Aerothermoelastic Post-Critical and Vibration Analysis of Temperature-Dependent Functionally Graded Panels

This paper deals with the aerothermoelastic post-critical and vibration characteristics of temperature-dependent functionally graded panels in a supersonic airflow. The structural formulation is based on the von Karman plate theory and material properties are assumed to be temperature-dependent and graded in the thickness direction according to power law distribution in terms of the volume fractions of the constituents. The two-dimensional panel under study is simply supported, for which the first order piston theory is used to account for the supersonic aerodynamic loading. The Galerkin method is applied to convert the partial differential governing equation into a set of ordinary differential equations. Panel vibration responses are investigated through time history responses, state-space trajectories, frequency spectra and the bifurcation diagrams of Poincare maps. Moreover, post-critical behaviors are detected using numerical and analytical methodologies such as bifurcation diagrams of Poincare maps, Lyapunov exponents and Lyapunov dimension. Finally, it is shown that the Lyapunov dimensions for stable and divergence conditions are zero value, while these values for limit-cycle and chaos vibration conditions are integer and non-integer quantity, respectively.