20000626-fem analysis of diesel piston-slap induced ship hull vibration and underwater noise

8/3/2019 20000626-FEM Analysis of Diesel Piston-slap Induced Ship Hull Vibration and Underwater Noise

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FEM/BEM analysis of diesel piston-slap induced

ship hull vibration and underwater noise

H. Zheng *, G.R. Liu, J.S. Tao, K.Y. Lam

Institute of High Performance Computing, 89C Science Park Drive, Singapore Science Park I,Singapore 118261, Singapore

Received 9 February 2000; received in revised form 10 May 2000; accepted 26 June 2000

Abstract

Numerical prediction of vibration transmission from a ship diesel via a resilient mounting

system to a stiened cylindrical hull is performed aiming to provide a clearer insight into the

signi®cance of piston-slap in the diesel excitations to the hull vibration, and consequently, theunderwater radiated noise. Finite element method (FEM) is employed to simulate the vibra-

tion response of the hull due to the excitations of diesel piston-slap and vertical inertia force

of reciprocating masses. Eects of the rotational stiness of resilient mounts on vibration

transmission are also numerically investigated through coupled multi-DOF isolation analyses.

Finite element solutions of the hull vibratory velocity are further used as boundary condition

of the hull boundary element model for consequent underwater radiated noise calculation.

The numerical results show that (1) piston-slap imposed rolling moment on the diesel frame

may cause a higher level of ship hull vibration and underwater radiated noise than that due to

the excitation of the vertical inertia force of reciprocating masses; (2) rotational stiness of

elastic mounts for resilient mounting system plays an important role in the diesel vibration

transmission to the hull, especially as exciting frequency increases; and (3) neglect of theexcitation component of piston-slap moment can lead to overestimates of hull vibration in

some cases. # 2001 Elsevier Science Ltd. All rights reserved.

1. Introduction

Among the main excitation sources of radiated underwater noise that compose

acoustic signature of a ship, the diesel engine is obviously one of the strongest

sources in most circumstances, no matter whether it is installed as the propulsion

Applied Acoustics 62 (2001) 341±358

www.elsevier.com/locate/apacoust

0003-682X/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved.

P I I : S 0 0 0 3 - 6 8 2 X ( 0 0 ) 0 0 0 4 6 - 3

* Corresponding author.

E-mail address: [email protected] (H. Zheng).



engine or the generating set for an electric driver. For a diesel engine mounted on a

ship, there are a variety of ways in which the sound is transmitted to the underwater

and accommodation areas. First, the diesel engine, excited by its internal excitation

sources, including combustion pressure and other mechanical forces, radiates air-borne sound from its external surfaces, which causes high noise levels inside the

engine room. This airborne sound excites the hull, bulkheads and deckhead of the

engine room and is also transmitted, as structure-borne sound by the steel structure

to other parts of the ship.

Secondly, the engine is connected to the ship hull through a large number of

mechanical components. The so-called structure-borne sound is transmitted through

all these components to the ship's steel structure. This sound is propagated along the

hull where it is radiated into the underwater. For a ship's engine, its structure-borne

sound transmission to the hull structure is normally more of concern in underwater

acoustics design. This is attributed to the fact that the air-borne noise is dealt with

more readily by using an acoustic insulation enclosure and/or absorption material to

eciently reduce and improve the noise level.

The solution to reduce the structure-borne sound due to diesel excitations is

usually to attempt to isolate the engine or the generating set from the surrounding

structure by interposing elastic elements. The simplest isolation mounting arrange-

ment normally used is to interpose a spring, often in the form of a rubber mount,

between the vibrating diesel and the underlying hull structure. Another conventional

but a more attractive arrangement for isolation is the so-called two-stage mounting

system where an intermediate mass is attached to both the diesel and hull structureby springs. It has been proven that, in nearly all cases, a two-stage mounting system

aords superior vibration isolation at high frequency to a simpler single stage

mounting.

Theories for vibration isolation and the attenuation of vibration using resilient

mounts have been investigated by many researchers. Comprehensive reviews of the

literature concerning many aspects of vibration isolation can be found in Refs. [1±3].

