vibration research

7/28/2019 Vibration Research

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Streamlining Design with Real-WorldVibration Analysis

S U M M A R Y

Mchaical dsigrs t us ibrati simulati as a timsaig

ad cst-cit altrati t th traditial apprach buildig,

tstig, mdiyig, ad rtstig thir dsigs. By idtiyig th actrs

that ifuc th rsps t a dyamic lad i a cmputr mdl, d-

sigrs ha th data dd t mak th right imprmts br

thy cut a sigl pic mtal. I additi t gratly dcrasig

th umbr actual prttyps rquird, ibrati aalysis als sigi-catly rducs th csts ild.

w h i t e p A p


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inroducon o dynamc smulaon

Dyamic simulati ca hlp mchaical dsigrs crat bttr prducts. Wh d-

sigig a prduct, yu t d t addrss pratial qustis, such as:

Hw much rrr will b itrducd i a tl by shakig i a xtur a millig

machi?

Ca playr atigu b lssd by rducig th ibrati lt thrugh a w tis

rackt r gl club?

Will cmpts ls du t th ibrati rad is wh trasprtig lc-

trics?

Hw thick shuld th mtr muts a autmti gi b withut r-

dsigig thm i wight r cst?

Is it pssibl t prdict whthr th spidl spd il wll-drillig machiry will

kp th systm i a sa pratig rgi withut ibratig apart?

D systms r structurs d t crm t MIL spc, Tlcrdia GR-63, r Ui-

rm Buildig Cd (UBC) ibrati r sismic rquirmts?

I th past, yu may ha aswrd ths typs qustis with had calculatis

ad a w build/tst/rdsig cycls. But w, yu ca tak th gusswrk ut th

iitial dsig phas by usig dyamic simulati.

Ay tim a cmpt r a assmbly is subjctd t a chagig r dyamic lad, it

may ract r ibrat i a way that rags rm mrly ayig t critically dagrus.

Csidr ths thr ral-wrld xampls: Althugh th ibrati i a prly dsigd

crdlss drill may t lad csumrs t rtur th prduct, thy might tll thir rids

t t purchas it. Durig a tst-dri, ucmrtabl rad-iducd ibratis culd

tur a prspcti buyr ad rsult i th lss a sal. Ad, th strss ibratis

th mchaical husig r sldr jits ssiti lctrics durig trasprt has

th pttial t b quit dstructi.

Th mai gal ibrati aalysis is t dtrmi i iputs that chag with tim cr-

at a uaccptabl rsps, i trms actual part ailur r usr prcpti. With

this dtaild kwldg, yu ca impr yur dsig br yu build a prt-

typ r a actual structur. I th llwig pags, sral apprachs r xamiig

ibratis ar discussd, as wll as thir impact th succss yur dsig.

Dscrbng r ys o vbraonsCsidr a xampl that illustrats th basic ccpts i ibrati ad th tchiqus

usd t simulat it. Yu wuld lik t discurag th ighbrs cat rm prchig

yur pl-mutd bird dr r a r luch. I yu gi th pl just a littl push, th

lcity ad displacmt th dr will b l iarly prprtial t th iput spd

ad magitud th push (Figur. 1a). I yu start shakig th pl with th sam

magitud iput but with gratr spd, hwr, yu will tually caus th pl

t whip at th tp ad thus achi yur cat-rmal gal (Figur. 1b).

S T R e A M L I n I n G D e S I G n W I T H R e A L - W o R L D v I B R A T I o n A n A LY S I S

Th mai gal ibrati

aalysis is t dtrmi i iputs

that chag with tim crat a

uaccptabl rsps, i trms

actual part ailur r usr

prcpti.

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Figure 1: Pole shaken slowly (a) compared with the whipping motion caused by

faster input (b)

This whippig ct idicats that yur shakig spd has xcitd rsac i th

bird dr systm: th utput (a) is w disprprtiatly high cmpard t th iput

(b), much t th chagri th cat.

This back-ad-rth mti rprsts a simpl iw what happs durig ibrati.

