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<p>The nonlinear dynamic behavior and stability characteristics of a supported Euler–Bernoulli beam—representative of material-based structures such as composite bridges and nano-engineered beams—subjected to a sequence of moving masses are investigated. The nonlinear response is based on the geometrical aspects of large transverse deflections of the beam, which contribute to changes in stability under traveling loads. Beam-moving mass systems arise in many realistic engineering problems and provide simplified models of flexible structural systems driven by time-varying excitation. The analysis is based on an accepted formulation that preserves the fundamental inertial effects of the moving mass. The paper focuses on the equilibrium topology and nonlinear response behavior near several equilibrium points. The modulation equations are obtained using the method of multiple scales (a two-variable expansion technique) to analyze the effects of system parameters and initial conditions on the dynamic response. The findings reveal clear equilibrium structures comprising nodal and saddle points, the evolution of which governs the transition between quasi-unstable and double-periodic responses. Phase-plane analysis and Poincaré maps show the presence of multiple attractors, leading to sensitivity of the long-term response to initial conditions. Damping is also analyzed, including the progressive collapse of heteroclinic and homoclinic structures into stable equilibria. The results highlight the importance of equilibrium-dependent nonlinear analysis for reliable stability evaluation and design of beam-moving-mass systems under time-varying loads.</p>

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Nonlinear dynamic transitions and equilibrium topology of a beam under sequential moving masses

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Ali M. Mohsen,
  • Rashid Mjheid Fadwi,
  • Muthanna K. Kareem,
  • Narinderjit Singh Sawaran Singh,
  • Younis Mohamed Atiah Al-zahy,
  • Salah S. Hamd,
  • Mahmut Taner,
  • Hani Sahramaneshi

摘要

The nonlinear dynamic behavior and stability characteristics of a supported Euler–Bernoulli beam—representative of material-based structures such as composite bridges and nano-engineered beams—subjected to a sequence of moving masses are investigated. The nonlinear response is based on the geometrical aspects of large transverse deflections of the beam, which contribute to changes in stability under traveling loads. Beam-moving mass systems arise in many realistic engineering problems and provide simplified models of flexible structural systems driven by time-varying excitation. The analysis is based on an accepted formulation that preserves the fundamental inertial effects of the moving mass. The paper focuses on the equilibrium topology and nonlinear response behavior near several equilibrium points. The modulation equations are obtained using the method of multiple scales (a two-variable expansion technique) to analyze the effects of system parameters and initial conditions on the dynamic response. The findings reveal clear equilibrium structures comprising nodal and saddle points, the evolution of which governs the transition between quasi-unstable and double-periodic responses. Phase-plane analysis and Poincaré maps show the presence of multiple attractors, leading to sensitivity of the long-term response to initial conditions. Damping is also analyzed, including the progressive collapse of heteroclinic and homoclinic structures into stable equilibria. The results highlight the importance of equilibrium-dependent nonlinear analysis for reliable stability evaluation and design of beam-moving-mass systems under time-varying loads.