Coupled squeeze film analysis by Reissner–Mindlin plate elements

Abstract

Squeeze film damping effects naturally occur if structures are subjected to loading situations such that a very thin film of fluid is trapped within structural joints, interfaces, etc. An accurate estimate of squeeze film effects is important to predict the performance of dynamic structures. This paper presents a finite element solution to the coupled fluid–structure problem of squeeze film dampers. The squeeze film is governed by the linearized isothermal Reynolds equation, which is known from lubrication theory. The structure which is modeled using Reissner–Mindlin plate theory is discretized by four-noded two-dimensional shear deformable isoparametric plate elements. The coupled finite element formulation is derived and an alternative solution to obtain damped eigenvalues and eigenvectors is presented. The coupling between fluid and structure is handled by considering the pressure forces and structural surface velocities on the boundaries. The effects of the driving parameters on the frequency response functions are investigated. It was found that the ambient pressure has no significant effect on the frequency responses, unlike on the damping force of dynamical MEMS systems. The results obtained from the presented model are compared with the experimental and analytical results available in the literature and a very good agreement is found.