The design criteria and guidelines for vibration isolation are available in many

design handbooks for the car, ship, and airplane industries.

In the prediction of vibration transmission from a diesel via the mounting system

to the ship's hull, one important issue is the determination of the diesel excitationlevel and property. This is also true in the design of a resilient mounting system

because the selection of appropriate mounting elements is highly constrained by

excitations. The exciting sources of a marine diesel are due to rotational imbalance

and reciprocating masses. Combustion, inertia of a reciprocating piston, rotational

inertia of the connecting rod and crankshaft, and the impact between the piston and

cylindrical liner result in the shaking force and moments on the engine block [4±7].

In the traditional isolation design of a diesel-mount system, only piston-crank iner-

tia loads are taken into account in determining the excitation level and source fre-

quency, while piston-slap induced exciting components of force and moment are of

much less concern in order to simplify the analysis and design. It has been demon-strated both analytically and experimentally that piston-slap is a major excitation

source of air-borne noise from an internal combustion piston engine, especially from

342 H. Zheng et al. / Applied Acoustics 62 (2001) 341±358



turbo-charged diesels [8]. The role that piston-slap plays in the excitation of a

vibratory diesel is still questionable when analyzing the engine vibration transmis-

sion via resilient mounts to the ship's hull and consequent underwater radiated

noise. Exploring the answer to this question is one part of this work.Furthermore, initial studies in design of diesel-mount systems have focused on

keeping the natural frequencies of the system away from the undesirable engine

operation frequency range. Often, when choosing isolators only the mass and

operational frequency of the engine to be isolated are considered, i.e. chosen only

for a force acting on the isolation in one direction. This classical only one DOF of

motion or only the translational DOFs of motion vibration isolation prediction will

not suce for diesel-mount systems where there exist a combined force and moment

excitation and a multiple-mounts system between engine and foundation. Previous

researchers have also studied vibration isolation including more than one DOF of

motion, often including only the translational stiness, or they are considered only

for rigid body motion. The shortcoming of modeling the engine source and foun-

dation as a rigid body can be improved by including their dynamic characteristics

which can be represented by their mobility or blocked impedance [9]. One more

important aspect of this paper is devoted to the eects of rotational stiness of

resilient mounts on vibration transmission.

Analysis of vibration transmission from a diesel engine to the ship's hull via a

resilient mounting system is very complicated, since the transmitted vibration is

characterized by a large number of parameters that in some cases cannot be directly

compared. Including both force and moment excitations and considering coupledmultiple-DOF transmission largely increases the complexity of the problem. On the

analysis of vibration transmission from a combined force and moment excited

source to a ¯exible receiver via a coupled multiple-DOF mounting system, a number

of publications [3,10±15] can be referred to in open literature. From the standpoint

of ease of interpreting the results, an analytical method of studying the isolation

problem is more advantageous than a numerical method by ®nite element analysis

(FEA). However, to perform the vibration transmission calculation, solutions of

mobilities or impedances of exciting source, resilient mounts and receiving structure

must be known in advance. Owing to the complexity of construction, it is nearly

impossible to obtain analytical solution of mobilities or impedances of such a com-plex vibration receiver as a ship's hull unless some biased assumptions are made.

FEA is an ecient numerical tool to achieve the target of vibration transmission

prediction of a complex source-mount-receive system.

2. Diesel excitations

The engine vibration can be divided into two categories [8]: vibration of engine

parts relative to each other, called internal vibration, and the movement of the

engine as a whole, called external vibration. Unbalanced forces and moments causethe external vibration. As for the vibration isolation, an engine is normally regarded

as a rigid-body having six degrees of freedom (DOF) about orthogonal axis through

H. Zheng et al. / Applied Acoustics 62 (2001) 341±358 343



its center of gravity: linear vibrations along each axis and rotations about each axis

(see Fig. 1). In the classical determination of diesel excitations, only three modes are

usually of consideration:

. vertical oscillations on the X axis due to unbalanced vertical forces,

. rotation about the Z axis due to unbalanced vertical forces in dierent trans-

verse planes,

. rotation about the Y axis due to cyclic variations in torque.