Tim-aryig iput that xcits rsac i a systm ca rsult i a dramatic,

catastrphic, rsps. Yt, a similar iput at a dirt spd that ds t xcit

rsac may t shw ay caus r ccr. Ths ccpts apply t all systms

ay cmplxity. As a rsult, ibrati aalysis abls yu t udrstad just wh

shakig will caus mir r catastrphic rspss lswhr i yur prduct.

vibrati ca b dscribd i thr ways, primarily by th atur r rm th driig

iput:

1. I th physical r time dmai, yu ca xpct t s th actual chagig m-

mt i ral tim. A simulati i th tim dmai is t calld a transientaalysis.

I th bird dr xampl ab, yu ca cut th rqucy pushs pr mi-

ut, as wll as masur th amplitud th push, ad th prid ths iputs

t a simulati. As th iput spd icrass i th simulati, yu wuld s th

sam gai i tip-spd ad displacmt as yu wuld s ad masur it i yur

yard. Athr utput culd b th tim r umbr scillatis it wuld tak rth pl t cm t rst du t atural dampingc th shakig stppd.


vibrati aalysis abls yu

t udrstad just wh shakig

will caus mir r catastrphic

rspss lswhr i yur

prduct.

P. 2

(a) (b)


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I th trasit mthd dscribig a dyamic t, ay paramtr (such as

spd, magitud, dircti, r umbr iputs) ca chag just as it might i a

ral-tim t. Th cmputr simulati such ts must rprt ths utputs

at spcic tim itrals as ppsd t displayig a ctiuus rspsth

digital rsus aalg dilmma. As th durati icrass, th sluti t ths

prblms csums mr tim ad rsurcs. Yu must spciy sucitly smalltim-stps t captur all chags as wll as th rspss t ths chags. A

cmm guidli r dtrmiig th umbr rquird tim-stps is pr

ry pak r ally i a rsps. As illustratd i Figur 2 blw, this umbr ca

quickly grw r a trasit aalysis a t.

Figure 2: Transient input for a shaker-table test

2. With a frequencydmai apprach, w ca ly spak i trms utput magi-

tud rsus iput at a gi rqucy. Yu must assum that all iputs ar cyclic,

r siusidal, i atur ad ha a cstat amplitud at that rqucy. This simpli-

d utput is mst cit wh th iput aris ly i spd, t i amplitud,

ritati, r umbr iputs. This mthd is cmmly usd t ary, r swp,

th iput rqucy acrss th pratig rag ad idtiy th maximum pssibl

rsps, as might d a shakr tabl (Figur 3).

Figure 3: Automated shaker device with variable frequency applied to bird

feeder, cat-removal problem


I th trasit mthd

dscribig a dyamic t,ay paramtr (such as spd,

magitud, dircti, r umbr

iputs) ca chag just as it

might i a ral-tim t.

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Th iput ca b a simpl pak rc, displacmt, r acclrati at a sigl

rqucy, r a cmplx ucti r tabl that dscribs hw th magitud th

iput chags with rqucy.

3. Th third way dscribig ibrati ils th dmai statistics ad prb-

abilitis. Cmm usag t misladigly labls this apprach as random vibra-tions. Situatis that rquir a radm ibrati study ar s whr th spd r

rqucy th iput ad th amplitud ar t rpatabl but ha a prdictabl

arag ladig. Csqutly, yu d t cmpil a mathmatically rprsta-

ti iput r a gi tim prid t prid a prbabl amut iput rgy at a

gi rqucy.

W ca rprst ths arius stimatd rgis at all rqucis ccr

i apower spectral density(PSD) cur r tabl. Usig a cmparati apprach is

th bst way t us th utput ths prblms, as yu ca s th icras r

dcras i th strss r displacmt a systm xprics r a gi chag i

ths iputs. Whil clarly a mr apprximat apprach tha th thr tw mth-

ds, th PSD cur r tabl is th ly way t dscrib a systms rsps t th

ariabl iputs ud i arthquaks r rad is (Figur 4).

Figure 4: Subjecting the bird feeder to a bumpy road could confuse the feline an-

tagonist due to the random nature of the vibration


W ca rprst ths arius

stimatd rgis at all r-

qucis ccr i a pwr

spctral dsity (PSD) cur r

tabl.

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Dfnng undamnals o vbraon smulaon

Static versus dynamic analysis

Static studis assum that lads ar cstat r applid ry slwly util thy rach

thir ull alus, thratr rmaiig cstat with tim. Bcaus this assumpti,

all irtial cts must b csidrd gligibl, icludig th lcity ad acclrati

th xcitd systm. Static studis thrr prduc strsss ad displacmtsthat ar cstat.

