Finite element model to investigate the dynamic instability of rectangular plates subjected to supersonic airflow

Abstract

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.