Thermoelastic non-linear flutter oscillations of rectangular plate

In this paper the stability of a rectangular plate in a supersonic flow in the presence of a temperature field, inhomogeneous across the thickness, is investigated. The temperature field inhomogeneity across the thickness leads to the buckling of the plate, and this buckled state is considered as the initial unperturbed state. Governing equations and boundary conditions are obtained for the unperturbed and perturbed states. The corresponding linear analysis leads to the stability conditions of unperturbed state of the thermal-fluid-elastic structure system. The stability boundary is determined as function of the flow speed, the middle surface temperature, and the temperature gradient normal to the plane. It is shown that the temperature field and the flow speed have interdependencies and regulate the stability process. It is also shown that the temperature field significantly affects the critical flutter speed. The nonlinear stability is also investigated, both cubic geometrical non-linearity and aerodynamic non-linearity of both quadratic and cubic types are considered. Compared with the case without thermal field, this study shows for the first time the existence of new types of “amplitude-frequency” limit cycles.