We seek to understand the behavior of a pendulum under parametric excitation coupled with a nonlinear absorber. First, the reference system without any coupled absorber, i.e., a simple pendulum, is analyzed with a multiple scale method thanks to supposed assumptions about the excitation. The equilibrium points of the system are calculated, and their stability is determined. The phase portraits are introduced in order to better predict the behavior of the system. Then the same analysis is performed on the pendulum coupled with the nonlinear absorber leading to detection of the slow invariant manifold and its dynamic characteristic points. Both systems are compared to estimate the effects of the absorber on the vibratory behaviors of the pendulum.

我们试图了解参数振动与非线性吸收器耦合作用下摆的行为。首先，由于关于激励的假设假设，使用多尺度方法分析了没有任何耦合吸收器的参考系统，即简单的摆锤。计算系统的平衡点，并确定其稳定性。为了更好地预测系统的行为，引入了相图。然后对与非线性吸收器耦合的摆进行相同的分析，从而检测出慢不变歧管及其动态特征点。比较两个系统，以估计吸收器对摆振动特性的影响。