VIBRATION CONTROL OF STRUCTURE USING MULTIPLE

PASSIVE VIBRATION ABSORBERS

DR. IZZUDDIN BIN ZAMAN @ BUJANG

YAACUB ZAKI BIN ALI

MAHYAN BIN NASOHA

Short Term Grant

VOT 1332

UNIVERSITI TUN HUSSEIN ONN MALAYSIA

FEBRUARY 20 1 5

EXECUTIVE SUMMARY

Vibrations are undesired phenomenon in mechanical structures. It can cause damage,

discomfort, destruction and disturbance of the system or the structure. In this study,

the application of passive vibration absorber is investigated and its effectiveness are

further researched by comparing the use of single and multiple absorber for the struc-

tural vibration control. The vibration absorber system is designed to minimize the

vibration amplitude of a simply-supported beam and a simply-supported plate. The

beam and plate's vibration characteristic, such as natural frequency and mode shape

are determined using three approaches: experimental testing, analytical equations and

finite element analysis. In the initial stage, a finite element simulation study is con-

ducted using Ansysm to validate the analytical equations of Matlab and experimental

results of a simply-supported beam and a simply-supported plate. The preliminary re-

sult indicates that the first four natural frequencies of a simply-supported beam and a

simply-supported plate are well-correlated between finite element, analytical and ex-

periment results. Later the research works are further performed with attached single

and multiple vibration absorbers. The result shows that multiple vibration absorber

produced better results compare to single vibration absorber attachment in reducing

the structural's resonance amplitude. The outcomes of overall global vibration reduc-

tion for multiple absorber is 9 times while single absorber is only 6 times. In the end,

we can conclude that multiple vibration absorber is more effective and shows better

result in reducing the resonance vibration of the structure.

3.3.1 Theoretical equations of simply-supported plate

The equation of motion of a simply-supported plate can be written as (Fuller, C. &

Nelson, 1996):

where E is the Young's modulus, I is the area moment of inertia, p is the density of

plate and h is thickness of plate. The area moment of inertia for plate is defined as in

Eq. (3.23), where v is the Poisson's ratio.

The solution of transverse modal displacement for a plate is given by the summation

of all of the individual modal amplitude responses multiplied by their mode shapes at

that point (Fuller, C. & Nelson, 1996).

~. - -

w ( x , y, t ) = z wm • ymn (x, Y ) eiuhi (3.24) m=l n=l

where W,, is the modal amplitude, Y,, ( x , y ) is the mode shape of plate, and m and n

are modal integers.

The general mode shape of a simply-supported plate can be calculated with two in-

dependent functions:

The two independent functions X, and Y, can be calculated from Eqs. (3.26) and

(3.27):

X, ( x ) = cash ( k , , ~ ) - cos (kmnx) - Pmn [sinh (k,,x) - sin (k,,x)] (3.26)

Yn ( Y ) = cash (kmny) - cos (kmny ) - Pmn [sinh (kmny) - sin (kmny )I (3.27)

where P, and k, are obtained in the respective Eqs. (3.28) and (3.29).

cosh (k , , l ) - cos (k,,L) mn - - sinh (k,,L) - sin (kmnL)

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