Analysis of partly corrugated rectangular diaphragms using the Rayleigh-Ritz method

In this paper, the Rayleigh Ritz method is applied to static analyses of partly corrugated four-edges-clamped rectangular diaphragms. We use coupled variational equations (derived from the principle of virtual displacement), and describe some practical considerations needed to analyze multiregional diaphragms by the method. We approximate a sinusoidal corrugation by an equivalent flat single layer, and derive equivalent in-plane and bending stiffnesses using the theory of engineering mechanics. We demonstrate the effectiveness and usefulness of the present method through examples (in one example, we compare the calculated deflection with that obtained by a finite-element program). We examine a partly corrugated rectangular plate with residual stress, and investigate the effects of corrugation parameter variations. The analysis technique presented in this paper is very convenient, efficient, and reliable for analyzing seemingly difficult microelectromechanical system devices built on partly corrugated thin diaphragms with various residual stresses.