The configuration andparameters of cross section of the backbone beam weredetermined to satisfy the stiffness distribution and two-nodevertical vibrational natural frequency of the model hull Theinner wall dimensions for width 119871 and height 119867 of thebackbone remain unchanged The backbone was howevermadewith different thicknesses 119905 and119889 at different sections soas to meet the stiffness distribution demand Strain gauges of

Shock and Vibration 3

Video

Bow accelerometer

GPS

Radio antenna

Rescue alarm

GPSINSdevice

Battery pack

Amidships accelerometer

Course top

Data collector

Stern accelerometer

Gear boxElectric motor

Drive unitSpeed control box

Backbone beamDeckhouse

Strain

Pressure sensor

20 18 16 14 12 8 6 4 2 0

receiver

gaugesposition

camera

Figure 1 Model equipment

12

3

4

640WL800WL960WL

Waterline

Spreading

Sailing speed

Large waveImpact

2 06

Figure 2 Sketch of bow-flare impact model

full-bridge circuit were mounted on the backbone surfacesat 2nd 4th 12th stations in order to measure sectionalvertical bending moment (VBM) and horizontal bendingmoment (HBM) acting on the model induced by waves Thesectional dimensions of the backbone and the arrangement offull-bridge strain gauges on the backbone surfaces are shownschematically in Figure 4 where1198811sim1198814 are strain gauges forVBM measurement and 1198671sim1198674 are strain gauges for HBMmeasurement The strain gauges have a range of 2000MPaand a measurement accuracy of 0001MPa The samplingfrequency was set at 50Hz during the tests The comparisonsof the expected value and design value of bending momentsof inertia distributions along the model length are shown inFigure 5

Fixing plates were adopted between each pair of the cutstations that is at the 15th 3rd 5th 13th stations tofix the segmented hulls on the continuous backbone beamstrongly The sketch of the ship model global vibrationalsystem is shown in Figure 6 In this simplified diagramthe segmented hulls are regarded as mass centralized on

the continuous backbone and the fluids around the hulls areregarded as added mass on the segmented hulls The wave-induced loads are transferred to the backbone beam by thesegmented hulls The sectional loads are measured by thestrain gauges located between each pair of the segmentedhulls

Since the sectional signal measured by full-bridge straingauges is strain (stress) the corresponding bending momentcan be expressed as follows

119872119898=120590119868

119911 (1)

where 120590 denotes the measured stress 119868 denotes the sectionalmoment of inertia 119911denotes the distance between the neutralaxis and the strain gauge and 119872

119898denotes the obtained

bending moment corresponding to model hullIn addition the bending moment corresponding to ship

prototype can be derived by the similitude law according tothe knowledge of ship hydrodynamic experiment

119872119904=119872119898

1205824 (2)

where 119872119904denotes the obtained bending moment corre-

sponding to ship prototype and 120582 denotes the model scaleratio

The derived conversion coefficients for bending momentcorresponding to model scale and full-scale are respectivelylisted in Table 2 In addition calibration tests were alsoconducted on the backbone beam by applying known staticloads and recording the corresponding strain values tovalidate the calculated conversion coefficients of model scaleThe confirmatory test results are in good agreement with thecalculations


(a) Hull structure (b) Backbone system

Figure 3 Photographs of the large-scale model hull

Table 2 Conversion coefficients

StationVBM HBM

Model(NsdotmMPa)

Prototype(MNsdotmMPa)

Model(NsdotmMPa)


2 428 167 443 1734 457 179 565 2216 720 281 936 3668 875 342 994 38810 899 351 1082 42312 934 365 1216 475

y

z

o

L

H

t

d

V1 V3

V2 V4

H1

H3

H2

H4

Strain gauge

Figure 4 Cross section of backbone beam

23 Testing System Three ships that is119860 119861 and 119862 are usedto allow for the execution of the experimental activities Ship119860 is the large-scale testing model Ship 119861 is an auxiliary yachtwhich moves around 119860 but keeps a distance of about 100mfrom 119860 during the testing measurement Ship 119862 situated atthe center of sailing trace of model ship 119860 is used for wavemeasurement A crew onboard 119861 steers the model ship 119860 viaradio signal to make it run at a desired speed and a desiredheading angle In addition another crew onboard 119861 usesvideo camera to record the scene of sailing information ofmodel ship 119860 Three pairs of radio stations are adopted andinstalled onboard of119860 and119861 to allow for the communicationsbetween the two ships

0

4000

8000

12000

16000

20000

0 2 4 6 8 10 12 14Station

Mom

ent o

f ine

rtia

(cm

4)

Ih design valueI design value

Ih expected valueI expected value

Figure 5 Comparison of moments of inertia

mEI

Q(t)

Mass Wet added massLoad Strain gauge

Madd

Figure 6 Sketch of the model hull global vibration system

The radio-controlled self-propelling model ship is fullyequipped with all the electronic technique apparatus whichare necessary to carry out the experiments The apparatusmainly includes GPS device propulsion system autopilotsystem and a data recorder Framework of the testing systemis shown in Figure 7 and the subsystems are generally con-cluded below [18 19]

The GPSINS-aided device is utilized to measure andrecord the position speeds heading angle andmotions of thetesting model 119860 Its measurement precision of heading angleis in 005∘ pitch and roll angle precisions are in 002∘ andthree unidirectional (eastern northern and vertical) speed


