Geometric considerations for the prevention of chaos in heated plate vibrations

In this paper, Lyapunov exponents are successfully calculated and employed to design a sinusoidally excited heated plate system representing hypersoni c skin panels on transatmospheric vehicles, for the prevention of chaotic o scillations. The single mode equation of motion governing the vibrations of the heated plate system is of Duffing form. The coefficients of the equati on are obtained as functions of the design variables. The boundaries of reg ular and chaotic regions of motion are defined in various two-dimensional p arametric spaces defined by the values of the largest Lyapunov exponent at each point. The critical buckling temperatures that transform the potential form from single-well to double-well are discussed for various plate aspec t ratios. It is shown that finding chaos-free aspect ratios is possible, an d chaos can be eliminated or delayed at the design stage simply by choosing the appropriate size and aspect ratio for the panel. The influence of the thickness of panels on the chaotic response of the system is investigated. The results of this research have direct impact on shape optimization consi derations for skin panels subject to high temperatures, and on the design o f various other dynamical systems that are influenced by a combination of t hermal loads and external excitation.