Stability Analysis of a Nonlinear Plate in Mean Flow

Abstract

A stability analysis of a nonlinear plate clamped to an infinite baffle in mean flow is given. The effect of structural nonlinearities induced by in-plane forces and shearing forces due to stretching of plate bending motion, and that of viscous damping are taken into account in the derivation of the plate equation. The plate flexural displacement is obtained by modal expansion based on Galerkin's method. The critical mean flow speeds at which local instabilities may occur are determined by Routh algorithm. The mechanisms that trigger the local instabilities are uncovered. The effect of structural nonlinearities, and that of plate aspect and plate length/thickness ratios on local instabilities are examined. Numerical examples of the transition from stable to locally unstable vibration, as the mean flow speed exceeds the critical values, are demonstrated. The results show that while the overall amplitude of the plate flexural displacement may be bounded when the mean flow speed exceeds the critical values, plate vibration may be locally unstable, jumping from one equilibrium position to another. Furthermore, the jumping may be random, and the plate vibration may seem chaotic. The results also show that viscous damping may stabilize plate flexural vibration and settle the plate in one of its equilibria.