In this study, an aeroelastic model that accounts for the fluid–structure interaction is developed to investigate vibration and stability of rectangular plates in contact with sloshing fluid on one side and under supersonic aeroelastic load on the other side. The fifth-order shear deformation theory, which is capable of considering rotary inertia and transverse shear stress, is employed to model the structure. Bulging and sloshing modes of the incompressible, inviscid and irrotational fluid are obtained with satisfying Laplace’s equation and fluid boundary conditions. The first-order piston theory is applied to consider the supersonic aeroelastic load. On the basis of Hamilton’s principle, the governing equations of the coupled fluid–structure system are derived and discretized using the Galerkin method. Numerical results for specific cases are compared with available results in the literature and an excellent agreement is observed. In the discussion section, influences of various parameters such as the dimensions of the fluid domain, plate dimensions and aerodynamic parameters on the natural frequencies and flutter behavior are studied.

中文翻译：

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与晃荡流体耦合的矩形板的气动弹性分析

在这项研究中，开发了一种考虑流固耦合的气动弹性模型，以研究矩形板在一侧与晃动流体接触和在另一侧在超音速气动弹性载荷下的振动和稳定性。采用能够考虑转动惯量和横向剪应力的五阶剪切变形理论对结构进行建模。满足拉普拉斯方程和流体边界条件，得到不可压缩、无粘性和无旋流体的鼓胀和晃荡模态。应用一阶活塞理论来考虑超音速气动弹性载荷。根据哈密顿原理，利用伽辽金方法推导出流固耦合系统的控制方程并离散化。将特定案例的数值结果与文献中的可用结果进行比较，观察到极好的一致性。在讨论部分，研究了流体域尺寸、板尺寸和空气动力学参数等各种参数对固有频率和颤振行为的影响。