Physics of a pneumatic vibration isolator revisited

Abstract

This paper gives detailed consideration to two phenomena that affect the performance of a pneumatic isolator but have not received adequate attention in the past. The first one is the thermal conductivity of gas. It is usually assumed that the compression of gas in the pneumatic chamber is an adiabatic process. Thermal conductivity can, nevertheless, affect the performance, especially in the low-frequency domain and for small-size isolators. A simple explicit expression for the acoustic compliance is derived from exact solution of conductive gas equations in the cylindrical domain. Another factor affecting the isolator response is the stiffness introduced by the diaphragm. A formula for the stiffness is derived based on the mathematical model of the diaphragm as an elastic membrane. Comparison to experimental data shows that adequate representation of these two factors results in accurate predictions of the isolator performance as a function of the supported load.