GPS receiver

GPSINS station

Radio

Interface

Ship trajectory speed and position

Autopilot radio

Computer unit

Control interface

Pilot drive unit

Sectional load

Vertical acceleration

Impact pressure

Data collector

Computer

Motor control device

Motors

Shafts propellers

Propulsion

Radio

Computer GPSINS station

Autopilot interface

Motor control

Video camera

Wave buoyComputer

A B

C

A

B

C

Figure 7 Framework of the overall testing system

precisions are in 002ms Data recorded by the GPSINS-aided device are transmitted to the auxiliary yacht 119861 by radiothen the laptop onboard 119861 processes and displays it to thecrew

Four screw propellers and double DC brushless electricmotors are used by the model to achieve the experimentalforward speeds Each electric motor is used to drive doubleshafts (the inner pair or outer pair) with the help of thededicated cross-connection gearboxes The schematicallyarrangement of the propulsion mechanism can be found inFigure 1 A set of rechargeable sulfuric acid storage batterypack is adopted to provide the necessary energy to propel theship model as well as to support all the electronic equipment

Twin rudders were installed behind and in alignmentwith the inner propellers A set of autopilot control systemwhich is the commercial production of GARMIN Companyis used to steer the model The autopilot system is made upof four subsystems They are the course computer unit theelectronic control unit the drive unit and the user controlinterface unit [20] A course top is used to feedback the courseofmodel ship in real timeThe autopilot controller supportedby a GPS-unit is based on the PID control algorithm Modelcourse is kept by the dedicated drive unit which adjusts therudder angle by its built-in hydraulic instrument When theship model 119860 needs to change course the crew will input acommanded heading angle using the dedicated user controlinterface onboard 119861 and then the signal will be transmittedby radio and received by the control computer unit onboard119860 Then the rudder angle will be adjusted and kept by thedrive unit

A commercial DONGHUA TEST 5902 data acquisitiondevice is adopted to record the sectional loads the impactpressures and the vertical axis accelerations at bow andstern areas during the trials The main purpose of the modeltests is to measure the sectional hull girder VBM and HBMloads induced by waves In addition bow impact and fluc-tuating pressures are measured by pressure transducers Theship sailing states and motions are measured by the afore-mentioned GPSINS-aided device Moreover the sea wavesare measured by a wave buoy

3 Experimental Campaign

The field tests were conducted at the nearshore seas of Hulu-dao China (north longitude 40∘661015840 east latitude 120∘931015840) inAugust 2015 Figure 8 shows an aerial view of the testing fieldThe running route was selected at about 6 km away from thebeach where the water surface is large enough to execute thetests During the tests two video cameras (one was supportedby a testing crew onboard the auxiliary yacht 119861 and the otherwas mounted onboard themodel ship119860) recorded the scenesof testing procedure from different views simultaneously Allthe crew highly cooperated to ensure all the testing systemsoperated in a good state so that the trials could proceedsmoothly and accurately

For each set of the sailing speed under a certain sea statethe responses at six different heading angles were tested [21]The runs were performed according to the desired run routesas illustrated in Figure 9 in which direction 1 is for headwave condition direction 2 is for following wave condition


HuludaoLaunching ramp

Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)

Figure 8 Voyage map of sea trial

12

3

4

5

6Buoy

Wave direction

0

Figure 9 Nominal sailing pattern

direction 3 is for port quarter condition direction 4 is forstarboard bow condition direction 5 is for port beam con-dition and direction 6 is for starboard beam condition

4 Sea State Estimation

It is essential to estimate the sea state model encounteredbecause the load andmotion responses are induced by the seawaves Sea waves were measured using a wave buoy meterDuring the measurement wave buoy was deployed at thecenter of the model runsThe buoy has an axis accelerometermounted at its COG to allow for the measurement of instan-taneous vertical acceleration of wave surface

An example of 50-second duration of the measured ver-tical acceleration of wave surface is given in Figure 10(a) Toprocess the obtained time-domain data spectral analysis wasdone using a programcode based on autocorrelation functionmethodThe autocorrelation function based theory considersthe wave signal to be linear and stationary The spectralresult can be derived according to the probability theoryand detailed information about this method can be found in[22]The significant wave height and characteristic period arealso acquired from the spectral analysis The wave spectrumobtained by possessing a measured 15-minute accelerationdata is shown in Figure 10(b) As seen from the result thereare two dominant frequency components in the waves Thepeak frequency of first dominant component is 0252Hz andthe second is 0527HzThe significantwave height and periodcalculated by the above-mentioned spectral analysis method

are 0266m and 1932 s respectively The significant waveheight and period respectively correspond to 665m and966 s of ship prototype which is about six-level sea state forfull-scale ship

5 Results and Analyses

51 Impact Hammer Test Impact hammer tests were per-formed after the model was launched in a relative calm seaarea in order to obtain the natural vibration frequencies ofthe ship model in wetted condition It is noted that the targettwo-node natural frequency for vertical bending mode of themodel hull in wetted condition is 2316Hz The stress timehistoriesmeasured by strain gauges at the 4th and 8th stationsduring a hammer test are shown in Figure 11(a) As seen fromthe curves there exist some low frequency load componentscaused by waves since the sea surface was not absolutelycalm but this has little influence on the resultThe frequency-domain results shown in Figure 11(b) are obtained by fastFourier transform (FFT) processing As seen from the spec-tral results vertical natural vibration frequencies of the firstthree modes of the model in wetted condition are 2273Hz6566Hz and 11364Hz respectivelyThe experimental resultand the prediction are in a good agreement with an errorof 186 for the two-node vertical vibration frequency Thehorizontal vibration frequencies are obtained by the samemethod The two-node and three-node horizontal vibrationfrequencies are 4922Hz and 9974Hz respectively

