Free vibration studies of shear deformable plates by the traditional superposition and Superposition-Galerkin method.

Abstract

In the first part of the present study, it is demonstrated that the traditional superposition method lends itself successfully to obtaining of eigenvalues and mode shapes for completely free shear deformable plates, namely, the thick isotropic plates and symmetric cross-ply laminated plates. The effect of transverse shear deformation is taken into account by means of the first order shear deformation relationship as developed by Mindlin. The governing differential equations are satisfied exactly throughout the plate domain and free edge boundary conditions are satisfied to any desired degree of accuracy. These appear to be the first accurate solutions to these important completely free plate vibration problems. Subsequently, a new modified Superposition-Galerkin method is developed for analyzing the free vibration problem of symmetric cross-ply plates with any combination of clamped and simply supported boundary conditions. It is shown that this new approach leads to vast simplification of computational procedures in comparison to the traditional superposition method. Nevertheless it is seen that excellent agreement is achieved when results obtained by the Galerkin-Superposition method are compared with those generated by previous researchers. It is expected that this new modified method will have application to various families of laminated plate vibration problems.