Free transverse vibrations of orthotropic thin rectangular plates with arbitrary elastic edge supports

A so-called Spectro-Geometric Method (SGM) is presented for the free transverse vibration analysis of orthotropic thin rectangular plates with arbitrary elastic supports along each of its edges, a class of problems which are rarely attempted in the literature. Regardless of boundary conditions, the displacement function is invariably and simply expressed, in spectral form, as a trigonometric series expansion with an accelerated polynomial rate of convergence as compared with the conventional Fourier series. All the unknown expansion coefficients are treated as the generalized coordinates, and determined using the Rayleigh-Ritz technique. This work allows a capability of modeling a wide spectrum of orthotropic thin rectangular plate under a variety of boundary conditions, and changing the boundary conditions as easily as modifying the material properties or dimensions of the plates. The accuracy and reliability of the SGM prediction are demonstrated though numerical examples. The SGM prediction can be readily and directly extended to other more complicated boundary conditions involving non-uniform restraints, point supports, partial supports and their combinations.