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<p>This paper investigates the infinite-dimensional homoclinic bifurcation leading to dynamic pull-in instability in TLMPs under principal parametric resonance. Through multi-scale perturbation techniques, the governing equation was equivalent to nonlinear wave equations. By integrating a dual-measurement approach combining the Melnikov method and geometric theory, an analytical criterion for predicting dynamic pull-in instability was established. Furthermore, the precision of the Melnikov integral was significantly improved through high-order Taylor expansion. The reliability of the derived theoretical thresholds was verified via the DQM. Within this framework, the dynamic responses of TLMPs under four typical boundary conditions were systematically examined. The results highlight the substantial influence of boundary constraints on bifurcation characteristics: under CCFF boundaries, TLMPs exhibit the earliest occurrence of dynamic pull-in instability along with the most extensive chaotic region as excitation amplitude varies. In contrast, the CCCC configuration demonstrates enhanced periodic stability over wider excitation ranges and the narrowest chaotic region. The dynamic responses for CCSS and SSSS boundaries are found to lie between these two extremes. This study provides a comprehensive and quantitatively accurate approach for predicting instability in parametrically excited laminated structures.</p>

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Dynamic instability on infinite-dimensional global bifurcations of ΤΜLPs under principal parametric resonance

  • 期刊论文

  • 发表日期：

    2025年10月6日

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  • Qiliang Wu,
  • Jiawei Wang,
  • Minghui Yao,
  • Bin Bai,
  • Cong Wang,
  • Yan Niu

摘要

This paper investigates the infinite-dimensional homoclinic bifurcation leading to dynamic pull-in instability in TLMPs under principal parametric resonance. Through multi-scale perturbation techniques, the governing equation was equivalent to nonlinear wave equations. By integrating a dual-measurement approach combining the Melnikov method and geometric theory, an analytical criterion for predicting dynamic pull-in instability was established. Furthermore, the precision of the Melnikov integral was significantly improved through high-order Taylor expansion. The reliability of the derived theoretical thresholds was verified via the DQM. Within this framework, the dynamic responses of TLMPs under four typical boundary conditions were systematically examined. The results highlight the substantial influence of boundary constraints on bifurcation characteristics: under CCFF boundaries, TLMPs exhibit the earliest occurrence of dynamic pull-in instability along with the most extensive chaotic region as excitation amplitude varies. In contrast, the CCCC configuration demonstrates enhanced periodic stability over wider excitation ranges and the narrowest chaotic region. The dynamic responses for CCSS and SSSS boundaries are found to lie between these two extremes. This study provides a comprehensive and quantitatively accurate approach for predicting instability in parametrically excited laminated structures.