52 Voyage Process Overview The sea trial was conductedat Huludao harbor of China on August 26 2015 The modelwas launched at 1140 am and was taken back at 350 pmThe analyses of the measured data were done as a postvoyageprocessThe loads pressures accelerations andmotions datarecorded during the overall trial process are summarized inFigure 12

The VBM and HBM loads measured at cut stations fromstation 2 to station 12 are displayed from bottom to top inFigures 12(a) and 12(b) respectivelyThe impact pressure datarecorded by gauges 1sim4 (locations are shown in Figure 2) areshown in Figure 12(c) Vertical axis accelerations at bow andstern areas are shown in Figure 12(d) Pitch and vertical speedat COG of the model are shown in Figures 12(e) and 12(f)respectively It should be noted that the curves of loads accel-erations and motions oscillate from a positive maximumto a negative minimum around the zero-mean value Thepressure values at initial and final regions of the time seriesmdashwhich are without the occurrence of water impactmdashare zeroHowever in order to save space and for the convenience ofcomparison the signals of the same category are presentedtogether in each figure The experimental results presentedin this paper are all given corresponding to model scale

From 0 to 3215 s the model was being transported andwas still on the ground which can be clearly seen from theresponses shown in the figures After themodel was launchedinto the sea the wave-induced responses were initially smallbecause the waves near the beach were relatively small As themodel started to sail away from the beach load and motionresponses increased gradually At the time of about 5600 s


0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)

(a) Time history of vertical acceleration

00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)

(b) Spectral analysis result

Figure 10 Sea waves measured and the spectral analysis result

00

04

08

12

4th station 8th station

Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12

(a) Time histories of stress

000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz

(b) Frequency-domain results

Figure 11 Hammer test of vertical vibrations in wetted condition

the waves that the model experienced were steady and thetests began Tests were finished at the time of about 12000 sand then the model was steered back to the coast Duringthe measurement there was a break from 8500 s to 9000 sMeanwhile the model was stopped thus the responses wererelatively small

Typical snapshots captured from the testing video record-ings are shown in Figure 13 In Figure 13(a) bow slammingphenomena are observed It is worth mentioning that specialattention should be paid to the impact loads acting on the hullcaused by slamming especially the structural strength at thebow area Figure 13(b) presents the turning circle movementof themodel during the voyage During the tests it was foundthat good propeller behavior and maneuverability of themodel are of great importance in steering the model

53 Short-Term Analysis In order to investigate the short-term responses of loads and motions of the ship model theabsolute speed and azimuth recorded by the GPSINS deviceare studied firstly Figure 14(a) illustrates the northern andeastern components of the model speed during a testingscheme period Figure 14(b) illustrates the sailing azimuthtime history of the corresponding time duration As seen

from the figures the sailing speeds and azimuth are stablefrom 7500 s to 8500 s The resultant velocity is about 2mswhich corresponds to real ship speed of 19 knotsThe azimuthis about 300 deg and it is port quarter condition consideringthe wave dominant direction during the testing period

It is known that the loads experienced by ships in severewaves can be split into twomain categories global wave loadsand slamming loadsUsually these two kinds of loads oscillateat different frequencies The Fourier transform provides ageneral method to allow for the transformation of signalsfrom time-domain to frequency-domain However there areseveral limitations of the Fourier spectral analysis the dataprocessed is limited to linear and stationary signals [23]However many vibrational phenomena can be approximatedby linear and stationary systems thus Fourier spectral analy-sis is still widely used to process such data

Load pressure acceleration and motion responses inthe time duration from 7500 s to 8500 s were extractedand are illustrated in Figure 15 Time histories and thecorresponding spectral results by FFT using the Originsoftware of VBMandHBMare presented in Figures 15(a) and15(b) respectively Vertical acceleration time histories andthe corresponding spectral results of bow and stern areas are


0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)

Section 2Section 6Section 10


(a) VBM time histories

0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)



(b) HBM time histories

00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4

(c) Pressure time histories

Bow accelerationStern acceleration

minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)

(d) Acceleration time histories

0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4

(e) Pitch time history

0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06

(f) Vertical speed time history

Figure 12 Time histories recorded during the whole trial process

(a) Bow-flare slamming (b) Turning circle movement

Figure 13 Snapshots of experimental scenes


0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)

North velocityResultant velocity

East velocity

(a) Sailing speed components

7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth

Figure 14 Sailing state in a short interval

shown in Figure 15(c) Time histories and the correspondingspectral results of pitch and vertical speed at COG of themodel are shown in Figures 15(d) and 15(e) respectively

As seen from Figure 15(a) the peak frequency of VBMmainly ranges from018Hz to 092Hz which is the interval ofencounter frequencies of themodel to the sea wavesThe highfrequency vibration components are mainly focused around2214Hz which is close to the two-node natural frequencyof vertical vibration Similar phenomena are observed fromthe HBM results The peak frequency of HBMmainly rangesfrom 026Hz to 091Hz and the high frequency vibrations aremainly focused around 487Hz

The dominant peak frequencies of accelerations pitchand vertical speed are 0608Hz 0605Hz and 0605Hzrespectively The peak frequencies of longitudinal motionsshow good agreement This indicates that the nonlinearity ofthe motions is not as pronounced as that of the loads It isnoteworthy that there exist high frequency components at thefrequency of 2214Hz in the acceleration spectral resultsThisindicates that the vibrations of ship model have an influenceon hull accelerations

