参数激励下具有非线性恢复磁力和旋转矩形杆的2DOF振子的解析与数值研究
Analytical and numerical study of a parametrically excited 2DOF oscillator with nonlinear restoring magnetic force and rotating rectangular rod
AI总结：
本文研究了参数激励下具有非线性磁力和旋转梁的二自由度振子，通过解析与数值方法分析其非线性动态行为，揭示了非线性刚度、质量对称性和摩擦效应的影响，为振动抑制和能量收集提供了理论基础。
摘要：
本研究详细探讨了一个受参数激励、磁性刚度非线性和干摩擦影响的非线性二自由度（2DOF）机械振子的解析和数值分析。所考虑的系统由两个耦合振子组成，两者均连接到一个旋转矩形梁，该梁引起时间周期性刚度变化。复平均（CxA）方法用于推导近似解析解，这些解通过时域仿真和分岔分析得到充分验证。动态分析揭示了丰富的非线性行为，包括周期性、准周期性和混沌响应。详细的分岔图、李雅普诺夫指数分析和庞加莱图展示了非线性刚度度、质量对称性和摩擦效应对系统稳定性和响应振幅的影响。所获得的结果对耦合非线性系统的动态行为有了显著理解，并为复杂振动抑制策略、能量收集设备和先进机械系统的发展建立了概念框架。
英文摘要：
This study investigates a detailed analytical and numerical investigation of a nonlinear two-degree-of-freedom (2DOF) mechanical oscillator 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 a time-periodic stiffness variation. The Complex 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, quasi-periodic, 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 give a significant understanding of the dynamic behavior of coupled nonlinear systems and establish a conceptual framework for the development of complex vibration abatement strategies, energy harvesting devices, and advanced mechanical systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
