Analytical modeling contribution of the vibration dynamics of FGM plates placed on elastic foundations

The present article uses the non-polynomial refined shear deformation theory (NP-RSDT) with four unknowns in order to determine the natural frequencies of functionally graded material (FGM) plates that are made with advanced materials without integrating a shear correction factor. These plates rest on elastic foundations. This study aims to analyze the effects of an elastic system, which is supposed to be represented by the two Pasternak and Winkler parameters on the dynamics of free vibrations of the FGM plates, while taking into account the fact that the Winkler springs have a variable modulus while the Pasternak layer is considered as a shear layer with a constant modulus. For the purpose of demonstrating the accuracy of the current theory used in this work, various numerical investigations which were conducted on the free vibrations of FGM plates resting on elastic foundations are presented. Additionally, the effects of varying various parameters, such as the elastic foundation parameters, power law index, aspect ratio, and plate geometry are also investigated. The results obtained with this method are then compared with those obtained with other methods reported in the literature. Once the current method was validated, we proceeded in the same field by carrying out a study on the free vibrations of FGM plates simply supported and resting on an elastic system, while considering that the Winkler parameters are variable. The results obtained are displayed through tables and graphs. They are then discussed.