Modal Interaction in the Response of Antisymmetric Cross-Ply Laminated Rectangular Plates

Abstract

A higher-order shear-deformation theory is used to analyze the interaction of two modes in the response of thick laminated rectangular plates to transverse harmonic loads. The case of a two-to-one au toparametric resonance is considered. Four first-order ordinary differential equations describing the modula tion of the amplitudes and phases of the internally resonant modes are derived using the averaged Lagrangian when the higher mode is excited by a primary resonance. The fixed-point solutions are determined, and their stability is analyzed. It is shown that besides the single-mode solution, two-mode solutions exist for a certain range of parameters. It is further shown that, in the multimode case, the lower mode, which is indirectly excited through the internal resonance, may dominate the response. For a certain range of parameters, the fixed points lose stability via a Hopf bifurcation, thereby giving rise to limit-cycle solutions. It is shown that these limit cycles undergo a series of period-doubling bifurcations, culminating in chaos.

Keywords

Composite plates chaos modal interactions internal resonance

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