The variation of torque, which balances the torque from the shaft and must be

absorbed by elements such as torsional elastic couplings outside the engine frame,

will not be considered here. For in-line engines with even number of cylinders, 4- or

6-cylinder diesels, force couples about Z-axis due to unbalanced vertical forces in

dierent transverse plane are fully balanced.

In general the rotating masses are carefully balanced but periodic forces due to the

reciprocating masses cannot be avoided. A crankshaft, connecting rod and piston

assembly, see Fig. 2, is subjected to a periodic force in the line of action of the piston

given approximately by [8]

f i mpR32 os R

Los2

I

for constant crankshaft rotational speed, 3, and where mp is the eective mass of thepiston and includes that fraction of the mass of connecting rod. R and L are

respectively the crank radius and connecting rod length. This inertia force associated

with piston reciprocating motion is of most concern in classical analysis of engine

vibration isolation. From the force diagram as shown in Fig. 2, the lateral piston-

slap force can be written as:

Fig. 1. Shaking force and moments on engine frame.




f x f p À f iÀ Á

tn P

The angle is related to the crank angle by

sin

vsin Q

from which it follows that for small angles

tn sin

1 À sin2

p

R

Lsin 1

1

2

R

L

2

sin2

4 5R

So the cross force imposed on the cylinder wall is given as

f x R

Lsin

%

4D2 p À mpR32 os

vos2

!S

neglecting RaL 2 terms which will introduce no more than a 5% error in the cal-

culations for the range of parameters found in practice. p in the equation is the

cylinder pressure of which the value may be found from the indicator diagram of

engine and D is piston diameter. One can see from Eq. (5) that piston-slap impact

are controlled by both cylinder pressure and inertia force imposed by the recipro-cating piston assembly. Two kinds of impact may be distinguished. One is the so-

called pressure-controlled impact, which occurs near the top-dead-center (TDC)

Fig. 2. Rigid-body model for force analysis.




position where the cylinder pressure value corresponds to the peak of pressure cycle.

Another one is called inertia-controlled impact which occurs in those parts of the

cycle for which the pressure forces are negligible. Hence, the lateral piston-slap force

may be written as:

f x f xp f xi T

where

f xp %

4D2 p

R

Lsin U

f xi Àmp32R os

R

Los2

R

Lsin V

For a multiple-cylinder in-line engine, the resultant unbalanced reaction force on

the frame is simply the summation of that from the individual pistons, i.e.:

f i mp3

2R

os i R

Los2 i

W

f x

%

4D2 pi À mp3

2R os i R

Los2 i

!R

Lsin i

& 'IH

When the cranks are evenly spaced, which is the usual arrangement, and is the

smallest angle between two cranks,

2%

N II

where N is the total number of crank positions. The angles 1Y 2Y 3, etc., for the

various cylinders may all be expressed in terms of one of them, for example, 1,

2 1

3 1 2F F F F F F F F F F F F

For the case of 4-stroke, 4-cylinder in-line engine with cranks at 180, %a2, the

®rst-order forces are fully balanced and unbalanced force will be second-order only,

i.e. 4mp32R RaL sin2 , where 3t. Similarly, the inertia-controlled piston-slap

force given in Eq. (8) can be calculated as

f xi Àmp3

2R

os i R

Los2 i

R

Lsin i 0 IP

Cylinder pressure controlled piston-slap force depends on the pressure-crankangle relation of each cylinder. It is generally dicult to express this relation by a

meaningful analytical function.