Autocorrelation function based spectral processing of themeasured time series was conducted to obtain the significantamplitude values Furthermore extreme amplitude valuesduring this testing period were extracted for comparativeanalysis The calculated and statistical results of load andmotion responses are listed in Tables 3 and 4 respectively

It can be found from the analysis result in Table 3 thatmaximum values of both significant and extreme VBM

Table 3 Statistical results of load responses

Station VBM (Nsdotm) HBM (Nsdotm)Significant Extreme Significant Extreme

2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584

Table 4 Statistical results of motion responses

Item Significant ExtremeBow acceleration (ms2) 128 242Stern acceleration (ms2) 092 188Pitch (deg) 096 185Vertical velocity (ms) 018 035

occurred at station 12 which is nearest to the longitudinalCOG of model Both significant and extreme VBM valuesincrease from station 2 at bow area to station 10 at amidshipsarea gradually The same conclusion can be made from thesectional HBM and the largest sectional HBM occurred at10th station It is worth mentioning that the HBM loads arenearly as large as VBM loads when the ship is sailing in severeoblique waves So enough attention should also be paid to thehorizontal strength of ships at ship design stage

To analyze the ratios of extreme value to significant valueof different responses graphical representations of the calcu-lated ratios are shown in Figure 16 As seen from the resultthe ratio of loads decreases from bow area to amidships areafor both VBM and HBM This can be explained by the factthat the instantaneous slamming loads are more likely to takeplace at bow area than amidships area However the ratiosof the four motion responses range in a narrow interval from189 to 204The results indicate that the nonlinear slammingeffects have more influence on loads than motions

54 Extremely Short-Term Analysis In order to describethe impact and vibrational dynamic responses of the shipafter encountering an oncoming wave impact pressure andvibrational responses in extremely short-term duration areinvestigated in particular Figure 17 shows the time historiesof impact pressure and the corresponding VBM at the 2ndstation when encountering several wave impact events Asseen from Figure 17(a) pressure gauge 3 impacted the wavesseven times during the time period from 8162 s to 8172 s Asevere flare slamming occurred between 8166 s and 8167 smeanwhile all of the three gauges impacted the oncomingwave Gauges 2 and 3 contacted with the wave respectively atthe times of 816632 s and 816636 s and the impact lasted forabout 05 s At the time of 816658 s gauge 1 contactedwith thewave and the impact lasted for about 02 s For this slammingevent the recorded peak pressures at positions 1sim3 are4237 kPa 8383 kPa and 6421 kPa respectively The result


0

10

20

30

40

7800 8000 8200 84007600Time (s)



1 2 3 40Frequency (Hz)



00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)

(a) Time and frequency series of VBM

2 4 60Frequency (Hz)



00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)

(b) Time and frequency series of HBM

000

005

010

015

020

025

PSD

of a

ccel

erat

ion

0 1 2 3 4Frequency (Hz)


7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)

(c) Time and frequency series of accelerations

7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2

(d) Time and frequency series of pitch

Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04

(e) Time and frequency series of vertical speed

Figure 15 Time series in a short interval and the corresponding spectral results

185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios

Figure 16 Ratios of extreme value to significant amplitude value

000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5

(a) Pressures of gauges 1 to 3

minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)

Resultant loadSlamming load

Wave load

(b) VBM of station 2

Figure 17 Time histories of pressures and loads in an extremely short interval

indicates that the largest slamming pressure occurred ataround the position of gauge 2 for this slamming event

As seen from Figure 17(b) a whipping phenomenonhappened on the backbone due to flare slamming at the timeof 816633 s and it lasted for about 3 s As seen from the result

the resultant loads of the ship in severe seas are composedof low frequency wave loads and high frequency slammingloads The FFT filter is used to decompose the load compo-nents from the total loads It can be seen from the analysisresult that the amplitude value of wave frequency load before


8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion

Figure 18 Time and frequency series of VBM at different stations

the slamming occurrence is about 9169Nsdotm However theslamming load has reached 33535Nsdotm which is 366 timesof the wave component load

The measured VBM loads from station 2 to station 12between 8162 s and 8172 s and the corresponding spectralresults are shown in Figure 18 As seen from the measuredtime histories the proportion of slamming load to total loaddecreases from bow area to amidships area that is the slam-ming loads are pronounced at 2nd station while they almostdisappeared at 12th station The same phenomenon can bealso found from the spectral results As seen from the spectralresults the dominant slamming components of the first fivestations are all around 638Hz which is close to the three-node natural frequency of the ship model The subdominant

slamming components of the six stations are all around229Hz which is close to the two-node natural frequencyof the ship model It is worth mentioning that the two-node vibrations are pronounced all along from 2nd station to12th station However the three-node vibration componentsdecrease from bow station to amidships station This can beinterpreted by the distributions of modal shapes along theship The frequencies of the wave-induced load componentsmainly range from 03Hz to 08Hz for the six stations

6 Conclusions and Recommendations

This paper presents a novel measurement technique forwave-induced hydroelastic vibrations of large elastic ships in


natural environment From the sea trial conducted and theanalyses of data acquired several conclusions can be made asfollows

(1) The sea trial performed atHuludao harbor inOctober2015 indicates that the testing systems presented inthis paper are competentThe testingmethod and sys-tems can be extended to a wide range of ship hydro-dynamic experimental research in natural environ-ment

