Appunti Mechanical System Dynamics

FUNDAMENTALS 9 EXERIHENTAU HODAL ANAtYSI

Our loim to dent ieY thPrrolMeterS Whiah are

SYStem jdemtifi

cutio hMathemaHical Modeu

From

CoMi MatheMatical

TXFerimenta Mbde

dauta AlgorithmS UKed for th

odel fosrometers idemtieicaltion Ter Com

idet ARCOt iOm OPeralte Mbsth EreaUmcy

tedhniques md qmdoMa in

Our aim 1s idetEY the Modal aromates X

We are gongto look at thu HechnqreS tha WOrKTn HreAUmCy dofmain

bases onfheleoST Sa UauTRMjaiMitátLon Of Hh diAEerenC between

RXperi Memial Omd fhe hUMeI CaL FRE,

We conSTe Hha analya

EXperMOta moda OmalYSLS Hical ARE COMiAg ETOM

Uced MOdalgUPer paSfon,

Charocter t ha dYnaMiC Aropertieg

O Hhe MedhanicalSISTeM

Model Ualidat ion Omd medeU Uuat ing Validote th finte

QeMo4 method

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health moniforing

Structural

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mollysi.sS

thu experiMetolLmosa

to aer{Y

order

n

reauire. hethemátiaT nsseu, agrith

EKPerimetat fRF,

A Set of exfe ciMatal FRES CoMin Erom exeerivbmts

A Mathe MotroalFomUiation l th FRE Aageeric Mea

SYTem, based onHheSuErOOSHt0n aMtRS

por

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agg Shokers

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Broadboma 2KtatTon(andOM, tlamSTAMT, AcSAQ SWeep

Stepsea he opalve

Slow S_SWeerS

lo or eerpmh eknerimondsWwTU heed Me accelero

AnëteS HhAt WT Ldauit

Th veseonsbetacdleomet ersWL heve Hhe follbuwhg orm

FANT DyhamoMityi Red iMebLSTve excitoton iSm

iMpatt hiaMMe O 0 ximtion OFh hearetical

MeUiS (Sicae delto function)

s s ble 6 Cno ose h fre=

ome 4hat COmbe ha

choase

Yproeef

xoites

ahmer S HiE chatact ortSTiCS

CRIHRhmne OIde fregUenro

naroE equRmdromge

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KWeaveote N DASaMpled Me hstoes for th

This me0mS Hhat_we haue eeotTN-eSSI

heedled e a m URa HomnA WJODMordern to reduce

lea g Hoh Sameres TWe obtainNTPat DF

JUldpiYDE dTgdreteSeectra

xi omdX

W (EmoUIe OMd CSh_FUnEtons

N X uXE[m

GXX 2W

OFE 2W

GXE 2wo

SnaUY we om CKPqess Rhe FREFUncT jon Cmd the lcoherem

X mwa)

EXP EXretMetal

Fk imwb Gre (muwo) FRF

Provides th conrelation betue_neUT Cmo

Cohererca FUnction otAt

G(-)1

YK =

(M wo) GxX ws)Er S fxe Unile MeasureE

n a typiaaegT Kx¢itationo

Memt Point ) Varies, sb, difkromtoat s a r Costcered.

The fRÉ Cam bereeceseTed as

f exP

G noise S_auoYS_prSeT.

