Chaotic Oscillations of a Suspended Curved Panel with Square Boundary

Abstract

Experimental results and analytical results are presented on chaotic oscillations of a suspended curved panel with square boundary. In the experiment, the panel is simply supported along all edges. The configuration of the panel is deformed by the gravity force and in-plane elastic constraint. Nonlinear periodic responses of the panel are examined under periodic lateral acceleration. Chaotic responses are observed and measured for modal inspection at four points of the panel simultaneously. In the analysis, the configuration of the panel is assumed as a suspended curved form with double arcs parallel to each edge. The Donnell type equation with lateral inertia force is introduced. The governing equation is reduced to nonlinear differential equations of a multiple-degree-of-freedom system by the Galerkin procedure. The nonlinear periodic responses are calculated by the harmonic balance method. The chaotic responses are numerically integrated by the Runge-Kutta-Gill method. The chaotic responses are inspected with the Fourier spectra, the Poincaré projections, the maximum Lyapunov exponents and the principal components by the Karhunen-Loéve-transformation. Both results of the experiment and the analysis show that the chaotic responses are generated within the frequency range of the same ratio to the each lowest natural-frequency. Poincaré projections of the both results coincide fairly well in detail. The number of modes generated in the chaos is counted as three by the maximum Lyapunov exponent and the Lyapunov dimension. The principal component analysis shows the predominant contribution of the lowest mode of vibration.