(2) The HBM loads are nearly as large as VBM loadswhen the ship is sailing in severe oblique waves Soenough attention should also be paid to the horizontalstructural strength of ships at ship design stage

(3) Spectral analysis results show that the sectional loadincreases from bow station to amidships station forboth VBM and HBM However the proportion ofslamming load component to total load decreasesfrom bow area to amidships area Furthermore thenonlinear slamming phenomenonhasmore influenceon loads than motions

(4) Severe bow impact will result in whipping responseswhich may produce enormous instantaneous loadsSo whipping is an issue of strength because theinstantaneous slamming loads are usually very highbut damp out quickly However the wave frequencyresponse of the hull girder is a fatigue issue for shipsbecause the number ofwave cycles is very large duringtheir whole lives

From the time-domain and frequency-domain results ofthe sectional loads it can be found that there are pronouncednonlinear components that are caused by slamming eventsThe spectral analysis methods adopted in this study areintrinsically linked to linear systems philosophy In the futurework nonlinear and nonstationary data processing meth-ods such as empirical mode decomposition (EMD) basedmethods will be developed to deal with the load data

In this work only one typical sailing condition fromthe voyage trial regarding vibrational and slamming charac-teristics of the ship is reported However the experimentalmethod proposed and data analysis results in this paperprovide a general research approach for the investigation ofhydrodynamic performance of ships in natural conditionsOther kinds of standard hydrodynamic tests can be con-ducted by the large-scale model testing system for instanceresistance seakeeping propulsion maneuverability and sta-bility tests by fitting the corresponding testing equipmentThese kinds of tests can be performed in both calm waterlakes and coastal wave seas

The advantages of performing ship hydrodynamic testsby using large-scale model in natural environments areobvious For example the errors induced by difference ofReynolds number can be reduced by using larger modelswhen performing ship resistance tests In addition the sailingroutes can be designed regardless of the model speed and sizewhen performing rapidity and maneuverability tests sincethe natural water surface is large enough However there arestill problems and difficulties that need further addressing

in respect of this novel testing approach For example insome weather conditions the speed and heading of large-scale model are not easy to control and adjust Moreover thelarge-scale model tests are expensive to perform and the timeconsumed is much longer than in a laboratory basin

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank Technical Engineer ZhaoXiaodong and all the master students at the INOM of HEUwho took part in the 2015-year sea trial activities for theirkind help during the preparation and conduction of the testsThis work was partially supported by the National NaturalScience Foundation of China (no 51079034) The authorswould like to express their gratitude to the foundation

References

[1] S Ivo M Sime and T Stipe ldquoInvestigation of ship hydroelas-ticityrdquo Ocean Engineering vol 35 no 5-6 pp 523ndash535 2008

[2] S E HirdarisW Bai D Dessi et al ldquoLoads for use in the designof ships and offshore structuresrdquoOcean Engineering vol 78 pp131ndash174 2014

[3] S E Hirdaris and P Temarel ldquoHydroelasticity of ships recentadvances and future trendsrdquo Proceedings of the Institution ofMechanical Engineers Part M Journal of Engineering for theMaritime Environment vol 223 no 3 pp 305ndash330 2009

[4] G J Grigoropoulos and G M Katsaounis ldquoMeasuring pro-cedures for seakeeping tests of large-scaled ship models atseardquo in Proceedings of the 13th IMEKO TC4 Symposium onMeasurements for Research and Industrial Applications pp 135ndash139 Athens Greece September-October 2004

[5] A Maron and G Kapsenberg ldquoDesign of a ship model forhydro-elastic experiments in wavesrdquo International Journal ofNaval Architecture andOceanEngineering vol 6 no 4 pp 1130ndash1147 2014

[6] J L Jiao H L Ren H Yang andD LMao ldquoDesign of channel-section backbone of segmented model for wave loads experi-mentrdquo Journal of Vibration and Shock vol 34 no 14 pp 11ndash152015

[7] J R Lin S L Zheng Y Sun and Y J Zhang ldquoExperimentaltechniques of the continued elastic modelrdquo Shipbuilding ofChina vol 2 pp 63ndash71 1992

[8] Z Y Chen H L Ren H Li and X Zhao ldquoThe wave loadexperimental investigation of a segmentedmodel of a very largeship based on variable cross-section beamsrdquo Journal of HarbinEngineering University vol 33 no 3 pp 263ndash268 2012

[9] G Thomas S Winkler M Davis et al ldquoSlam events of high-speed catamarans in irregular wavesrdquo Journal of Marine Scienceand Technology vol 16 no 1 pp 8ndash21 2011

[10] Z-Y Chen H-L Ren H Li and K-H Zhang ldquoExperimentaland numerical analysis of bow slamming and whipping indifferent sea statesrdquo Journal of Ship Mechanics vol 16 no 3 pp246ndash253 2012

[11] The Seakeeping Committee ldquoFinal report and recommenda-tions to the 26th ITTCrdquo in Proceedings of the 26th International


TowingTankConference vol 1 Rio de Janeiro Brazil September2011

[12] The Seakeeping Committee ldquoFinal report and recommenda-tions to the 27th ITTCrdquo in Proceedings of the 27th InternationalTowingTankConference vol 1 CopenhagenDenmarkAugust-September 2014

[13] S Z Sun H L Ren X D Zhao and J D Li ldquoExperimentalstudy of two large-scale models seakeeping performance incoastal wavesrdquo Brodogradnja vol 66 no 2 pp 47ndash60 2015

