A nonlinear energy sink is designed to control the oscillations of a 2 degrees-of-freedom pendulum under the following types of excitations: horizontal and vertical base displacements and initial energy. Coupled nonlinear governing system equations are treated with the multiple-scale methods with different assumptions depending on applied loads. Fast and slow system dynamics are revealed leading to detection of different possible dynamical regimes. The choice of the design parameters of the nonlinear energy sink is discussed, and a tuning method is proposed. The efficiency of the control is validated by an experimental study: a physical model of the pendulum is excited by the shake table. The response of the system shows that the nonlinear energy sink is able to control the main system.

中文翻译：

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2自由度摆的非线性吸波器设计及实验验证

非线性能量汇被设计为在以下类型的激励下控制 2 自由度摆的振荡：水平和垂直基位移和初始能量。耦合非线性控制系统方程用多尺度方法处理，根据施加的载荷具有不同的假设。揭示了快速和缓慢的系统动力学，导致检测不同的可能的动力学状态。讨论了非线性能量汇设计参数的选择，并提出了一种调谐方法。通过实验研究验证了控制的效率：振动台激发了摆的物理模型。系统的响应表明非线性能量汇能够控制主系统。