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Nonlinear dynamics of composite laminated circular cylindrical shell clamped along a generatrix and with membranes at both ends

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Abstract

In this paper, the nonlinear oscillations of a composite laminated circular cylindrical shell clamped along a generatrix and with the radial pre-stretched membranes at both ends are studied for the first time. The dynamic effect of membranes on the circular cylindrical shell is replaced by a nonlinear elastic excitation with the damping. Meanwhile, the parametric excitation of the changing temperature is also considered. Based on Reddy’s third-order shear deformation theory and von Kármán-type nonlinear kinematics, the nonlinear partial differential equations of motion for the composite laminated circular cylindrical shell clamped along a generatrix are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The asymptotic perturbation method is applied to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Corresponding to several selected values of the parameters, the frequency–response curves are obtained by numerical method. It is found that the static bifurcations, the jump phenomena as well as the hardening-spring-type nonlinearity behaviors are exhibited and that different parameters change the frequency–response curve shape. The numerical results based on the averaged equations are obtained to exhibit some intrinsically nonlinear dynamic behaviors of the composite laminated circular cylindrical shell clamped along a generatrix using the bifurcation diagram, waveform, phase plots and Poincaré maps. It is also found that there exist alternately the periodic and chaotic motions of the circular cylindrical shell clamped along a generatrix with the parameter excitation of temperature increases in a certain range.

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Acknowledgements

The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through Grant Nos. 11290152 and 11427801, and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (PHRIHLB).

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Authors and Affiliations

  1. Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    T. Liu, W. Zhang & J. F. Wang

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  1. T. Liu
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  2. W. Zhang
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  3. J. F. Wang
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Correspondence to W. Zhang.

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Liu, T., Zhang, W. & Wang, J.F. Nonlinear dynamics of composite laminated circular cylindrical shell clamped along a generatrix and with membranes at both ends. Nonlinear Dyn 90, 1393–1417 (2017). https://doi.org/10.1007/s11071-017-3734-4

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