[14] A Coraddu G Dubbioso S Mauro and M Viviani ldquoAnalysisof twin screw shipsrsquo asymmetric propeller behaviour by meansof free running model testsrdquoOcean Engineering vol 68 pp 47ndash64 2013

[15] F Fossati I Bayati F Orlandini et al ldquoA novel full scale labo-ratory for yacht engineering researchrdquo Ocean Engineering vol104 pp 219ndash237 2015

[16] J L Jiao H L Ren and C A Adenya ldquoExperimental andnumerical analysis of hull girder vibrations and bow impact of alarge ship sailing in wavesrdquo Shock and Vibration vol 2015Article ID 706163 10 pages 2015

[17] G Jacobi GThomasM R Davis andGDavidson ldquoAn insightinto the slamming behaviour of large high-speed catamaransthrough full-scale measurementsrdquo Journal of Marine Scienceand Technology vol 19 no 1 pp 15ndash32 2014

[18] S-Z Sun J-D Li X-D Zhao J-L Luan and C-T WangldquoRemote control and telemetry system for large-scalemodel testat seardquo Journal of Marine Science and Application vol 9 no 3pp 280ndash285 2010

[19] J L JiaoH L Ren S Z Sun andCAAdenya ldquoInvestigation ofa shiprsquos hydroelasticity and seakeeping performance bymeans oflarge-scale segmented self-propelling model sea trialsrdquo Journalof Zhejiang UniversitymdashSCIENCE A In press

[20] GARMIN GHPtrade 12 Installation Instructions Garmin Interna-tional Inc 2011

[21] U D Nielsen and D C Stredulinsky ldquoSea state estimation froman advancing shipmdasha comparative study using sea trial datardquoApplied Ocean Research vol 34 pp 33ndash44 2012

[22] Y X Yu Random Wave and Its Applications to EngineeringDalian University of Technology Press Dalian China 1992

[23] N E Huang Z Shen S R Long et al ldquoThe empirical modedecomposition and the Hilbert spectrum for nonlinear andnon-stationary time series analysisrdquo The Royal Society of Lon-don Proceedings Series A Mathematical Physical and Engineer-ing Sciences vol 454 no 1971 pp 903ndash995 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



the modelrsquos freedom of motions in some sense In summarythe above statements reflect some of the challenges of theconventional tank model tests

In fact the real sea conditions where ships sail are quitedifferent from those simulated in the tank In the sea thereexist wave diffraction refraction and breaking as well as theassociated effects caused by winds and currents Sea wavesspread along a dominant direction with components fromdifferent directions superimposed onto one another whilethe tank waves are usually unidirectional Although a fewnovel tank facilities allow for the generation of two directionscrossed irregular waves [12] the waves generated are stillmore or less different from the actual sea waves It is consid-ered that full-scale ship sea trial measurement reflects whatreally happens on the ship However the data acquisition isquite difficult since the weather and wave states are uncon-trollable Moreover the extreme high sea states desired forinvestigation are rarely suffered by a full-scale large ship

A new alternative approach to the laboratory basin mea-surement and full-scale sea measurement introduced in thispaper is to perform tests by large-scalemodels in real sea con-ditions [13ndash15] The measurements are carried out in short-crested directional spreading andwind-generated seawavesThe scale effects can be reduced by testing relatively largerscale models The large-scale models can be tested with theequipment of superstructures and appendages thus the windand current associated effects are taken into accountThe testscan be carried out at any arbitrary heading angle In a wordthis testing condition can be regarded as more realistic com-pared with the laboratory basin condition However therealso exist disadvantages regarding the proposed approachsuch as the fact that the sea wave conditions cannot be con-trolled and thus the trial procedure lasts a long time waitingfor the expected wave conditions

The characteristics of hydroelastic vibrations and bow-flare slamming of a small-scale model in regular waves havealready been studied through laboratory tank tests which canbe found in the authorsrsquo previous work [16] In the presentwork a large-scale model corresponding to the same pro-totype as that of the small-scale model was designed andmanufactured to allow for themeasurement of wave-inducedhydroelastic vibrations and slamming experienced in coastalwaves

In this paper the large-scale model structural design andexperimental system are introduced first Then a 5-hourvoyage trial performed at Huludao harbor of China in August26 2015 is presented Finally the hydroelastic vibrationaland bow impact characteristics of the large-scale model aredescribed and analyzed from different terms based on theexperimental results

2 Experimental Design

21 Hull Structural Design To investigate the hydroelasticvibrational behavior of a large ship a large-scale segmentedmodel hull was designed and built The principal parametersof the prototype and model are listed in Table 1 whereVCG denotes vertical center of gravity (COG) LCG denotes

Table 1 Principal parameters

Description Ship prototype Model hullScale 11 125Length overall (m) 313 1252Length waterline (m) 292 1168Moulded breadth (m) 395 158Depth (m) 255 102Draft (m) 10 040Displacement (t) 71875 46VCG from BL (m) 16 064LCG from AP (m) 1405 562

longitudinal COG BL denotes baseline and AP denotes aftperpendicular

The model hull was constructed by fiberglass reinforcedplastic (FRP) material A continuous backbone beam wasinstalled at the mean neutral axis height of the segmentedmodel to connect the segmentsThe shipmodel was designedto have 20 stations in total with station 0 at bow area and sta-tion 20 at aft areaThemodel hull was divided into seven inde-pendent segments by using the 2nd 4th 12th divisions atthe manufacture stage Sectional loads at the six cut divisionsare measured by using unidirectional strain sensors mountedon the backbone surfaces The monolithic large space fromthe 12th station to 20th station at aft area is used for housingpropulsion system General arrangements of the ship modelstructure and the onboard experimental apparatus are shownschematically in Figure 1

