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<p>In-plane linear and nonlinear vibrations of slightly curved beams have been extensively studied using the shape imperfection beam model which heavily relies on the static condensation assumption (the axial inertia of a beam may be neglected). A general curved beam model is complicated, but it simplifies a lot when a beam has constant curvature. In this study, it is considered as the reference one to assess the validity limits of the shape imperfection beam model for analysis of linear (eigenfrequencies and eigenmodes) and nonlinear (hardening/softening) vibrations. In the linear case, exact solutions are obtained, while in the nonlinear one, the classical multiple scaled method is used. Furthermore, we consider nonlinear modal interaction in the case of an internal parametric resonance. To validate our reference model of a beam with constant curvature, its predictions are compared with results of linear and nonlinear finite element simulations in ANSYS.</p>

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In-plane vibrations of slightly curved beams: two models compared

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月24日

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  • Behnam Firouzi,
  • Sergey Sorokin

摘要

In-plane linear and nonlinear vibrations of slightly curved beams have been extensively studied using the shape imperfection beam model which heavily relies on the static condensation assumption (the axial inertia of a beam may be neglected). A general curved beam model is complicated, but it simplifies a lot when a beam has constant curvature. In this study, it is considered as the reference one to assess the validity limits of the shape imperfection beam model for analysis of linear (eigenfrequencies and eigenmodes) and nonlinear (hardening/softening) vibrations. In the linear case, exact solutions are obtained, while in the nonlinear one, the classical multiple scaled method is used. Furthermore, we consider nonlinear modal interaction in the case of an internal parametric resonance. To validate our reference model of a beam with constant curvature, its predictions are compared with results of linear and nonlinear finite element simulations in ANSYS.