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<p>Combining the Chebyshev polynomials and the incremental harmonic balance (IHB) method, a nonlinear mathematical model of the laminated circular plate is established, taking into account geometrical nonlinearities, and the forced vibration characteristics of the model are investigated. Utilizing the first-order shear deformation theory and the Von-Kármán large deformation theory, the Lagrangian energy generalization of the laminated circular plate is derived, and then the nonlinear vibration equations are obtained by the Rayleigh–Ritz method, and then the equations are resolved by the IHB method. The accuracy of the model calculations is firstly attested by performing the convergence analysis about the truncation number and wave number, and then the exactness of the model is further attested by comparing with the literature and numerical results. Finally, the impacts of material parameters, thickness, damping ratio and load amplitude on the nonlinear frequency response of the laminated circular plate are investigated to provide a reference for the optimal design of laminated composite circular plates when geometrical nonlinearity is considered.</p>

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A Chebyshev-IHB solution for nonlinear vibrations of laminated circular plates

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Xiao Wu,
  • Rui Zhong,
  • Ruihua Wang,
  • Qingshang Wang

摘要

Combining the Chebyshev polynomials and the incremental harmonic balance (IHB) method, a nonlinear mathematical model of the laminated circular plate is established, taking into account geometrical nonlinearities, and the forced vibration characteristics of the model are investigated. Utilizing the first-order shear deformation theory and the Von-Kármán large deformation theory, the Lagrangian energy generalization of the laminated circular plate is derived, and then the nonlinear vibration equations are obtained by the Rayleigh–Ritz method, and then the equations are resolved by the IHB method. The accuracy of the model calculations is firstly attested by performing the convergence analysis about the truncation number and wave number, and then the exactness of the model is further attested by comparing with the literature and numerical results. Finally, the impacts of material parameters, thickness, damping ratio and load amplitude on the nonlinear frequency response of the laminated circular plate are investigated to provide a reference for the optimal design of laminated composite circular plates when geometrical nonlinearity is considered.