All possible exact solutions are successfully obtained in terms of 10 sets of distinct eigensolutions for the free in-plane vibration of isotropic rectangular plates. The plates have simply supported condition at two opposite edges and any combination of classical boundary conditions at the other two edges. The exact solutions are validated through both mathematical proof and comparisons with the solutions of differential quadrature method. Some unusual phenomena are revealed in free in-plane vibrations of rectangular plates due to one of the eigenvalues being zero. This work constitutes an improved version of very recent corresponding work by the same authors [Int. J. Mech. Sci., 2009, 51: 246-255]. Both the solution forms and solving procedures in the previous work are substantially simplified. Some new results are also given, which are useful for validation purpose in future. © 2011 The Chinese Society of Theoretical and Applied Mechanics.
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