Fr may practical cass, hwr, lads ithr ar t applid slwly r thy chag

with tim r rqucy. Irtia ad dampig bcm rlat, ad maigul simula-

ti dmads th us a dyamic study. A t misusd practic is th applicati

a static rc t simulat th dfcti that a structur might xpric i a sis-

mic r impact t. Ths ts il acclratis r dclratis that act

all th mass i th systm rywhr, t just at a pit r at th ctr graity

ach cmpt. Additially, i th cas sismic r shakr-tabl ladig, i th ap-

plid ladig is rrsd as a systm is rspdig rm th iitial applicati, iducdacclratis i cmpts ca b ry dicult t prdict withut a dyamic simula-

ti. Csqutly, a static simplicati ca b ry misladig. Bcaus thr is

csistcy as t whthr it will b csrati r csrati, a static simplica-

ti is iapprpriat r mst cass.

General modal analysis

Th buildig blcks all dyamic slutis ar th natural frequencies r modes th

systm. All bdis display rsat r atural rqucis idpdt ay ladig.

This phm is s as th r ibrati a systm atr a bump r a rapidly

rmd displacig rc. Th lwr atural rqucis, dd i hertz(cycls pr

scd), ar th drmd shaps, r mode shapes, that rquir th last amut rgy t achi. Fr th lg ad slim catilr, which is similar t a yardstick (Fig-

ur 5), clarly much lss rgy is rquird t dfct th part i (a), th lwst atural

rqucy tha i (b), a highr atural rqucy.

Figure 5: Two natural frequencies of a thin beam


Th buildig blcks all dy-

amic slutis ar th atural

rqucis r mds th

systm.

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As a rsult, dsigrs ar usually itrstd ly i th rst w mds sic ths

ar whr mst th acti happs. Wh highr rqucis ar rsatd, th

rsps amplicati is typically smallr tha at lwr rqucis. Hwr, r lg-

trm ibrati whr small strsss might caus atigu ailur, th rsps at highr

rqucis may still b sigicat ad s shuld b xamid.

Bll mti maks a asciatig study mds. Yu ca isualiz a wbblig ct i

a rigig bll whs dg is physically ripplig i a xaggratd mti as dirt

ts rsud. Th suds ary ad last r dirt lgths tim, dpdig

gmtry, prcisi i castig, ad matrial. Th rall sud is a cmpilati th

ts simultausly gratd by ach dirt pattr mmt (md) th

bll as s i Figur 6 blw.

Figure 6: Mode shapes of a ringing bell. Actual tone is the superposition of the tones

resulting from each movement.

A critical actr i dtrmiig whthr r t a dyamic sluti is rquird is th r-

qucy r puls durati th iput. Grally, i th rqucy a iput is similar

t r largr tha th lwst atural rqucy th cmpt r systm, dsig-rs shuld cduct a dyamic study. I cass whr th dyamic iput is a puls, th

simulati shuld cmpar th durati th puls with th prid th atural

rqucis, whs md shap might b xcitd by that puls.

Th prid a rqucy is th irs that rqucy; r xampl, th prid

a 10 Hz warm is 1/10, r 0.1 scds. I th durati th puls is similar t th

prid a applicabl atural rqucy, csidr prrmig a dyamic aalysis.

Time-based analysis

Time history (transient) analysis is t usd t s th magitud strsss r

dfctis gi a shrt durati puls (Figur 7). I this xcits a rsat rqucy,th rsultig strss r dfcti may b gratr tha that r a static lad qual

magitud. Th actual tim durati is als critical, hwr. I th sam lad is applid

ad rlasd ar mr quickly, it may cm ad g br th systm has had tim

t ract; i that cas, prblm will aris. I a similar way, i th lad is applid at a

much slwr rat, th rsps will als apprach that a static situati; ad agai,

th rsps may b urmarkabl. Trasit aalysis will illumiat all thr situatis.


A critical actr i dtrmiig

whthr r t a dyamic slu-

ti is rquird is th rqucyr puls durati th iput.