The pressure response behaviors of flare impact and bot-tom impact at bow area are studied in particular [17] Threepressure gauges intended to measure the bow-flare impactpressure and one intended to measure the bottom fluctuatingpressure are disposed at the center line of bow area whosepositions can be seen in Figure 2 The pressure gauges havea range of 100 kPa and an accuracy of 10 Pa for measure-ment The sampling frequency of pressure gauges was set at100Hz during the measurements

Photographs of the large-scale model are illustrated inFigure 3 Figure 3(a) shows the large-scale model onshorebefore the experimental activities at Huludao harborFigure 3(b) shows the backbone beam and its fixing instru-ments after model assembly in the laboratory of the Instituteof Naval Architecture and Ocean Engineering Mechanics(INOM) of Harbin Engineering University (HEU) where themodel was assembled and debugged

22 Backbone System Steel backbone beam with rectangulartubular structure was designed for the model to allow forthe measurement of ship wave loads The configuration andparameters of cross section of the backbone beam weredetermined to satisfy the stiffness distribution and two-nodevertical vibrational natural frequency of the model hull Theinner wall dimensions for width 119871 and height 119867 of thebackbone remain unchanged The backbone was howevermadewith different thicknesses 119905 and119889 at different sections soas to meet the stiffness distribution demand Strain gauges of


Video

Bow accelerometer

GPS

Radio antenna

Rescue alarm

GPSINSdevice

Battery pack


Course top

Data collector

Stern accelerometer




Strain

Pressure sensor

20 18 16 14 12 8 6 4 2 0

receiver

gaugesposition

camera


12

3

4

640WL800WL960WL

Waterline

Spreading

Sailing speed

Large waveImpact

2 06






119872119898=120590119868

119911 (1)





119872119904=119872119898

1205824 (2)








StationVBM HBM

Model(NsdotmMPa)


Model(NsdotmMPa)


2 428 167 443 1734 457 179 565 2216 720 281 936 3668 875 342 994 38810 899 351 1082 42312 934 365 1216 475

y

z

o

L

H

t

d

V1 V3

V2 V4

H1

H3

H2

H4

Strain gauge



0

4000

8000

12000

16000

20000

0 2 4 6 8 10 12 14Station

Mom

ent o

f ine

rtia

(cm

4)




mEI

Q(t)


Madd





GPS receiver

GPSINS station

Radio

Interface


Autopilot radio

Computer unit

Control interface

Pilot drive unit

Sectional load


Impact pressure

Data collector

Computer


Motors

Shafts propellers

Propulsion

Radio


Autopilot interface

Motor control

Video camera

Wave buoyComputer

A B

C

A

B

C











Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)


12

3

4

5

6Buoy

Wave direction

0













0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Video

Bow accelerometer

GPS

Radio antenna

Rescue alarm

GPSINSdevice

Battery pack


Course top

Data collector

Stern accelerometer




Strain

Pressure sensor

20 18 16 14 12 8 6 4 2 0

receiver

gaugesposition

camera


12

3

4

640WL800WL960WL

Waterline

Spreading

Sailing speed

Large waveImpact

2 06






119872119898=120590119868

119911 (1)





119872119904=119872119898

1205824 (2)








StationVBM HBM

Model(NsdotmMPa)


Model(NsdotmMPa)


2 428 167 443 1734 457 179 565 2216 720 281 936 3668 875 342 994 38810 899 351 1082 42312 934 365 1216 475

y

z

o

L

H

t

d

V1 V3

V2 V4

H1

H3

H2

H4

Strain gauge



0

4000

8000

12000

16000

20000

0 2 4 6 8 10 12 14Station

Mom

ent o

f ine

rtia

(cm

4)




mEI

Q(t)


Madd





GPS receiver

GPSINS station

Radio

Interface


Autopilot radio

Computer unit

Control interface

Pilot drive unit

Sectional load


Impact pressure

Data collector

Computer


Motors

Shafts propellers

Propulsion

Radio


Autopilot interface

Motor control

Video camera

Wave buoyComputer

A B

C

A

B

C











Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)


12

3

4

5

6Buoy

Wave direction

0













0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













StationVBM HBM

Model(NsdotmMPa)


Model(NsdotmMPa)


2 428 167 443 1734 457 179 565 2216 720 281 936 3668 875 342 994 38810 899 351 1082 42312 934 365 1216 475

y

z

o

L

H

t

d

V1 V3

V2 V4

H1

H3

H2

H4

Strain gauge



0

4000

8000

12000

16000

20000

0 2 4 6 8 10 12 14Station

Mom

ent o

f ine

rtia

(cm

4)




mEI

Q(t)


Madd





GPS receiver

GPSINS station

Radio

Interface


Autopilot radio

Computer unit

Control interface

Pilot drive unit

Sectional load


Impact pressure

Data collector

Computer


Motors

Shafts propellers

Propulsion

Radio


Autopilot interface

Motor control

Video camera

Wave buoyComputer

A B

C

A

B

C











Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)


