Free vibration of bi-directional functionally graded plates subject to different thermal environment

In this study, a comprehensive three-dimensional analysis of the free vibration behavior of functionally graded plates is carried out in a thermal environment. The plates are examined under two types of boundary conditions: simply supported and clamped. The material properties of the considered plates are assumed to be temperature-dependent, meaning that as the temperature changes, the mechanical properties – such as stiffness, density, and thermal expansion coefficients of the material – also change. The material composition of the plates is graded in two directions. One direction is along the thickness (z-direction) of the plate and the other is along an in-plane direction (x-direction). This bi-directional material grading is modeled by means of a power-law distribution. To solve this problem, the Ritz method is used. This method is a well-known mathematical approach considered for approximating the solutions of boundary value problems in structural mechanics. In this study, the Ritz method is combined with Chebyshev polynomials, which are used as the basis functions to represent the displacement field. The present study investigates the effects of the temperature, material composition and plate geometry on the free vibration frequencies of functionally graded plates. Both linear and nonlinear temperature distributions across the plate are considered in the analysis. The results of this analysis can inform the design of more efficient, durable, and thermally stable components in engineering applications which would require high resistance to both mechanical and thermal stresses.