P. 6


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Figure 7: Sample plot of displacement versus time at a single point on a structure,

with the initial displacement due to a transient load

Harmonic, or frequency response, analysis

Harmonic analysis is imprtat r aalyzig a structur wh th applid rc at

r mr atural rqucis ctius r tim (Figur 8).

Figure 8: Acceleration versus. frequency spectrum for electronics testing

Th classic xampl a ctiuus rgy-pumpig disastr is th cllaps th

Tacma narrws suspsi bridg acrss Pugt Sud, Washigt, ur mthsatr its pig i 1940. As a cst-saig masur, th rigial dsig had b

chagd t dcras th amut bridg-dck stiig by mr tha a actr

ur. early mrig, wids 35 t 46 mils pr hur startd a ripplig mti

th bridg with a up-dw displacmt thr t t. Withi hurs, th wids

ct shitd s that a twistig md was xcitd. This grw strgr util chuks

th ccrt radbd brk up. Fially, a tir scti sappd r, ad larg

parts drppd it th rir. Frtuatly, was ijurd as cials had clsd th

bridg by 10 AM.

Random vibration analysis

Radm ibrati iputs ar drid rm a t that lasts a it amut tim,but whr th dtails th t ar t tim-dpdt (Figur 9). Th lgr th

aluatd prid tim, th bttr th statistical samplig i th rqucy dmai.

Th rsultig data supplid t th dyamic aalysis is sstially a summary th

ttal rgy at all th rqucis xcitd by th iput t. variatis i rad-surac

gmtry r th radm rcs a arthquak ar xampls such iputs.


Radm ibrati iputs ar d-

rid rm a t that lasts a

it amut tim, but whr

th dtails th t ar t

tim-dpdt.

P. 7


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Figure 9: PSD representation of ground displacement near building a demolition site

Aroacs or rormng dynamc analyss

Mchaical girs must dtrmi which, i ay, th thr pssibl liar

dyamic stwar simulatistim histry (trasit) aalysis, harmic aalysis, r

radm ibrati aalysisar apprpriat r thir girig challg. As statdpriusly, th bst idicatr th study rquirmts is th rm iput data that

yu ha. Fr all thr, th rcmmdd stwar squc is: crat a apprpriat

CAD mdl, st up ad prrm a rqucy aalysis t idtiy th applicabl rs-

at rqucis, ad th st up ad ru th slctd dyamic aalysis.

Create an appropriate CAD model

Dyamic simulatis ar typically tim-csumig ad mmry itsi. Fr ths

tw rass al, cratig a simplid ad cit CAD mdl usually pays . Th

guidlis r mdl typ chicbam/li mdls, shll/surac mdls, r slid

mdlsar mr imprtat t csidr r ths studis. Fr strss rsults,

CAD dtail is critical; whil r displacmt r acclrati data, a simplr CAD mdlmay suc. Wh cratig yur gmtry, als kp i mid th rlati ll ap-

prximati r th dirt studis. Sic a trasit aalysis uss ral iput with

littl ltrig r simplicati, th larg rsurc rquirmts a dtaild slid mdl

may pay . o th thr had, sic harmic aalyss us simplid datasts, ad

radm ibrati studis urthr simpliy th rigial tim-basd iputs, th alu

highly dtaild CAD dscriptis bgis t dcras rapidly.

Perform the frequency analysis

A dyamic aalysis is typically basd th atural rqucis i a systm. Br pr-

cdig with a mr dtaild study th tim-aryig rsps, yu must idtiy ths

rqucis (i.., dtrmi th mdal rsps). I mst stwar simulati tls, yuca d this rsps br dig th dyamic aalysis, r yu ca ha it d aut-

matically as th rst stp i thr pssibl dyamic-aalysis squcs.


Dyamic simulatis ar typically

tim-csumig ad mmry

itsi. Fr ths tw rass

al, cratig a simplid ad

cit CAD mdl usuallypays .

P. 8


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Th utput th rqucy study (Figur 10) icluds mdal shaps, mdal rqu-

cis, ad mass participation factors. This last utput is a idicati hw sigicatly

yu might xpct ach calculatd md t participat i a dyamic rsps.

