In this paper, a numerical method is presented to study the dynamic behaviour of an isotropic rectangular plate subjected to aerodynamic loads induced by parallel supersonic airflow. A finite element model, based on bi-dimensional polynomial displacement functions and linear Piston theory, is used to study the dynamic behaviour of the solid plate coupled with aerodynamic loads. The developed approach is able to model flat plates and shallow shells in which the fluid–structure coupling at the interface is applied synchronously using a monolithic method. The solid model is based on Sanders’ shell theory. The stiffness and damping matrices that result from application of the aerodynamic load are coupled with those obtained from a structural model and are calculated using analytical integration. By assembling the matrices, the global mass, damping and stiffness matrices for the plate are obtained and then dynamic equations of the governing problem are derived. The eigenvalues of the system are calculated using the equation reduction technique. The critical non-dimensional aerodynamic pressure of the airflow that induces flutter of the structure is determined for various boundary conditions and geometries. The obtained results are compared with other published research works and very good agreement is observed.

本文提出了一种数值方法来研究各向同性矩形板在平行超声速气流引起的气动载荷作用下的动力学行为。基于二维多项式位移函数和线性活塞理论的有限元模型被用来研究固体板的气动特性和气动载荷。所开发的方法能够对平板和浅壳进行建模，其中使用整体方法同步应用界面处的流固耦合。实体模型基于Sanders的壳理论。由施加空气动力载荷产生的刚度和阻尼矩阵与从结构模型获得的刚度和阻尼矩阵相结合，并使用解析积分进行计算。通过组装矩阵，整体质量，得到了板的阻尼和刚度矩阵，然后导出了控制问题的动力学方程。使用方程约简技术计算系统的特征值。对于各种边界条件和几何形状，确定了导致结构颤动的气流的临界无量纲空气动力学压力。将获得的结果与其他已发表的研究成果进行比较，并观察到很好的一致性。