A semi-analytical solution for free vibration of variable thickness two-directional-functionally graded plates on elastic foundations

The present paper investigates free vibration of variable thickness two-directional-functionally graded circular plates, resting on elastic foundations. The results are obtained for clamped, free, and simply supported edge conditions. Variations of the material and geometrical parameters are monitored by five distinct exponential functions. Therefore, the resulted non-dimensional solution may be used for a wide range of the practical problems. Mindlin’s plate theory and the differential transformation technique are used to obtain the governing equations of the natural frequencies of the circular plates. Effects of variations of the material properties in the radial and thickness directions, geometric parameters (e.g., the thickness-to-radius ratio in the center of the plate), stiffness parameters of the foundation, and various boundary conditions on the natural frequencies are investigated. Results reveal that by choosing a suitable combination of the material properties, the free vibration behavior of the thick plates may be enhanced without the need to change the geometric parameters.