FREE VIBRATION ANALYSIS OF COMPLETELY FREE RECTANGULAR PLATES BY THE SUPERPOSITION–GALERKIN METHOD

The superposition-Galerkin method for analyzing the free vibration of thin isotropic and orthotropic plates as well as transverse-shear deformable plates was introduced in recent years. It has an advantage over the traditional superposition method in that it gives equally accurate results but requires much less work on the part of the analyst. Unfortunately, it has not been possible up to this time to apply it to plates with free edge conditions. This was due to mixed derivatives appearing in the formulation of free edge boundary conditions. In this paper it is shown how, with the superposition of specially selected sets of forced vibration solutions (building blocks), the above limitations are avoided. While the technique is applied here to the analysis of fully symmetric modes, only, it is demonstrated how the superposition-Galerkin method can be applied to any of the above plate problems regardless of the combination of free edge boundary conditions to be imposed.