CANTILEVER.docx

8/16/2019 CANTILEVER.docx

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EMM 3243

VIBRATION LAB REPORT 1

Mass-Spring-Damper System of Single Degreeof Freedom using Cantilever Beam

NAME: SYED IZZUDDIN AL-HADY BIN SYED MOHAMMED AL-HADY

MATRIC NO. : 2130052

GROUP MEMBER:

1) MUHAMMAD (213004)2) MUHAMMAD !AIZ BIN ARI!!IN (2130051)

3) MAATHI"ARMAN A#L ANBARASEN (2130054)

4) P$DT SYAHIDATUNNUR BINTI SEMAON TUDM (21300%2)

LECTURER: DR !"#SBULL$" "UD"$


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TITLE

Mass-spring-damper system of single degree of freedom using%antilever &eam

ABSTRACT

'i&ration is %(ara%teri)ed as tedious movement of an o&*e%t +it(respe%t to a stationary point %asing of referen%e or &alan%e position #n t(istest, t(e t(ing t(at +e are interested is t(e relation &et+een single degree of freedom and free response frame+or To e.amine t(e normal for t(e singledegree of freedom of spring-mass-damper frame+or and to de%ide springsti/ness and damping %oe0%ient estimation of t(e single degree of freedomframe+or, t(e main goal of t(e test +as to %reate t(e numeri%al model forit Referring to t(e 1e+ton2s se%ond la+ +e %an see t(at t(e single degree of freedom and free response frame+or +as spoen to utili)e one mass, onespring and one damper and displayed utili)ing T(e impa%t of mass on t(e

normal re%urren%e and damping proportion +ere a/e%ted &y t(e mass of t(eframe+or t(at a%t as manipulated varia&le Contrasting all t(e %(arts of displa%ement versus time, it +as demonstrated t(at t(e pattern of t(e %(arts+ere sinusoidal +ave +(ere displa%ement diminis( e.ponentially +it( timeand in t(e long run go to a stop +(ere )ero movement (appen T(e 3uantityof +ave in t(e diagram +as a/e%ted &y t(e spring sti/ness +(ile t(e idealopportunity for a frame+or to %ome to )ero movement +as a/e%ted &ydamping %oe0%ient #n t(is investigation, spring sti/ness and damping%oe0%ient stay steady T(e main varia&le t(at +as manipulated +as t(emass T(e &ene4t of spring sti/ness and damping %oe0%ient %an &e a%3uired&y tuning t(e parameters in t(e s%ienti4% model T(e estimation of spring

solidness is 567 18m +(ile t(e &ene4t of damping %oe0%ient is 556 1s8m T(e mass do impa%t t(e 3uantity of sinusoidal +ave in t(e %(art and time forframe+or to grind to a (alt $t t(e point +(en mass &uild, t(e 3uantity of sinusoidal +ave diminis(ing and time for frame+or to grind to a (altde%line T(is demonstrates t(e regular re%urren%e and damping proportiondiminis( Regular re%urren%e and damping proportion are %ontrarily relativeto mass

OBJECTIVE

To investigate t(e &e(avior of mass-spring-damper system using single

degree of freedom systemSCOPE

5 To develop mat(emati%al model of single degree of freedom of mass-spring-damper system

9 To analy)e t(e %(ara%teristi% of t(e single degree of freedom of mass-spring-damper system


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To o&tain a suita&le spring sti/ness and damping %oe0%ient value forsingle degree of freedom mass-spring-damper system

INTRODUCTION

'i&ration (appens all over t(e pla%e in our day &y day life T(e

e.ample of vi&ration in%ludes ride nature of a %ar and %ruiser T(is (as &een%(ara%teri)ed as monotonous movement of an arti%le in respe%t to astationary point edge of referen%e or &alan%e position !eeping in mind t(eend goal to e.amine vi&ration e/ortlessly, vi&ration is grouped &y degree of freedom and nature of information or *olt to t(e frame+or T(e &asenum&er of displa%ement fa%ilitates e.pe%ted to spea to t(e position of massin t(e frame+or is %alled degree of freedom T(e least %omple. %on%eiva&lemodel to portray t(e displa%ement dire%tions of mass in a frame+or ismodel of single degree of freedom $fter de%ide t(e 3uantity of degree of freedom, nature of info or &oost to t(e frame+or +ill &e de%ide 1ature of info %an &e %lassi4ed into free response, %onsonant information and general