Both pressure-controlled and inertia-controlled piston-slap forces, which are

balanced with equal and opposite reactions on the main bearing, tend to cause

rotation of the whole engine about the crankshaft axis (Y-axis in Fig. 1). This gives

rise to an unbalanced moment, called piston-slap moment or rolling moment M y, inthe transverse plane of engine, given by:

M y f xS f x Ros Los IQ

where S is the distance of piston pin from crankshaft axis, given by

S % Ros v 1 À1

4

R

L

2

1 À os2

4 5IR

Using the above procedure, the reciprocating mass exerted vertical inertia force

and piston-slap imposed rolling moment on the frame of a 4-stroke, 4-cylinder in-

line diesel operating in the speed of 600 rpm are calculated in time-domain and are

further transposed to the frequency-domain through FFT. Diesel data required for

the calculation are described in Table 1. Showed in Fig. 3 is the gas-force-crank-

angle curve of the engine where cycle-to-cycle variation of cylinder pressure, which is

beyond the topic of this paper, is not taken into account. Fig. 4a and b depicts the

time-history and frequency spectrum of vertical inertia force and rolling moment,

respectively. One can see that the frequency spectrum of vertical inertia forcebehaves in single harmonically component. This is true for all diesels with even-

number cylinders. However, the spectrum of piston-slap induced rolling moment

Table 1

Data of diesel engine

Cylinder

bore (mm)

Stroke

(mm)

Connecting-rod

length (m)

Mass of

piston (kg)

Mass of

connecting-rod (kg)

Compression

ratio

280 300 0.45 14 7 13:1

Fig. 3. Cylinder force as a function of crank angle.




Fig. 4. Time-history and frequency spectra of engine excitations: (a) vertical inertia force; (b) piston-slap

exerted rolling moment on engine.




behaves multiple-harmonically. Apparently, the piston-slap excitation is more

important than the vertical inertia force as the frequency increases. These frequency

spectra will be used as the loading condition in the ®nite element modeling of diesel

vibration transmission via a resilient mounting system to the ship's hull.On the topic of diesel excitation, the piston-slap induced shaking moment is nor-

mally not considered as a crucial excitation in practice. This works well if the diesel

is of a light-type, as can be found in the automobile industry, and operates at high

rotating speed, for example, higher than 2000 rpm. However, most marine diesel

engines are often of heavy-duty and their working speeds are generally less than

1000 rpm [16]. In these circumstance, the role that piston-slap induced shaking

moment plays in the diesel excitations should be investigated, if the transmitted

vibration from a diesel via a mounting system to hull is to be accurately predicted.

3. FE/BE model

Considering underwater radiated noise due to the excitation of a diesel source to

the hull, the amount of sound energy ultimately radiated to the water depends upon

the vibration of the shell plating in contact with the water. The prediction of the

underwater noise level will, therefore, crucially depend upon a knowledge of the

vibration level of the hull shell where there is signi®cantly induced vibration.

To achieve a reliable prediction of diesel induced hull vibration, a comprehensive full-

ship model is required taking into account nearly all the construction details. However,the process of modeling in this way would be very tedious and associated computational

time is also a problem. Owing to the fact that our major concern here is diesel induced

hull vibration and underwater radiated noise, the FE model generated is a diesel engine

room virtually ``cut'' from a real submarine design, as this part is the dominant con-

tributor of diesel induced underwater acoustic signature. Key physical dimensions are

depicted in Fig. 5 and the FE meshing of the model is shown in Fig. 6.

Major parts of the FE model include a cylindrical hull with an internal deck plate,

two end-plates representing partition walls, a four-cylinder diesel engine, and a two-

stage, multiple-mount system, resiliently connecting the engine and hull. The

cylindrical hull, deck plate and end-plates are broken into shell elements while the

Fig. 5. Geometry of cylindrical hull and engine.




All rubber or elastic mounts are modeled as six-DOF, i.e. three translational and

three rotational, linear springs with properly de®ned damping coecients. In order

to examine the in¯uence of the rotational stiness of resilient mounts on eective-

ness of the mounting system, two sets of mount stiness combinations are respec-tively de®ned for two modeling cases where the stiness of all mounts are kept the

same in three translational DOFs. The parameters of these mounts are tabulated in

Table 2. The frequency dependence of the elastic mounts is not considered here.

