Vibration Characteristics of Functionally Graded Plates with Non-Ideal Boundary Conditions

An analytical investigation is carried out to determine the vibration behavior of functionally graded plates with non-ideal boundary conditions. The plate has three edges simply supported while the other edge has a small non-zero deflection and moment. The effective material properties are estimated by the Mori-Tanaka scheme. The classical plate theory is employed to obtain the frequency equation. The proposed analytical solution involves the Levy method and Lindstedt-Poincare perturbation technique. Results are presented for various functionally graded beams, showing the vibration frequencies, and mode shapes are influenced by the aspect ratio, volume fraction index, and edge support conditions.