An instrument is attached to a rubber mounting having a static deflection of 3.6
mm. The supporting structure vibrates at a frequency of 30 Hz. If the damping
is 3% of critical, estimate the % reduction in the transmitted support motion
I'll give a hint and I hope that you will solve the rest of the problem.
The static deflection dx is related to the supporting stiffness k and the supported mass m as
k dx = m g.
The mass and the stiffness yields the natural frequency of the supported structure
Ω^2 = k / m.
Combining these the equations yields
Ω^2 = g / dx.
Now, you just need to obtain the magnitude response of a kinematically excited single DoF oscillatory system which is excited at the given frequency (30 Hz) and whose D equals to 0.03.
The f0 can be estimated from the deflection: 16/(3,6)^0,5 = 8,4 Hz. There are probably more resonance freqencies, as there are several supports. Rocking, swing etc. However the first vertical mode is the one we look at here.
For the transmission loss you can look for the classsic viscoelastic transfer function using the above f0 and 3% of critical damping converted to the loss factor.
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