Eigen-analysis of an inviscid channel flow with a finite flexible plate in one wall

Abstract

A state-space method is used to investigate the surface instabilities of a flexible plate comprising one wall of an inviscid channel flow computationally modelled with a finite-difference method coupled with a boundary-element method. Simple elastic and spring-backed plates are considered and in both cases it is found that reducing the height of the channel causes divergence and modal-coalescence to occur at lower flow velocities. An analytical prediction for an infinitely long plate is also developed and the divergence-onset predictions are compared with those obtained by the state-space method for a spring-backed plate.