Figure 10: Typical modal frequency list with mass participation factors

Review the frequency results

Fr th rst dyamic simulati a systm, yu shuld always sl r th mdalrsps ad riw it br dcidig whthr r t dyamic aalysis is rquird; i it

is dd, yu must th dcid which dyamic aalysis t us.

I rsat rqucis ar i th rag itrst r prati, yu prbably d

t d t llw up with a dyamic aalysis. e i rqucis ar i th rag

pratial iputs, yu shuld sur that thy rprst shaps which th ap-

plid lads wuld actually xcit. Fr xampl, a latral lad may stimulat a rsat

rqucy, but th md shap at that rqucy may b lgitudial. I this cas, th

dyamic aspct th lad will ha ry littl ct th rsults.

I th pratial rqucis ar likly t xcit sral atural rqucis ad mdshaps, yur rst stp shuld b t mdiy th dsig by pushig th calculatd atu-

ral rqucis ab th pratial rqucis. This task is calld modal avoidance.

Cmm tchiqus iclud wight rducti r rdistributi, additi stiig

aturs, r matrial chags.

I yu cat mdiy th dsig such that th tir pratig spd rag is blw

th rst atural rqucy, it is t accptabl t push th lwr mds lwr.

excitati at lwr spds crrspds t lwr rgis, s th rsultig ibrati will

b miimizd. May dsigrs ha s th cts this wh a pic machiry

shuddrs as it is cmig up t spd, ly t ha all th ticabl ibratis dissi-

pat at wrkig spds. I yu ar uabl t adjust yur dsig s that atural rqu-cis ca b accptably aidd, yu prbably shuld prrm a dyamic aalysis.


I th pratial rqucis ar

likly t xcit sral atural

rqucis ad md shaps,

yur rst stp shuld b t

mdiy th dsig by pushig th

calculatd atural rqucis

ab th pratial rqu-

cis.

P. 9


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Set up the dynamic analysis

Sic th mdal sluti is th buildig blck r subsqut dyamic study, yu will

d t mak sur that ugh mds ha b idtid t charactriz th systm.

At a miimum, yu shuld calculat ugh mds t iclud a atural rqucy

at last twic yur maximum pratig rqucy. Fr xampl, i yur iput rqucy

rags rm zr t 50 Hz, yur atural rqucy list shuld iclud ugh mds ticlud 100 Hz.

I additi t this guidli, yu shuld als riw mass participati actrs r th

spcid dircti iput. Th mass participati actrs icludd shuld add up t at

last 0.8 (r 80 prct). This may rquir yu t iclud mr mds tha twic yur

maximum iput spd, r it may suggst that yu iclud wr mds. D t rduc

th umbr icludd mds byd twic th maximum iput rqucy, hwr.

T d s may caus th sluti t igr rspss at that rqucy, which culd

cmbi with lwr rqucy rsults t push utput byd a accptabl rag.

Th cssary iputs r dyamic aalysis iclud lad magitud, dircti, pit rara itrst, dampig, ad rqucy rag r tim spa. With th utput alus,

yu ha th ability t cmpar such paramtrs as strss, acclrati, ad displac-

mt with th kw limits r yur systm. This allws yu t dtrmi i ailur is

likly r i cst rducti is pssibl.

Fr a trasit aalysis, yu shuld apply th lads ad rstraits xactly as yu wuld

i a static aalysis, with th xcpti that th lads shuld b dd t ary with tim.

Wh usig a harmic aalysis, yu must ibrat th systm with th applid lad.

Yu ca d a tabl r ucti r yur lads that icrass r dcrass thir

amplitud as th rqucy aris. Altratily, yu may ibrat yur systm at th rstraits, which is calld base excitation. Mathmatically, this is aalgus t a

shakr-tabl tst.

Althugh sttig up a radm rsps aalysis is similar t prparig a harmic

aalysis, th iputs t th lad r bas xcitati ar i trms PSD rsus simpl

rc, displacmt, lcity, r acclrati. Th utput th radm ibrati

aalysis prids th RMS (rt ma squar) ad PSD alus th rsps (dis-

placmts, lcitis, acclratis, ad strsss). This data actually rprsts th

prbabl maximum th xpctd rsps at a gi rqucy. Sic th iput is a

statistical samplig, th utput cat b ay mr prcis. Hwr, this is th mst

cit way t gt rliabl dsig data i radm ts.


