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Study on the rectangular bistable composite laminated plate through dynamic modeling, numerical simulation and experiment

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Abstract

In this paper, a rectangular bistable composite laminated plate is studied through dynamic modeling, numerical simulation and experiment. A theoretical model is elucidated, elaborating the dynamic snap-through and nonlinear dynamics of the rectangular bistable composite laminated plate. The potential energy curve, the restoring force curve and the stiffness curve are graphically presented, exhibiting differences from those of square bistable plates. The two potential wells and the negative stiffness region are asymmetric. The dynamic snap-through elucidated by curvature and displacement is graphically presented in phase diagrams and time history diagrams. Due to the asymmetry of the double potential wells, the dynamic snap-through may be unidirectional rather than repeated, and the nonlinear dynamic responses around the two potential wells are asymmetric, which depends on initial positions. In frequency sweep, the frequency-amplitude response curves are characterized by the softening nonlinear stiffness effect and the hysteresis, where there are multiple peaks displaying the first several modes of the rectangular bistable plate around one stable state. The nonlinear dynamic responses are characterized by the periodic and chaotic vibrations, the 1/2 subharmonic resonance, the unidirectional dynamic snap-through and the repeated dynamic snap-through. When the excitation frequency is equal to the first mode frequency for the lower stable state or the third mode frequency for the upper stable state, the dynamic snap-through is found to occur. Linear mode frequencies can show the mechanism of the snap-through to a certain extent. At mode frequencies, sufficient energy is gathered to actuate the snap-through. Unlike square bistable plates, rectangular bistable plates may only be characterized by the unidirectional snap-through under the specific energy input, which depends on initial positions. For rectangular bistable plates, two opportune excitation frequencies that have to be selected can lead to the repeated snap-through. This research is beneficial to the development of aerospace structures, bistable energy harvesters and vehicle vibration isolation devices. Compared to the old work, this work is more in line with the actual situation, where a high aspect ratio morphing wing can adjust its airfoil according to different tasks based on rectangular bistable plates which are more suitable for potential applications in the future.

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Acknowledgements

The authors gratefully acknowledge the support of National Natural Science Foundation of China (NNSFC) through grant Nos. 12102031.

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Authors and Affiliations

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

    Xiaotian Guo

  2. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    Ting Dong

  3. Beijing Key Laboratory of Performance Guarantee on Urban Rail Transit Vehicles, Beijing University of Civil Engineering and Architecture, Beijing, 102616, China

    Zhenkun Guo

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  1. Xiaotian Guo
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Correspondence to Ting Dong.

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Guo, X., Dong, T. & Guo, Z. Study on the rectangular bistable composite laminated plate through dynamic modeling, numerical simulation and experiment. Acta Mech 234, 4297–4313 (2023). https://doi.org/10.1007/s00707-023-03614-2

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  • DOI: https://doi.org/10.1007/s00707-023-03614-2

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