3D Free Vibration Analysis of Functionally Graded Plates with Arbitrary Boundary Conditions in Thermal Environment. Issue 5 (7th August 2021) - Kang, Rui; Xin, Fengxian; Shen, Cheng; Lu, Tian Jian
Abstract : An analytical method for free vibration of functionally graded (FG) plates with arbitrary boundary conditions in thermal environments is developed based on 3D elasticity theory. Material properties of the FG plate are assumed to be temperature dependent but graded along with its thickness. At the edges of the plate, three different sets of linear springs are introduced, so that its boundary condition can be altered by changing the spring stiffness. Each displacement component of the plate is expanded as a standard Fourier cosine series, supplemented with closed‐form auxiliary functions. With thermal environment effects duly accounted for, the energy method is used to derive eigenvalue equations, whereas the Rayleigh−Ritz procedure is utilized to calculate the natural frequencies of the FG plate. Numerical examples show that the present method converges quickly and gives satisfactory results. The method is then utilized to calculate the natural frequencies of FG plates having different aspect ratios, volume fractions, and elastic boundaries. Abstract : Based on 3D elasticity theory, an analytical method is developed to predict the free vibration performance of a functionally graded plate with arbitrary boundary conditions in thermal environments. The natural frequency drops to zero at a critical temperature for weak boundary constraints. The sensitivity of plate natural frequency to spring stiffness increases with the number of elastic edges.