Three dierent loading conditions are de®ned at the gravity center of the engine

for, respectively, simulating individually excited hull vibration by vertical inertia

force and piston-slap exerted rolling moment as well as their combined eect. As

depicted in Fig. 4a and b, the applied vertical inertia excitation on the engine block

is a harmonic force of which the frequency is twice the engine rotational speed while

the piston-slap excitation is a multiple harmonic moment about the crankshaft axis.

Direct frequency response analyses for three loading cases are carried out by using

MSC/NASTRAN code. Nodal vibration levels of the cylindrical shell and two end-

plates are speci®ed for output and further for comparison purposes.

The noise radiation is the ultimate concern in the analysis of ship underwater

acoustical signatures. To implement the prediction of diesel induced underwater

noise radiation, a cylinder shell boundary element model is developed for its radiated

sound pressure calculation. The BE model is abstracted from the FE model given in

Fig. 6 and consists of 1170 boundary elements. Previously obtained structural

vibration velocities of the hull are used as the boundary condition of the boundary

element model and sound pressure level is computed in LMS-SYSNOISE.Acoustic direct collocation BEM for the exterior problem is selected for the cal-

culation. The method relies on a boundary integral formulation of the Helmholtz

equation that solves the problem in a quite straightforward way. Under given nodal

velocities on the boundary surface, the unknowns to be solved for the exterior pro-

blem are the surface nodal pressures. Both boundary pressures and nodal velocities

are further used to calculate, directly, the ®eld acoustics variables, including pressure

and particle velocity at any point outside the boundary surface. Calculation output

of the acoustic direct method comprises pressure, velocity and intensity values at

®eld points, input power, output power and radiation eciency of the radiator.

For the purpose of simplicity, the coupling between ¯uid and structure is notconsidered at the moment. It is believed that this interaction process aects the

acoustic radiation of underwater structures. The detailed study on this issue is cur-

rently being carried out.

Table 2

Stiness parameters of elastic elements

Stiness parameter

of elastic mounts

Translational kx ky kz Rotational k k k y

Case 1 Case 2 Case 1 Case 2

First stage 1.5E+6 2.5E+5 2.5E+7

Second stage 1.5E+7 2.5E+6 2.5E+8




4. Numerial results and discussion

Fig. 8a and b represents a comparison of the velocity of a node on the hull close to

mounting area excited, respectively, by vertical inertia force and piston-slap inducedmoment. The chosen node is on the hull just underneath one elastic mount. It can be

easily seen that the piston-slap induced hull vibration level is apparently higher than

that induced by the vertical inertia force. Comparing the vibration level at a funda-

mental exciting frequency of 20 Hz, the nodal velocity under excitation of vertical

inertia force is À2.683E-6 m/s while that under piston-slap moment is À1.987E-5 m/s.

This indicates that neglecting the excitation exerted by piston-slap might cause

erroneous results in the analysis and design of diesel vibration isolation, if only

vertical inertia forces are considered.

In addition to the excitation level and frequencies, the vibration transmission from

a diesel engine to the hull is also dependent upon the physical parameters of all ele-

ments of the mounting system, including translational and rotational inertia of the

engine, stiness of elastic or viscoelastic mounts, and ®nally, the bending stiness of

stiened hull structure. From Fig. 8b, it can be observed that the hull response at a

frequency of 100 Hz is higher than those at a frequency from 20 to 80 Hz, even

though the excitation levels at these frequencies are lower (see Fig. 4). The ®gure

shows the eect of engine-mounts and hull dynamic properties on the vibration

transmission.

The vertical inertia force of the diesel and the piston-slap moment induced

underwater radiated noise levels are compared in Fig. 9, where the sound spectra ata ®eld point of 1 m away from the hull are given. As above, the vibration analysis

results showed, the underwater radiated noise level of the hull, excited by piston-slap

moment, is higher than that by vertical inertia force of diesel. At the fundamental

exciting frequency of the engine, i.e. f 20 Hz, piston-slap moment causes 75.52 dB

while the vertical inertia force induces a 71.14 dB noise radiation from the hull. At a

high order of exciting frequencies, the piston-slap moment induced underwater

sound levels are respectively 65.58 dB for 1-order harmonics ( f 40 Hz), 66.82 dB

for 11/2-order ( f 60 Hz), 68.54 dB for 2-order ( f 80 Hz), 53.33 dB for 21/2-order

( f 100 Hz), and 28.74 dB for 3-order ( f 120 Hz). These results are in the ten-

dency coincident with what have been found in [17] where they are compared withthe mean quadratic velocities of a stiened plate excited by a unit moment and a

unit force respectively.

