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Vibration analysis of the trapezoidal bi-stable composite laminate plate with four free edges

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Abstract

In this paper, a two layers carbon fiber reinforced resin matrix trapezoidal bi-stable composite laminate plate with unsymmetric cross-ply is considered. It is assumed that the trapezoidal bi-stable composite laminate plate is fixed at origin point, and the four boundaries are free. In order to obtain the stable configurations and the natural frequencies of the trapezoid bi-stable composite laminate plate with the given boundary condition, a set of polynomial displacement functions including 17 coefficients is employed to express the displacements. By using the classical laminate plate theory, von Karman nonlinear geometric relationship, minimum potential energy principle and Newton Raphson iterative method, the stable configurations of the trapezoidal bi-stable laminate plate are obtained. The calculation of stable configurations is verified by comparing the classical results with the present equilibrium solution curves. Then, with the help of continuous algebraic polynomial functions, Lagrange multiplier method and Rayleigh–Ritz method, the natural frequencies are computed. After verification, the influences of different geometric parameters and layering angle on the natural frequency are researched in detail.

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Acknowledgements

The authors acknowledge the financial support of National Natural Science Foundation of China through grant nos. 11872127, 11832002, 11732005, Qin **n Talents Cultivation Program, Bei**g Information Science & Technology University QXTCP A201901, the Project of High-level Innovative Team Building Plan for Bei**g Municipal Colleges and Universities No. IDHT20180513.

Funding

National Natural Science Foundation of China, 1187212711732005, Y.X. Hao, 11832002,W. Zhang, Qin **n Talents Cultivation Program, Bei**g Information Science & Technology University, QXTCP A201901, Y.X. Hao, Project of High-level Innovative Team Building Plan for Bei**g Municipal Colleges and Universities, IDHT20180513, Y.X. Hao

Conflict of interest statement

All the authors declare that we have no conflicts of interest to this paper. There are no financial and personal relationships with other people or organizations that can inappropriately influence our work.

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Authors and Affiliations

  1. College of Mechanical Engineering, Bei**g Information Science and Technology University, Bei**g, 100192, People’s Republic of China

    J. Q. Chen, Y. X. Hao & L. T. Liu

  2. College of Mechanical Engineering, Bei**g University of Technology, Bei**g, 100124, People’s Republic of China

    W. Zhang

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  1. J. Q. Chen
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  2. Y. X. Hao
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  3. W. Zhang
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  4. L. T. Liu
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Correspondence to Y. X. Hao.

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Chen, J.Q., Hao, Y.X., Zhang, W. et al. Vibration analysis of the trapezoidal bi-stable composite laminate plate with four free edges. Int. J. Dynam. Control 10, 1415–1423 (2022). https://doi.org/10.1007/s40435-022-00909-5

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  • DOI: https://doi.org/10.1007/s40435-022-00909-5

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