Lumped Parameter Analysis of an Enclosed Incompressible Squeeze Film and a Central Gas Bubble

Abstract

A lumped-parameter dynamic model for an enclosed incompressible squeeze film with a central gas bubble has been derived. A new approach was applied to derive closed-form expressions for the lumped-parameter mass and damping coefficients caused by liquid motion. It was assumed that plate motions were small and the fluid behaved as a continuum. The values of the lumped-parameter mass and damping were found to depend on the aspect ratio and nondimensional squeeze-film thickness. The nondimensional thickness was given by the ratio of the actual squeeze-film thickness to the viscous penetration depth of the liquid. A nondimensional squeeze-film thickness of a value of 5 was found to divide between categories of thick and thin incompressible squeeze films. Amplification of the liquid mass and damping over and above squeeze films open to the atmosphere at the edges was found. The amplification was attributed to converging flow caused by enclosed boundaries. Comparisons between the lumped-parameter model predictions and finite-element computations showed a surprising degree of accuracy for the lumped-parameter model despite large liquid velocities in the squeeze film.