Analytical solutions for supersonic flutter in a rectangular thin plate were developed to examine the vibration behavior and stability of rectangular plates subjected to supersonic airflow on one side. A comprehensive analysis of fluid-structure interaction (FSI) was conducted using the extended Hamilton principle and the extended Galerkin method. The aerodynamic pressure exerted by the supersonic airflow on the plate was calculated using first-order piston theory. The validity of the systematic analysis of the FSI problem was confirmed by comparing numerical results for plates with simply supported boundary conditions on all four edges (SSSS plate) with those in the published paper and obtained from the finite element method. To solve the supersonic flutter of a rectangular thin plate with arbitrary boundary conditions, the solutions for free vibration of rectangular plates based on Kirchhoff plate theory using superposition plate method were used as basis functions in the extended Galerkin method. The Superposition-Galerkin method was validated by comparing the numerical results for plates with clamped-free-clamped-free boundary conditions (CFCF plate) with those obtained using beam method, which uses beam functions as basis functions in the extended Galerkin method, and COMSOL finite element simulations, respectively. The analytical results match better with those obtained from finite element method than those determined using beam method, in terms of critical velocity, eigenfrequency, displacement, aerodynamic pressure, strain, and stress. Thus, the solutions can be used as benchmarks in future studies. The non-dimensional dynamic pressure and frequency were discussed in terms of different plate thickness. It was found that the two parameters are almost constant under critical flow velocity, and the plate thickness does not change the flutter behavior of the system.
Ji et al. (Fri,) studied this question.