The Reddy plate theory is widely used in the vibration analysis of thick plates, but there are few closed-form analytical solutions for free vibration of rectangular Reddy plates with arbitrary homogenous boundary conditions. This work is to develop the extended separation-of-variable (SOV) method for the free vibration analysis of rectangular Reddy plates. In the present method, the mode functions are in an explicit and closed form, and the natural frequencies corresponding to two-direction eigenfunctions are mathematically assumed to be independent of each other. According to two pairs of boundary conditions, the closed-form mode functions and frequency equations are achieved. The present method is numerically compared with other approximate and analytical methods, and some valuable observations are presented. The present solutions are exact for the plates with at least two opposite sides simply supported, and agree well with the results in literatures for other boundary conditions.
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