Nonlinear Oscillation of FGM plates under Aerodynamic Load

Large amplitude flexural vibration characteristics of functionally graded material plates under aerodynamic load are investigated here using the finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution and the effective material properties are evaluated based on the rule of mixture. The formulation is developed based on the first-order shear deformation theory considering the physical / exact neutral surface position. The shear correction factors are evaluated from the energy equivalence principle. The geometric nonlinearity, based on von Kármán’s assumptions is introduced and the first-order high Mach number approximation to linear potential flow theory is employed for evaluating the aerodynamic pressure. The harmonic balance method is applied to study the nonlinear free flexural vibration frequencies of FGM plates and flexural vibration amplitude of FGM plates under supersonic air speeds. Further, the nonlinear equation of motion is solved using Newmark’s time integration technique to understand the flexural vibration behavior (limit cycle oscillations or chaotic) of FGM plates under aerodynamic load.