Considering the vibration of a Tuned Mass Damper (TMD), a dynamic model composed of the cable and TMD is investigated. Different from the other studies, this paper is mainly devoted to nonlinear behaviours of the model by considering the participation of the damper in energy transfer and coupling interaction between the cable and damper. According to the extended Hamilton’s principle, the classical equations of motion of the cable and TMD are derived. Based on the equations of motion of the cable and TMD, the one-to-one internal resonance of the system is studied when external primary resonance of the cable occurs. By applying the Galerkin’s method, a set of ordinary differential equations (ODEs) are obtained. To solve the ODEs, the multiple time scale method is used and the modulation equations are derived. The stable solutions of the modulation equations are acquired by Newton-Raphson method and continued by pseudo arclength algorithm. Meanwhile, the parametric analyses of some key parameters, such as the excitation amplitude, the spring stiffness, the damping ratio and position of the TMD and the sag of the cable, are carried out through frequency-/force-response curves to explore the nonlinear behaviours of the system. The results show that the TMD plays an important role in both energy consumption and energy transfer.

考虑到调谐质量阻尼器（TMD）的振动，研究了由电缆和TMD组成的动力学模型。与其他研究不同，本文主要通过考虑阻尼器参与能量传递以及电缆与阻尼器之间的耦合相互作用来研究模型的非线性行为。根据扩展的汉密尔顿原理，推导了电缆和TMD的经典运动方程。基于电缆和TMD的运动方程，研究了发生电缆的外部主共振时系统的一对一内部共振。通过应用Galerkin方法，可以获得一组常微分方程（ODE）。为了求解ODE，使用了多重时间标度方法并推导了调制方程。通过牛顿-拉夫森方法获得调制方程的稳定解，并通过伪弧长算法继续求解。同时，通过频率/力-响应曲线，对激振幅度，弹簧刚度，TMD的阻尼比和位置以及垂度等关键参数进行了参数分析，探索了非线性。系统的行为。结果表明，TMD在能耗和能量转移中都起着重要作用。通过频率/力响应曲线进行分析，以探索系统的非线性行为。结果表明，TMD在能耗和能量转移中都起着重要作用。通过频率/力响应曲线进行分析，以探索系统的非线性行为。结果表明，TMD在能耗和能量转移中都起着重要作用。