Free vibration and aeroelastic analyses of rectangular cantilever plates including correlation with experiment

In the present study, the free vibration and aeroelastic problems of rectangular cantilever plates with varying aspect ratio have been investigated. The classical plate theories based on the Kirchhoff hypothesis have been adopted to simulate the structural response of the plate. The Peter’s theory is selected to model the aerodynamic pressure on the plate due to the incompressible air flow. To discretize the partial deferential equations of the system, the ayleigh-Ritz method has been applied and by using Lagrange equations, the mass, damping, and stiffness matrices have been derived. Various numbers of mode shapes are used to show the convergence of the response of the system . The theoretical results including the natural frequencies and flutter speed have been evaluated by using the experimental data obtained from the ground vibration experiment carried out at Duke University. It has been shown that fora relatively low aspect ratio rectangular cantilever plate, using some techniques in Rayleigh–Ritz method leads to an improvement of the results for both the natural frequencies and flutter speed. This technique ends up having two sets of decoupled equations and consequently, the number of equations that have to be solved simultaneously is divided by two. This could lead to a reduction of computational time significantly.

Keywords:

Rayleigh-Ritz method , Rectangular cantilever plates , Classical plate theory , Aeroelasticity , Flutter