谐和与随机噪声联合作用下单自由度非线性碰撞系统的响应

Response of a single-degree-of-freedom non-linear vibroimpact system to combined deterministic harmonic and random excitation

研究了单自由度非线性碰撞系统在谐和与随机噪声联合激励下的响应问题。用多尺度法分离了系统的快变项,讨论了系统的阻尼项、非线性项和随机项等参数对系统响应的影响。在一定条件下,当约束距离较大时对应于不同的初始条件,系统具有两个非碰撞的稳态响应;而当约束距离不大时对应于不同的初始条件,系统也可以有两个不同的稳态响应,其中一个是发生碰撞的响应,而另外一个则不发生碰撞。随机扰动可以使得系统的响应从一个极限环变为一扩散的极限环。数值模拟表明本文提出的方法是有效的。

An investigation is made into the resonance of single-degree-of-freedom non-linear vibroimpatct oscillator to combined deterministic and random excitation. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The effects of damping, detuning, bandwidth and magnitudes of random excitations on the system are analyzed. Under some certain conditions, the system may have two steady state responses, one of which is a non-impact response, and the other is an impact one. Theoretical analyses and numerical simulations show that the nontrivial steady state solution may change from a limit cycle to a diffused limit one while the intensity of the random excitation increases. It is concluded that the method proposed in the paper is effective.