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Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

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Abstract

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors. The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified. The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated, and the four-dimensional (4D) nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method. The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed. The discussion focuses on investigating the effects of key parameters, e.g., excitation amplitude, damping coefficient, and detuning parameters, on the resonance responses. The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system. Furthermore, the significant motions under particular excitation conditions are visualized by bifurcation diagrams, time histories, phase portraits, three-dimensional (3D) phase portraits, and Poincare maps. Finally, the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell, yielding results that are qualitatively consistent with the theoretical results.

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Author information

Authors and Affiliations

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Beijing, 100871, China

    Meiqi Wu, Pengyu Lv, Hongyuan Li, Jiale Yan & Huiling Duan

  2. Nanchang Innovation Institute of Peking University, Nanchang, 330096, China

    Meiqi Wu

  3. Department of Mechanics, Guangxi University, Nanning, 530004, China

    Wei Zhang

Authors
  1. Meiqi Wu
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  2. Pengyu Lv
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  3. Hongyuan Li
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  4. Jiale Yan
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  5. Huiling Duan
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  6. Wei Zhang
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Contributions

Credit authorship contribution statement Meiqi WU: methodology, software, formal analysis, investigation, and writing-original draft. Pengyu LYU: formal analysis. Hongyuan LI: validation. Jiale Yan: software. Huiling DUAN: conceptualization, methodology, resources, supervision, and writing review editing. Wei Zhang: conceptualization, validation, and investigation.

Corresponding author

Correspondence to Huiling Duan.

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Conflict of interest Huiling DUAN is an editorial board member for Applied Mathematics and Mechanics (English Edition) and was not involved in the editorial review or the decision to publish this article. The authors declare no conflict of interest.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 12293000, 12293001, 11988102, 12172006, and 12202011)

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Wu, M., Lv, P., Li, H. et al. Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode. Appl. Math. Mech.-Engl. Ed. 45, 581–602 (2024). https://doi.org/10.1007/s10483-024-3105-6

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  • DOI: https://doi.org/10.1007/s10483-024-3105-6

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