The dB values depend not only on the hull vibrating velocity but also the vibra-

tion pattern at these exciting frequencies. For example, although the vibration level

of the hull at f 80 Hz (2-order harmonic) is lower than that at f 100 Hz, the

underwater radiated noise level is more than 5 dB higher. This result indicates the

eect of the hull vibration pattern on its sound radiation.

Using a simple model of beam-isolator-beam, Sanderson examined the error level

in power transmission predictions when rotational stiness of isolators are not

included [18]. He pointed out that it is worthwhile to study the rotational transmis-sibilities in a comparable manner to the displacement transmissibility. Here the

in¯uence of the rotational stiness of elastic elements for the mounting system on




Fig. 8. Hull vibration velocity of a node under elastic mount: (a) under excitation of vertical inertia force;

(b) under piston-slap moment.




Fig. 9. Comparison between vertical inertia force and piston-slap moment induced underwater radiated

noise: (a) under excitation of vertical inertia force; (b) under piston-slap moment.




Fig. 10. Piston-slap induced underwater noise: (a) rotational stiness: 2.5E+5 Nm; (b) rotational sti-

ness: 2.5E+7 Nm.




vibration transmission from the engine and hence on induced underwater noise can

be observed through comparing the results shown in Fig. 10. Fig. 10b represents hull

radiated underwater noise for the case where three rotational stinesses of all ®rst-

and the second-stage elastic elements are 100 times the rotational stiness of thecorresponding elastic element for the case described in Fig. 10a. The excitation level

of piston-slap moment and translational stinesses of all elements are kept the same

for two cases. The dB values calculated in SYSNOISE are tabulated in Table 3. One

can see that the noise levels at f 20 and 40 Hz are nearly the same for the two

cases. In higher exciting frequencies, i.e. at f 60, 80, 100 and 120 Hz, however, the

underwater noise radiation due to piston-slap moment varies largely when the rota-

tional stiness of the mounting elements is changed. The variance also behaves fre-

quency-dependent. This demonstrates that as the frequency increases, rotational

stiness of the elastic mounts plays an increasingly important role in vibration

transmission from diesel to hull via the resilient mounting system.

The predicted underwater noise levels at each exciting frequency are listed in

Table 4 for the case when both vertical inertia force and piston-slap induced

moment on the engine block are applied as excitation to the model. It can be found

that the underwater radiated noise level of the hull under combined excitations is

not a simple summation of the noise level under each individual excitation, but

lower than the noise level under each of them. For the case of lower rotational

stiness of mounting elements, the 1-m noise level of the hull at 20 Hz is 71.14 dB

Table 3dB values in two rotational stiness cases

Frequency (Hz) 20 40 60 80 100 120

Case 1 75.52 65.48 66.82 68.54 53.33 28.74

Case 2 75.43 65.15 58.05 62.99 51.54 17.52

Dierence 0.09 0.33 8.77 5.55 1.79 11.22

Table 4

Predicted underwater noise levels

Excitation Frequency

12-order

(20 Hz)

1-order

(40 Hz)

1 12-order

(60 Hz)

2-order

(80 Hz)

2 12-order

(100 Hz)

Vertical force 71.14

Rolling moment

(case of lower rotational stiness)

75.52 65.58 66.82 68.54 53.33

Combined (1) 67.51 67.51 67.51 67.51 67.51

Rolling moment

(case of higher rotational stiness)

75.43 65.15 58.05 62.99 51.54

Combined (2) 67.09 67.09 67.09 67.09 67.09




when the vertical inertia force is applied and 75.52 dB when the piston-slap moment

is applied. When these two excitations are applied simultaneously, the underwater

noise level is 67.51 dB. This cancelling eect of the excitations can be useful in the

design of a resilient mounting system to reduce the diesel excited hull vibration andthe consequent underwater radiated noise.

