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<p>For the axially moving viscoelastic beams subjected to the plane excitation, non-planar dynamical responses and internal resonance are studied analytically. The governing equation describing the in-plane and out-of-plane vibration is derived from the generalized Hamilton principle. The nonlinear modal interaction originated from one-to-one internal resonance between the in-plane and out-of-modes is investigated. The method of multiple scales is employed to solve the governing equation to obtain the modulated equation describing the amplitude and phase angles involving modes. The response of the system is presented in the form of frequency–response curves. The effect of the excitation amplitude and the viscoelastic coefficient on the response of the system is studied. Moreover, numerical simulation by the Galerkin method verifies the results obtained by the method of multiple scales.</p>

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Non-planar Response of Axially Moving Beam Under Planar Excitation

  • 期刊论文

  • 发表日期：

    2025年8月21日

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  • Wang Ze,
  • Liang Jintao,
  • Zhang Yanchao,
  • Guo Jiangyuan

摘要

For the axially moving viscoelastic beams subjected to the plane excitation, non-planar dynamical responses and internal resonance are studied analytically. The governing equation describing the in-plane and out-of-plane vibration is derived from the generalized Hamilton principle. The nonlinear modal interaction originated from one-to-one internal resonance between the in-plane and out-of-modes is investigated. The method of multiple scales is employed to solve the governing equation to obtain the modulated equation describing the amplitude and phase angles involving modes. The response of the system is presented in the form of frequency–response curves. The effect of the excitation amplitude and the viscoelastic coefficient on the response of the system is studied. Moreover, numerical simulation by the Galerkin method verifies the results obtained by the method of multiple scales.