effect of temperature on the natural frequency of multi-directional functionally graded rectangular plates on an elastic foundation using three-dimensional elasticity theory

This research focuses on the analysis of free vibration of a rectangular plate made of multi-directional functionally graded materials on an elastic foundation, taking into account the effect of temperature. the temperature at different points of the plate may differ from its initial temperature, leading to the development of initial stresses within the plate. in this research, gradual variations in the mechanical properties of the material are possible in all three coordinate directions. additionally, the mechanical properties of the material, except for the thermal conductivity coefficient, can be temperature-dependent. the governing equations are derived based on three-dimensional elasticity theory and discretized using the generalized differential quadrature method (gdqm). the validation of the proposed method demonstrates the high accuracy of the employed approach. subsequently, several cases are solved, considering the effects of variations in the mechanical properties of the material in each coordinate direction or a combination of different directions, and the results are compared. the effects of temperature, elastic foundation stiffness, aspect ratio, thickness, power-law indices, and boundary conditions are investigated. the results indicate that an increase in temperature leads to a reduction in the vibrational frequency. furthermore, the effect of temperature on frequency reduction is less pronounced for softer plates. in the case of one-directional property distribution, the frequency decreases with an increase in the power-law index. for multi-directional property distribution, the frequency initially decreases with an increase in the power-law index and then remains relatively unchanged.