Abstract

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.

摘要

在本文中，研究了矩形板在超音速流中在温度场存在的情况下的稳定性，该温度场在整个厚度上是不均匀的。厚度方向上的温度场不均匀会导致板屈曲，这种弯曲状态被认为是初始的不受干扰状态。获得了不受干扰和受干扰状态的控制方程和边界条件。相应的线性分析得出了热流弹结构系统无扰动状态的稳定性条件。确定稳定性边界是流速，中间表面温度和垂直于平面的温度梯度的函数。结果表明，温度场和流速具有相互依存关系，并调节稳定过程。还显示出温度场显着影响临界颤振速度。还研究了非线性稳定性，同时考虑了二次方和三次方的立方几何非线性和空气动力学非线性。与没有热场的情况相比，这项研究首次显示了新型的“幅频”极限环的存在。