Free vibraton analysis of functionally graded plates resting on elastic foundation

In this study, free vibration analysis of plates made of functionally graded material on elastic foundation has been conducted. In this analysis, the first-order shear deformation theory has been used for the determination of displacement fields. The mechanical properties of the plate are assumed to vary continuously along the thickness of the plate, following a power-law distribution of volume fractions for the constituents, while the Poisson ratio is considered constant. The equations of motion for functionally graded plates on elastic foundation have been derived using the Hamiltonian principle. The obtained equations of motion have been solved using the Navier method, and the fundamental frequencies have been determined. An algorithm has been developed in the Mathematica programming language for this solution. To demonstrate the accuracy of the developed algorithm, free vibration analyses have been performed and compared with examples found in the literature. Subsequently, in parametric studies, free vibration analysis has been conducted to investigate the effects of various elastic foundation parameters, material change parameters, aspect ratios, modes, and material properties on the analyses.