Question

A vibrationisolation unit consists of two blocks of hard rubber with a modulus of rigidity G=9MPa bonded to a plate AB and to rigid supports as shown. Denoting by P themagnitude of the force applied to the plate and by δ the corresponding deflection, determine the effective spring constant, k=p/δ, of the system.

Answer 1

Two blocks of hard rubber are bonded to the plate AB (on which force P is acting) and to rigid supports as shown in the figure below.

Calculate Shear stressinduced in single hard rubber block due to the forceacting on the plate AB using the equation

Here, F is the shear force acting on the single rubber block. A is shearing area.

Since two rubber blocks are bonded to the plate AB, a shearing force is induced on each.

…… (1)

Calculate the A using the equation

Here, l and b are length and breadth of the rubber block.

Substitute for l and for b

Therefore,

Due to the force acting the plate AB deflects. Since, rubber blocks are bonded to it, they deflect through a shearing strain as shown in the figure-1.

Calculateusing relation

From the figure-1,

Therefore,

Calculate the force using the relation

Here, G is the rigidity of modulus.

Substitute for G

Calculate effective spring constantof the system using the equation

Therefore, the effective spring constant of the system is