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<p>This study conducts a detailed analytical and numerical investigation of a nonlinear two-degree-of-freedom (2DOF) mechanical oscillator that is subjected to parametric excitation, magnetic stiffness nonlinearities, and dry friction. The considered system consists of two coupled oscillators, both of which are connected to a rotating rectangular beam that induces time-periodic stiffness variation. The complexification-averaging (CxA) method is employed to derive approximate analytical solutions, which are thoroughly validated through time domain simulations and bifurcation analyses. The dynamic analysis reveals a rich spectrum of nonlinear behaviors, including periodic, quasiperiodic, and chaotic responses. Detailed bifurcation diagrams, Lyapunov exponent analysis, and Poincaré maps demonstrate the influence of nonlinear stiffness degree, mass symmetry, and frictional effects on system stability and response amplitude. The obtained results provide a significant understanding of the dynamic behaviour of coupled nonlinear systems and establish a conceptual framework for the development of complex vibration abatement strategies, energy harvesting devices, and advanced mechanical systems.</p>

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Analysis of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular beam

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Muhammad Junaid-U-Rehman,
  • Grzegorz Kudra,
  • Krystian Polczyński,
  • Kevin Dekemele,
  • Jan Awrejcewicz

摘要

This study conducts a detailed analytical and numerical investigation of a nonlinear two-degree-of-freedom (2DOF) mechanical oscillator that is subjected to parametric excitation, magnetic stiffness nonlinearities, and dry friction. The considered system consists of two coupled oscillators, both of which are connected to a rotating rectangular beam that induces time-periodic stiffness variation. The complexification-averaging (CxA) method is employed to derive approximate analytical solutions, which are thoroughly validated through time domain simulations and bifurcation analyses. The dynamic analysis reveals a rich spectrum of nonlinear behaviors, including periodic, quasiperiodic, and chaotic responses. Detailed bifurcation diagrams, Lyapunov exponent analysis, and Poincaré maps demonstrate the influence of nonlinear stiffness degree, mass symmetry, and frictional effects on system stability and response amplitude. The obtained results provide a significant understanding of the dynamic behaviour of coupled nonlinear systems and establish a conceptual framework for the development of complex vibration abatement strategies, energy harvesting devices, and advanced mechanical systems.