The Influence of Supersonic Stream on the Dependence “Amplitude-Frequency” of Nonlinear Vibrations of Flexible Plate

The stability analysis of plates and shells in high speed flow deals with the determination of the flutter instability boundary. A linear analysis is made using the basic principles of the theory of aero-elasticity of isotropic bodies, the theories of flexible plates, the stability equations and associated boundary conditions obtained through a linear formulation. Herein, the nonlinear stability of flexible plate immersed in a high speed gas flow is considered. The model takes into account quadratic and cubic aerodynamic nonlinearities as well as cubic geometric nonlinearities. It is shown that the inclusion of quadratic aerodynamic nonlinear components can lead to the appearance of “amplitudefrequency” phenomena in both the pre-critical as well as in the post-critical flow speed regimes. The influence of the free stream flow speed on the “amplitude-frequency” dependence phenomena is also presented.