this Nole in orthe absorbe that xk tion. defined such the of an absorber drift a

Question

this Nole in orthe absorbe that xk tion. defined such the of an absorber drift and the amplitut that the useful range of effective driving fo 1, becomes an amplification the tion actualy (5.24) with tk/Fo ields the two solutions this for Solving For the slem Example 5.3.1 u 0.25, so that the second solution become of 1.1180 The condition that Irk/Fil 1 is also satisfied for Xk/Fo 1. Substitution of ti into equation (5.24) followed by some manipulation yields 2 (u 1) which is quadratic in (eo/ooa). Using the values of 0/18.29. 2600 T3k and u 025, this simplifies to 14.5 The prece robustness tha values kas e lustrates that is stated in the the robustnes are examined 5.4 DAMPING IN V As mention tial for dest fully by dr absorbers of a vibrat by dissipa bration do Firs absorber sorber sy system form by

Explanation / Answer

solution:

1)when auxillary spring mass system of absorber is added to primary system then system vibration will reduce and such type of vibration absorber is known as dynamic vibration absorber.

2)here equation of motion are

mpxp''+(kp+ka)xp-kaxa=fosinwt

maxa''-kaxp+kaxa=0

where

mp=mass of initial system

ma=mass of absorber

xp=primary system displacement

xa=absorber displacement

mu=ma/mp,beta=wa/wp,r=w/wa

here we have beta=1 and mu=.25

hence bandwidth range possible for system is given by

X/Fo=(1-r^2)/[(1+mu*beta^2-r^2)(1-r^2)-mu*beta^2]

here we have X/Fo=1

so we get equation on simplifying as

r^2=1.25

hence value r=+-1.1180

hence w/wa=+-1.1180

hence value of w reduced resonance amplitude at peak as suggested by smith ,must be in the range of

-(1+mu)^.5<(w/wa)<(1+mu)^.5

-1.1180<(w/wa)<1.1180

here for our system ,to reduce magnitude of amplitude of vibration at resonance condition,value of w/wa should be within limit specified by above equation

as our lower limit is greater than,-1.1180,hence we choose .3929 but our upper limit cross limit by above equation and hence we have excluded frequency by excitation of w=1.1382 to reduce amplitude of vibration X at resonance.

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