Finite Element Modal Formulation for Hypersonic Panel Flutter Analysis with Thermal Effects

Abstract

A finite element time-domain modal formulation for analyzing nonlinear flutter of panels subjected to hypersonic airflow has been developed. Von Karman large deflection plate theory is used for description of the structural nonlinearity, and third-order piston theory is employed to consider the aerodynamic nonlinearity. The thermal loadings of uniformly distributed surface temperatures and temperature gradients through the panel thickness are considered. By the application of the modal truncation technique, the number of governing equations of motion is reduced dramatically so that the computational costs are reduced significantly. All possible types of panel behavior, including flat and stable, buckled but dynamically stable, limit cycle oscillation (LCO), periodic motion, and chaotic motion were observed. Examples of the applications of the proposed methodology were flutter responses of isotropic and composite panels. Special emphasis was placed on the boundary between LCO and chaos and on the route to chaos. Time history, phase plane plot, Poincare map, bifurcation diagram, and Lyapunov exponent are employed in the chaos study. It is found that at low or moderately high dynamic pressures, the fluttering panel typically takes a period-doubling route to evolve into chaos, whereas, at high dynamic pressures, the route generally involves bursts of chaos and rejuvenations of periodic motions.