| In the recent years, the plate structures have been widely used in civil engineering industries. Many linear bending and vibration studies have been made for moderately thick plates resting on homogenous elastic foundations. However, relatively few have been made on the bending and vibration analyses for the plates with free edges resting on non-homogenous elastic foundations, in particular involving initial stresses due to in-plane mechanical loads and temperature fields. In practice, the plate-foundation interactions need to be put into consideration and the elastic foundation may be non-homogenous. In the present study we focus on the bending and vibration analyses of moderately thick plates with four free edges resting on a non-homogenous elastic foundation of Pasternak-type. The effects of initial stresses are also included.The plate system is modeled as a moderately thick plate resting on a non-homogenous elastic foundation of Pasternak-type. Based on Reissner-Mindlin plate theory, total energy function of the plate system is formulated. A set of mathematically complete two-dimensional polynomials is used as admissible displacement functions and the pb-2 Ritz method is employed to determine the deflections and bending moments of the plate in the case of the bending analysis, the natural frequencies in the case of the linear eigenvalue problem of vibration, and the dynamic response of the plate under impulsive loads. Extensive parametric studies are undertaken to show the effects of the non-homogenous region of the foundation, the plate side-to-thickness ratio, the plate aspect ratio, and initial membrane stresses and thermal stresses on the bending and vibration characteristics.The present method is easy to extend to the cases of the plate with various boundary conditions resting on non-homogenous elastic foundations. It is hoped that the present results will give better understanding for engineering design.
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