5. Concluding remarks

Piston-slap exerted excitation on the engine frame may cause a higher level of ship

hull vibration and underwater radiated noise than the excitation exerted by diesel

vertical inertia force of reciprocating masses. In the diesel vibration isolation design,

unreliable solutions might be found if the contribution of piston-slap moment to

excitation is neglected.

When the moment excitation is considered, the rotational stiness of elastic

mounts for the resilient mounting system plays an important role in diesel vibration

transmission to the ship's hull via the mounting system, especially as the frequency

increases. Analysis of vibration isolation should include both translational and

rotational transmission in order to provide accurate information for the mounting

design and element selection.

The underwater radiated noise level of the hull under combined excitations of

vertical inertia force and piston-slap moment is not the simple summation of noise

level under each individual excitation, but lower than the noise level under each of them. The combined force-moment excitation provides a cancelling eect.

References

[1] Snowdon JN. Vibration isolation: use and characterization. Journal of Acoustical Society of the

America 1979;66(5):1245±74.

[2] Mead DJ. Passive vibration control. New York: John Wiley & Sons, 1998.

[3] Gardonio P, Elliott SJ, Pinnington RJ. Active isolation of structural vibration on a multiple-degrre-

of-freedom system, Part I: the dynamics of the system. Journal of Sound & Vibration 1997;207(1):

61±93.

[4] Talor CF. The internal-combustion engine in theory and practice. Revised ed. The MIT Press, 1986

[5] Plint M, Martyr A. Engine testing 2nd ed. Butterworth-Heinemann, 1999.

[6] Suh C-H, Smith CG. Dynamic simulation of engine-mount systems. SAE Paper 971940.

[7] Snyman JA, Heyns PS, Vermeulen PJ. Vibration isolation of a mounted engine through optimiza-

tion. Mech Mach Theory 1995;30(1):109±18.

[8] Ross D. Mechanics of underwater noise. Peninsula Publishing. CA: Los Altos, 1987.

[9] Ungar EE, Dietrich CW. High-frequency vibration isolation. Journal of Sound & Vibration

1966;4(2):224±41.

[10] Soliman JI, Hallam MG. Vibration isolation between non-rigid machinesa and non-rigid founda-

tions. Journal of Sound and Vibration 1968;8(2):329±51.

[11] Pinnington RJ, White RG. Power ¯ow through machine isolators to resonant and non-resonant

beams. Journal of Sound & Vibration 1981;75(2):179±97.

[12] Petersson B, Plunt J. On eective mobilities in the prediction of structure-borne sound transmission

between a source structure and a receiving structure, Part I: theoretical background and basic

experimental studies. Journal of Sound & Vibration 1982;82(4):517±29.




[13] Petersson B, Plunt J. On eective mobilities in the prediction of structure-borne sound transmission

between a source structure and a receiving structure, Part II: procedures for the estimation of

mobilities. Journal of Sound & Vibration 1982;82(4):517±29.

[14] Petersson B. Structural acoustic power transmission by point moment and force excitation, Part I:beam- and frame-like structures. Journal of Sound & Vibration 1993;106(1):43±66.

[15] Petersson B. Structural acoustic power transmission by point moment and force excitation, Part II:

plate-like structures. Journal of Sound & Vibration 1993;106(1):67±91.

[16] Woodyard D. Pounder's marine diesel engines. 7th ed. Butterworth-Heinemann, 1998.

[17] Berry A, Nicolas J. Structural acoustics and vibration behavior of complex panels. Applied Acous-

tics 1994;43(3):185±215.

[18] Sanderson MA. Vibration isolation: moments and rotations included. Journal of Sound & Vibration

1996;198(2):171±91.


20000626-fem analysis of diesel piston-slap induced ship hull vibration and underwater noise

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