%onstraining %apa%ity Free response refers to analy)e t(e vi&ration of t(eframe+or %oming a&out &e%ause of non-)ero starting displa%ement and8ornon-)ero speed of t(e frame+or +it( no e.ternal for%e or minute %onne%ted To %reate essential %ompre(ension of vi&ration frame+or, single degree of freedom and free response frame+or +ill &e taled a&out in t(is trialSpring-mass-damper frame+or is t(e model of all vi&rating or os%illationsystem T(e single degree of freedom and free response frame+or %an &espoen to &y utili)ing one mass, one spring and one damper T(e%on4guration is s(o+n &elo+

To model t(is single degree of freedom and free response system, &ydra+ing out t(e free &ody diagram and using 1e+ton2s se%ond la+ of motion, +(ere F ; ma,


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T(e e3uation form is


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T(e ne+ e3uation form is´ x2(t )=

−cm x

2 (t )−

k

m x

1(t )

By tuning t(e parameters +it( respe%t to t(e e.perimental result, t(evalue of sti/ness and damping %oe0%ient %an &e determined To get t(e

value of natural fre3uen%y, , and damping ratio, ,

ωn=√ k

m ζ =

c

2mωn

APPARATUS

Computer +it( DasyL$B, M$TL$B, and Simulin soft+are, MCC D$ USB

%onne%tor, a%%elerator, -%lamp, steel ruler, mass (older, 5 mass of 577 g

and 9 mass of 67 g

PROCEDURE

5 T(e apparatus +as set up as s(o+n in t(e 4gure &elo+

9 $ laptop +it( all t(e programs a&ove +as s+it%(ed on DasyL$B +as a%tivated and t(e program +as %ali&rated &y using

multimeter T(e MCC D$ USB %onne%tor +as %onne%ted to t(e laptop6 $ steel ruler +as %lamped at t(e edge of t(e ta&le &y using -%lamp

T(e distan%e from t(e edge of ta&le to t(e mass (older is 57 %m


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G $ mass of 577 g +as inserted to t(e mass (olderH $%%elerometer +as atta%(ed to t(e &ottom of t(e mass (older, +(i%(

no+ %ontains t(e mass of 577 g and t(en %onne%ted to t(e MCC D$I T(e mass (older +as pulled do+n until t(e displa%ement of t(e

&ending is %m

J T(e Kplay &utton in DasyL$B +as pressed as soon t(e release of t(emass (older T(e data of a%%eleration +as re%orded

57 (en t(e vi&ration stopped, stop t(e running soft+are55 $ll t(e data t(at +ere re%orded in DesyL$B +ill &e presented in

s%atter plot +it( t(e (elp of M$TL$B soft+are59 Step 5 to 55 +as repeated &y adding up 67 g to t(e mass (older

until t(e mass is 977 g in total

SAMPLES OF CALCULATION

To o&tain 4ltered grap( of a%%eleration versus time, Simulin in M$TL$B +as%reated T(e data of a%%eleration o&tained in t(e e.periment +as set as t(e

input By using (ig( pass 4lter of 4lter order I and pass &and edge fre3uen%y

of 7 rad8s in analog 4lter, 4ltered grap( of a%%eleration %an &e o&tained &y

vie+ing it in S%ope 9 To o&tain e.perimental grap( of displa%ement versus

time, again, t(e Simulin is used T(e data of a%%eleration +as 4ltered and

integrated t+i%e &efore entering into S%ope 5 T(e data of displa%ement +ere

o&tained after t+o times of integration and %an &e vie+ in S%ope 5 To o&tain

t(eoreti%al grap( of displa%ement versus time,


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CANTILEVER.docx