$2\mathrm{.}36.$ A typical vibration isolation device consists of a rubber

cylinder of diameter $d$ compressed inside of a steel cylinder by a

force $Q$ applied to a steel rod, as schematically depicted in Fig.

P$2\mathrm{.}36.$ Find, in terms of $d,Q,$ and Poisson's ratio $v$ for the

rubber, as needed: $($a$)$ an expression for the lateral pressure $p$

between the rubber and the steel cylinder and $($b$)$ the lateral

pressure $p$ between the rubber and the steel cylinder for

$d=50mm,v=0\mathrm{.}3,$ and $Q=5kN.$ Assumptions: $1.$ Friction

between the rubber and steel can be neglected; $2.$ The steel

cylinder and rod are rigid.

Answer

$p=\frac{4vQ}{d^2(1-v)}=1\mathrm{.}091$MPa$(C)$