In ondey Horeduce Hha ERFetDA 2

o S Passiie to eifogm 4

mdthan Cveria3

h e MaXtmUm frequemOY t wKTCA thu FREiS defined, Corres Pohds to

thMaxiMUM fequemcY oe thdisdreRfoen tromspEM lof th

orcz am botionSignd We have Ho 1eroeely SoleCA TR

amelh freayene1 QUccordina

t 0

fthe reaomCY Hh Hh INyqUsHShamion maorem,

T Ootualu

fRESShalleraha K actuol

bomdw.dth_ b£ the r c e w e have

to UseCm atialiosih8 tifer

Aralyticaexpress ionD fhiFRA

EkTeRe(f Stecd

STate

XtERE(X e Tresponse

Modal Syrer postHon: X

Moda COprdimates

V.btotion indscrete

nea sure me ocat onsLJoiui modro

Then th mealsucenomt Co be writte JS

-X0

Accordi1 MoclaSuperebsit ion Welore 90in tohave ecoueled

MoHon Pauatioms k i T

force

uSH8erolised

in

The ho Force,md TAL VIbrqiton

betwe th ode

FO

nKCoTeseondA

Nalca

Sho e Me

MDDCFK ex XkFuo

(U3vale dlla dimgstro ti

Necthia h Camdgre nota imn

tddi X Kko

FG

acanMOersHoHh EiT-

VioroTtido_ Moej

FRF-based_NtiMO

de_Oirve- fiAingMthod

A RK 4)

23 w twi

EXerimatal data set

Mathematicau_mbde lngredies ofthe exeeri

Mmta Mcd malys S

AgorHhm forHhe Tdent?fiatioh

tn he eeeriMta fFRE| h TMothe Macalmodel

432S3

Leo SAuareS MiniM2dtton Dgerotes ia aUSe-d finDd freguemcy

bamd nich NglucS OLCtainhuMbe n DE VOatigni_ modes

iS

minii2ed

be

function to

eror

The

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NUM

NUM 6jKG)*

G

(6

E 6 l o w freq. Freg

We select a aertan frequemçY

thsFceqen

CY response thQgh

a MoRCPrevious LY reprted,

=We cAm Eit a nUmbe ofMocey

we SUM_ U ha ontr+hution Of h Odesthn each one oE Hhem

eAresmtativ o O+eCM in Ah Omd Hhen, by SuMmih UP aL 0E

RaM, e Obtajin Ahu. toTal fRA.

We haye Ome Contribution

S COming from Low freqymcy Modes amd

from The hi8h SreaUmcy odes, We wom inMR AYy=

tRrmic, beTWLOhth CnalY

Thi lu FrequeMCY Modes wTL Ebe worung in SSMiC re3ion Wth reSPect

thu frecyoncy amgHha are Cans:aering,

WAie 3n freauncy

nDdes ae in quaS gTatic regton

=)]LE Mo bes = fUnction

H . MOde onstom fUnct On

frrst teME Modes n the freqtncy YO8e 23,w nt w:

Low FrequeneY Modes n

Second Rm SSMIC reon Rk

hird ecm: High freruen cy modes in RUK

qUsSTatic regton

S al3othm alous o

uS h Whole FRE

ProcesS data get

T tina O odOEcY md of

The oruS Consi

procass bY oderin3hg data of a MeasyeMent

Th

Chmnels cat t h Sam tiMV Sothe +inal duTeUt ffor each_Uibration

Mo re (

Nactutal frequemcY X Vares Wth th_Measure

Memtchnne

Mocal da MPing ratio The resutb ordifferemt

The dhomyno

X

MOde share

imeliFedsaRle-Modle idemtiFicotion procedureL453 0]

ok Vali thehothesyf Tt domPng oMd

OEFICie Solde mdHuro frèduemciec di

Se lo SMorzammto ebassOechi

Visononta Son Srett

EW&o AIS Cade, in Yelative[Y harcoWbamd cemtered

onh essnonc e hon-resonamt

th

of

bfioy

COHY

L Rgiece e foa sRle Mole timne

on per

Ntur eaueMdies Co be ldirect detific from tha S

on ofth resdadmde poaS He ekeerimomtol FRE.

AhViQtY eHhe-h rRsonomce peaA

We onY ConsideHhe

YegondMt Mode

m nci+ki

h Hompune ratio S Cam b dotified Aromh SoPe lofPR

ph sedigmminconroSondem HhUU

he Slope of the tomF

W darelainH lated uttht am<