Vibrational investigation of the spinning bi-dimensional functionally graded (2-FGM) micro plate subjected to thermal load in thermal environment

This article presented a numerical method for discovering the free vibration of a spinning bi-dimensional functionally graded materials (FGM) micro circular plate exposed to thermal load based on Winkler–Pasternak foundation for the first time. Thermomechanical properties of bi-dimensional FGM micro plate are supposed to change during the thickness and radius directions of the plate. The small effect is taken into consideration the modified couple stress theory. Linear temperature rise during thickness and radius direction is investigated. First-order shear deformation theory is employed to derive the governing equations and boundary conditions of the bi-dimensional FGM circular plate in the thermal environment via Hamilton’s principle. The differential quadrature method is used to achieve the frequency of bi-dimensional FGM micro circular plate exposed to the thermal environment. A parametric analysis is led to assess the efficacy of Winkler and Pasternak parameters, FG power index, coefficients of bi-dimensional FGM, size dependency, non-dimensional angular velocity, temperature changes and thermal loading on the natural frequencies of bi-dimensional FGM micro plate.