Free vibration of functionally graded quadrilateral microplates in thermal environment

Abstract

As a first attempt, the influences of thermal environment together with the geometrical parameters and material properties on the free vibration characteristics of the functionally graded (FG) quadrilateral microplates are investigated. The governing equations are based on the modified strain gradient theory (MSGT) together with the first-order shear deformation theory (FSDT) of plates. Both the temperature dependence of the material properties and the initial thermal stresses are included in the mathematical modeling of the problem. The Chebyshev–Ritz method is employed to extract the free vibration eigenvalue equations from the higher-order governing equations. Chebyshev polynomials in conjunction with suitable boundary functions are used as the admissible functions of the Ritz method to handle the microplates with different set of boundary conditions. After demonstrating the fast rate of convergence and the accuracy of the method, the effects of the temperature rise, length scale parameters, material gradient index, and the length-to-thickness ratio, on the free vibration behaviors of skew and symmetric trapezoidal microplates subjected to different boundary conditions are studied.