We analyze the dynamics of a nonlinear mechanical system under the influence of an external harmonic force. The system consists of a linear oscillator (primary mass) and attached nonlinear dynamic absorber. It is supposed that the frequency of the external force is close to the natural frequency of the main mass. Assuming that the parameters of the system are uncertain, the stability conditions of the stationary regimes of the averaged equations are obtained analytically; these regimes correspond to the quasi-periodic motions of the original input system. An analytical approach to the problem of selecting the parameters of a dynamic absorber is proposed in order to reduce the amplitude of oscillations of the main system. The results obtained are compared with the results of the numerical integration of the equations of the motion with different initial conditions and parameter values.

我们分析了在外部谐波力影响下的非线性机械系统的动力学。该系统由线性振荡器（主要质量）和附加的非线性动态吸收器组成。假定外力的频率接近主质量的固有频率。假设系统参数不确定，则通过解析求出平均方程平稳态的稳定性条件。这些状态对应于原始输入系统的准周期运动。为了减小主系统的振荡幅度，提出了一种对动态吸收器的参数选择问题进行分析的方法。