THE RESPONSE OF A NONLINEAR SYSTEM WITH A NONSEMISIMPLE ONE-TO-ONE RESONANCE TO A COMBINATION PARAMETRIC RESONANCE

Abstract

The Galerkin procedure is used to discretize the nonlinear partial differential equation and boundary conditions governing the flutter of a simply supported panel in a supersonic stream. These equations have repeated natural frequencies at the onset of flutter. The method of multiple scales is used to derive five first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the excited modes. Then, the modulation equations are used to calculate the equilibrium solutions and their stability, and hence to identify the excitation parameters that suppress flutter and those that lead to complex motions. A combination of a shooting technique and Floquet theory is used to calculate limit cycles and their stability. The numerical results indicate the existence of a sequence of period-doubling bifurcations that culminates in chaos. The complex motions are characterized by using phase planes, power spectra, Lyapunov exponents, and dimensions.