Forced vibration of an axially moving beam with nonhomogeneous boundary

IF 2.2 3区工程技术 Q2 MECHANICS Archive of Applied Mechanics Pub Date : 2025-01-22 DOI:10.1007/s00419-025-02760-4

Liang Jintao, Wang Ze, Li Xingli, Li Chongbo

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Abstract

Nonlinear vibration of axially moving systems has been a hot research topic. In the present paper, the influence of nonhomogeneous boundaries caused by wheel curvature on the dynamics of axially moving beams is explored. The equilibrium deformation of axially moving beams with nonhomogeneous boundaries is solved by using the iterative scheme developed by the differential quadrature method (DQM). Moreover, the forced vibration response of the system is evaluated by using the multi-scale method. The stability of the solutions for given parameters was determined. The results of the multi-scale method are verified by using the Galerkin truncation method (GTM). Numerical examples disclose that nonhomogeneous boundary conditions exhibit specific phenomena, namely an increase in the amplitude of the steady-state response, a decrease in the nonlinear characteristics, and an upward shift of the instability boundary. The discovery of this phenomenon is of great significance for the analysis of the dynamic response of axially moving beams under nonhomogeneous boundary conditions caused by wheel curvature. It is helpful for structural optimization and performance improvement in corresponding engineering fields.

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非均匀边界轴向运动梁的受迫振动

轴向运动系统的非线性振动一直是一个研究热点。本文探讨了车轮曲率引起的非均匀边界对轴向运动梁动力学的影响。采用微分正交法（DQM）提出的迭代格式求解具有非均匀边界的轴向运动梁的平衡变形。此外，采用多尺度法对系统的强迫振动响应进行了评估。确定了给定参数下解的稳定性。采用伽辽金截断法（GTM）对多尺度方法的结果进行了验证。数值算例表明，非均匀边界条件表现出稳态响应幅度增大、非线性特征减小、不稳定边界向上移动等特殊现象。这一现象的发现对于分析车轮曲率引起的非均匀边界条件下轴向运动梁的动力响应具有重要意义。对相应工程领域的结构优化和性能改进具有一定的指导意义。

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来源期刊

Archive of Applied Mechanics 物理-力学

CiteScore

4.40

自引率

10.70%

发文量

234

审稿时长

4-8 weeks

期刊介绍： Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.