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Finite element modeling was applied for the first time in this work to analyze the free vibration responses of functionally graded plates porous with varying thickness resting on two-parameter elastic foundations in temperature conditions. The mechanical qualities of materials are supposed to alter along the thickness direction of plates using the Voigt model, temperature conditions fluctuate according to a nonlinear law, and porosity is suggested according to even and un-even distributed principles. The thickness of the plate is a function of the two directions,  x  and  y , and it is supported by an elastic foundation Pasternak’s with two stiffness factors. A quadrilateral element model was created and employed to handle the difficulties of FG plates with diverse boundary conditions based on the revised higher-order shear deformation theory. The correctness of the current theory and mechanical model is validated by comparing the numerical data of this study with those of trustworthy sources. A great variety of factors have been examined to capture the influence of the vibration response of the plate on geometric and material features. The article's results are scientifically noteworthy, contributing to computational mechanics' understanding of the mechanical behavior of this intricate structure.

Thermal vibration analysis of functionally graded porous plates with variable thickness resting on elastic foundations using finite element method