Stability of Rectangular Plates With Free Side-Edges in Two-Dimensional Inviscid Channel Flow

Abstract

The linear stability of rectangular plates with free side-edges in inviscid channel flow is studied theoretically. The Galerkin method and Fourier transform technique are employed to solve the plate and potential flow equations. A new approach is introduced to treat the mixed fluid-plate interaction boundary condition, which leads to a singular integral equation. Divergence, single-mode flutter, and coupled-mode flutter are found for plates supported differently at the leading and trailing edges. In some cases, single-mode flutter at vanishingly small flow velocity is predicted. The effects of mass ratio and channel-height-to-plate-length ratio on critical velocity are studied. An energy balance analysis shows how different types of instability arise for plates with different supports. [S0021-8936(00)01801-8]