A finite element study on the large amplitude flexural vibration characteristics of FGM plates under aerodynamic load

The large amplitude flexural vibration characteristics of functionally graded material (FGM) plates are investigated here using a shear flexible finite element approach. Material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of the constituents. The effective material properties are then evaluated based on the rule of mixture. The FGM plate is modeled using the first-order shear deformation theory based on exact neutral surface position and von Kármán’s assumptions for large displacement. The third-order piston theory is employed to evaluate the aerodynamic pressure. The governing equations of motion are solved by harmonic balance method to study the vibration amplitude of FGM plates under supersonic air flow. Thereafter, the non-linear equations of motion are solved using Newmark’s time integration technique to understand the flexural vibration behavior of FGM plates in time domain (simple harmonic or periodic or quasi-periodic). This work is new in the sense that it deals with the non-linear flutter characteristics of FGM plates under high supersonic airflow accounting for both the geometric and aerodynamic non-linearities. Some parametric study is conducted to understand the influence of these non-linearities on the flutter characteristics of FGM plates.