Composite Circular Plates With Residual Tensile Stress Undergoing Large Deflections

Abstract

Many micromachined electroacoustic devices use thin plates in conjunction with electrical components to measure acoustic signals. Composite layers are needed for electrical passivation, moisture barriers, etc. The layers often contain residual stresses introduced during the fabrication process. Accurate models of the composite plate mechanics are crucial for predicting and optimizing device performance. In this paper, the von Kármán plate theory is implemented for a transversely isotropic, axisymmetric plate with in-plane tensile stress and uniform transverse pressure loading. A numerical solution of the coupled force-displacement nonlinear differential equations is found using an iterative technique. The results are verified using finite element analysis. This paper contains a study of the effects of tensile residual stresses on the displacement field and examines the transition between linear and nonlinear behavior. The results demonstrate that stress stiffening in the composite plate delays the onset of nonlinear deflections and decreases the mechanical sensitivity. In addition, under high stress the plate behavior transitions to that of a membrane and becomes insensitive to the composite nature of the plate. The results suggest a tradeoff between mechanical sensitivity and linearity.