Bifurcation behavior of steady vibrations of cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow

Abstract

Cantilever plates with geometrical nonlinearities interacting with three-dimensional inviscid potential flow are considered. The new method for analysis of stability and bifurcations of the plate self-sustained vibrations is suggested. The basis of this method is the solution of the singular integral equations with respect to aerodynamic derivatives of the plate pressure drop. The Von Karman equations with respect to transversal displacements and a stress function are used to describe the plate vibrations with geometrical nonlinearity. The combination of the shooting technique and the continuation algorithm are used to analyze bifurcations and stability of the plate self-sustained vibrations. The plate aeroelastic self-sustained vibrations lose stability due to the Naimark-Sacker bifurcation. As a result of this bifurcation, almost periodic and chaotic vibrations are observed. It is shown, when it is acceptable to use one-dimensional models of plate self-sustained vibrations and when the plate model must be two-dimensional.