12

3

4

5

6Buoy

Wave direction

0













0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










GPS receiver

GPSINS station

Radio

Interface


Autopilot radio

Computer unit

Control interface

Pilot drive unit

Sectional load


Impact pressure

Data collector

Computer


Motors

Shafts propellers

Propulsion

Radio


Autopilot interface

Motor control

Video camera

Wave buoyComputer

A B

C

A

B

C











Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)


12

3

4

5

6Buoy

Wave direction

0













0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Huludao harbor

Trace

12089 12091 12093 12095

4066

4067

4068

4069

N

A

B

Radio

C(Buoy)


12

3

4

5

6Buoy

Wave direction

0













0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50

0

2

4

Time (s)

minus2

minus4

Acce

lera

tion

(ms2)


00 03 06 09 1200000

00005

00010

00015

00020

00025

Frequency (Hz)

f1 = 0252Hz

f2 = 0527Hz

S 120577(120596

)(m

2middots

)



00

04

08

12


Vert

ical

ben

ding

stre

ss (M

Pa)

0 2 4 6 8Time (s)

minus04

minus08

minus12


000

003

006

009

012

015


PSD

0 5 10 15 20 25Frequency (Hz)

f1 = 2273Hzf2 = 6566Hz

f3 = 11364Hz










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40Ve

rtic

al b

endi

ng st

ress

(MPa

)

0 5000 10000 15000 20000Time (s)




0

10

20

30

Hor

izon

tal b

endi

ng st

ress

(MPa

)

5000 10000 15000 200000Time (s)




00

01

02

03

Impa

ct p

ress

ure (

MPa

)

5000 10000 15000 200000Time (s)

Gauge 1Gauge 3

Gauge 2Gauge 4



minus5

0

5

10

Vert

ical

acce

lera

tion

(ms2)

5000 10000 15000 200000Time (s)


0 5000 10000 15000 20000

0

2

4

Pitc

h (d

eg)

Time (s)

minus2

minus4


0 5000 10000 15000 20000

00

03

06

Vert

ical

spee

d (m

s)

Time (s)

minus03

minus06






0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

2

4Ve

loci

ty (m

s)

minus2

minus47600 8000 8400 88007200

Time (s)


East velocity


7200 7600 8000 8400 8800

0

100

200

300

400

Azi

mut

h (d

eg)

Time (s)

(b) Sailing azimuth









2 14575 75908 14961 909754 44119 225484 59317 2417956 113555 390520 104148 3336928 177870 448452 150758 40450410 219559 524268 180660 39421512 220477 536366 105858 195584







0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40

7800 8000 8200 84007600Time (s)






00

01

02

03

04

05

PSD

of V

BM

Vert

ical

ben

ding

mom

ent (

kNmiddotm

)





00

01

02

03

04

05

PSD

of H

BM

0

10

20

30

40

7800 8000 8200 84007600Time (s)



Hor

izon

tal b

endi

ngm

omen

t (kN

middotm)


000

005

010

015

020

025

PSD

of a

ccel

erat

ion



7600 7800 8000 8200 8400Time (s)


minus4

0

4

8

Vert

ical

acce

lera

tion

(ms2)


7600 7800 8000 8200 8400

0

1

2

Pitc

h (d

eg)

Time (s)0 1 2 3 4

000

003

006

009

012

PSD

of p

itch

Frequency (Hz)

minus1

minus2


Figure 15 Continued


7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










7600 7800 8000 8200 8400

00

02

04Ve

rtic

al sp

eed

(ms

)

Time (s)0 1 2 3 4

0000

0005

0010

0015

0020

0025

PSD

of v

ertic

al v

eloci

ty

Frequency (Hz)

minus02

minus04



185243218239

268252

320344

408

511

608

Station12108642

521

VBMHBM

0

1

2

3

4

5

6

7

Ratio

(a) Load ratios

194196204189

00

05

10

15

20

25

Ratio

Pitc

h

Velo

city

Acce

lera

tion

stern

Acce

lera

tion

bow

(b) Motion ratios


000

002

004

006

008

010

012

Pres

sure

(MPa

)

8162 8164 8166 8168 8170 8172Time (s)

Gauge 1Gauge 3

Gauge 2

000002004006008010

8166

0

8166

5

8167

0

8165

5

8167

5


minus04

minus02

00020406081012

VBM

(kNmiddotm

)

8164 8166 8168 8170 81728162Time (s)


Wave load







8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

001530

Time (s)

minus15

minus30

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

012

Time (s)

minus1

minus2

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000408

Time (s)

minus08minus12

minus04

(kNmiddotm

)

8162 8164 8166 8168 8170 8172

000204

Time (s)

minus02

minus04

(kNmiddotm

)

0 2 4 6 8000002004006008

PSD

2nd

stat

ion

Frequency (Hz)

f1 = 230Hz f2 = 638Hz

000004008012016

PSD

4th

stat

ion


f1 = 229Hzf2 = 638Hz

0001020304

PSD

6th

stat

ion


f1 = 230Hz f2 = 639Hz

00

02

04

06PS

D 8

th st

atio

n


f1 = 230Hz f2 = 639Hz

0002040608

PSD

12t

h st

atio

n


f1 = 230Hz

0002040608

PSD

10t

h st

atio

n


f1 = 230Hzf2 = 639Hz

VBM

2nd

stat

ion

VBM

4th

stat

ion

VBM

6th

stat

ion

VBM

8th

stat

ion

VBM

10t

h st

atio

nV

BM 1

2th

stat

ion



















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation





















Acknowledgments


References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article experimental investigation of wave-induced ship hydroelastic vibrations by...

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