Th cssary iputs r dy-

amic aalysis iclud lad mag-

itud, dircti, pit r ara

itrst, dampig, ad rqucy

rag r tim spa.

P. 1


12/13

Damping

A dyamic aalysis is usually maiglss withut a mdal dampig actr. Dampig

() rprsts th amut rgy lst i th systm du t th ibratry mmt.

Withut dampig, a xcitd systm wuld ibrat rr. May surcs dampig

ctribut t th dampig actr, icludig matrial cts, ricti, is, ad ir-

mtal cts such as fuid itracti. This actr is typically i th rag 0.01 rlightly dampd systms (sigl stl parts) t 0.15 r highly dampd systms. Wh

thr is thr data dampig, tw prct (0.02) is a cmmly chs dault.

Haig a alid dampig actr is crucial t guidig ralistic dsig chics.

Figur 11 shws th typical gai (Acclrati, A) i a systm at arius rqucis

whr th X alu 1 rprsts xcitati a systm at th rst atural rqucy

( = xcitati rqucy; n = atural rqucy). Yu ca s that at a dampig ac-

tr () 0, th dyamic amplicati (gai) ca, thrtically, b iit. As dampig

icrass, th gai dimiishs rapidly. Basd th rsults, this ca gratly ifuc

th dcisi yu mak. Simpl tstig ca aid i dtrmiig th applicabl dampig.

Figure 11: System gain when a system resonates with various damping factors

Nonlinear dynamics

Athr aspct dyamic aalysis t csidr is that all th simulati tchiqus

discussd thus ar ar liar studis, i that all th ruls r a liar aalysis apply. Yu

must prrm a liar dyamic study i th matrial itsl displays liar prpr-

tis, thr is liar ctact btw cmpts, r th systm udrgs larg

displacmts rquirig a nonlinearsluti. Mst liar dyamic slutis prat

i th physical r tim dmai, as th basic mathmatical apprach mdal rqu-

cis ds t wrk wll with liar bhair.


May surcs dampig c-tribut t th dampig actr, i-

cludig matrial cts, ricti,

is, ad irmtal cts

such as fuid itracti.

P. 1


13/13

Concluson

Sic mst prducts ha mig parts ad ar hadld r md by a xtral

rc, simply durig trasprtati, dyamic simulati is a atural xtsi

ay prdicti simulati prgram. Haig arly data prduct rsps t ibrati

r cllisi allws cmpais t mak crrspdigly arly dsig-chag dcisis.

This isight t ly rducs th d r dlpmtal prttyps, but als sursthat th prttyp ad tst pla ar as cti as pssibl.

Fr xampl, tlcmmuicatis cabit mauacturr istd ur t six wks

i buildig, shippig, ad tstig a sigl prttyp r sismic ibratis i thr

axs, ly t lar that sm wlds aild th rst tst. Thy th had t discard all

subsqut tst rsults. Whil cst was imprtat, th lst prjct tim was mr

critical. I rsps, thy bga prrmig irtual shakr-tabl tstig usig harmic-

rsps aalysis ad wr abl t dtrmi th likly aras ailur. This data -

abld th dsigrs t idtiy cit ad cst-cti xs t rduc th chacs

ths ailurs. Thy als plad th rdr prttyp tstig such that th tst

mst likly t caus ailur cam last. As a rsult, th risd dstructi-tstig pr-gram rd th maximum bt with littl r wastd tim, my, r rt.

Yu will d th tchiqus dscribd i this papr i maistram dsig simulati

tls. Sm rsis ar itgratd i ppular CAD systms, such as Slid-

Wrks 3D CAD stwar rm SlidWrks Crprati. Sic dyamic simulati ca

hlp yu dsig bttr prducts, yu might csidr xplrig this tchlgy i mr

dpth r yur w applicatis. Listd blw ar thr diti wrks ibrati

aalysis.

Rrncs:

Elements of Vibration Analysis; Lard Miritch; McGraw-Hill, Ic., 1986.

Mechanical Vibrations (fourth edition); Sigirsu S. Ra; Pars educati, Ic., 2005.

A Finite Element Dynamic Primer; D. Hitchigs (d.); nAFeMS; Glasgw, Sctlad 1992.

w w w . s o l i d w o r k s . c

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