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Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics

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Abstract

This paper presents the analysis of the nonlinear dynamics for a composite laminated cantilever rectangular plate subjected to the supersonic gas flows and the in-plane excitations. The aerodynamic pressure is modeled by using the third-order piston theory. Based on Reddy’s third-order plate theory and the von Kármán-type equation for the geometric nonlinearity, the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate under combined aerodynamic pressure and in-plane excitation are derived by using Hamilton’s principle. The Galerkin’s approach is used to transform the nonlinear partial differential equations of motion for the composite laminated cantilever rectangular plate to a two-degree-of-freedom nonlinear system under combined external and parametric excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation of the non-automatic nonlinear system. The case of 1:2 internal resonance and primary parametric resonance is taken into account. A numerical method is utilized to study the bifurcations and chaotic dynamics of the composite laminated cantilever rectangular plate. The frequency–response curves, bifurcation diagram, phase portrait and frequency spectra are obtained to analyze the nonlinear dynamic behavior of the composite laminated cantilever rectangular plate, which includes the periodic and chaotic motions.

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Authors and Affiliations

  1. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    M. H. Zhao & W. Zhang

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  1. M. H. Zhao
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  2. W. Zhang
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Correspondence to W. Zhang.

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Zhao, M.H., Zhang, W. Nonlinear dynamics of composite laminated cantilever rectangular plate subject to third-order piston aerodynamics. Acta Mech 225, 1985–2004 (2014). https://doi.org/10.1007/s00707-013-1035-7

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  • DOI: https://doi.org/10.1007/s00707-013-1035-7

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