Transverse vibrations of elliptical plate of linearly varying thickness with half of the boundary clamped and the rest simply supported

The Rayleigh–Ritz method has been applied to study the problem of transverse vibrations of elliptical plate with half of the boundary clamped and the rest simply supported. The thickness of the plate is varying linearly in the space coordinates. For the same thickness variation, the tabulated results in case of mixed boundary conditions lies between those reported for the two extreme cases when the entire boundary is either clamped or simply supported. Convergence of the results is indicated by increasing the order of approximation. Some results for a circular plate of linearly varying thickness with half of the boundary clamped and the rest simply supported have been obtained as special case. Comparisons have been made with the known results. Three-dimensional mode shapes have been drawn for some selected cases.