Nonlinear vibration analysis of a membrane based on large deflection theory

Abstract

This paper investigates nonlinear vibration of a simply supported rectangular membrane based on large deflection theory. Dynamic stress caused by transverse displacement of the membrane is considered in modeling the membrane. The assumed mode method and the nonlinear finite element method (FEM) are both used as discretization methods for the membrane. In the assumed mode method, an approximate analytical formula of the natural frequency is derived. In the nonlinear FEM, a three-node triangular membrane element is proposed. The difference between the membrane’s dynamical characteristics obtained by these two discretization methods is revealed. Simulation results indicate that natural frequency of the membrane will rise along with the increasing of the vibration amplitude of the membrane, and the natural frequency obtained by the nonlinear FEM is larger than that obtained by the assumed mode method. When the membrane vibration is small, the assumed mode method may achieve a reasonable result, but it may lead to a big error when the membrane vibration is large.