Solutions of the Lévy type for the free vibration analysis of diagonally supported rectangular plates

A Lévy type solution is developed for the vibratory response of a simply supported rectangular plate subjected to a harmonic force distributed along the diagonal. The solution is then extended to determine the free vibration response of the same rectangular plate with inelastic lateral support on the diagonal. It is found that there is an excellent agreement between computed eigenvalues obtained here and those obtained by the author in an earlier paper in which a Navier type solution was utilized. The significant advantages inherent in the present Lévy type solution are discussed.