窄带随机噪声作用下单自由度非线性碰撞系统的响应

研究了单自由度非线性单边碰撞系统在窄带随机噪声激励下的次共振响应问题。用Zhuravlev变换将碰撞系统转化为速度连续的非碰撞系统,然后用随机平均法得到了关于慢变量的随机微分方程。在没有随机扰动情形,得到了系统响应幅值满足的代数方程;在有随机扰动的情形下,给出了系统响应稳态矩计算的迭代公式。讨论了系统阻尼项、非线性项、随机扰动项和碰撞恢复系数等参数对于系统响应的影响。理论计算和数值模拟表明,系统响应幅值将在激励频率接近于次共振频率时达到最大。而当激励频率逐渐偏离次共振频率时,系统响应迅速衰减。

Subharmonic response of a single-degree-of-freedom nonlinear vibroimpact system to a narrow-band excitation

The subharmonic response of single-degree-of-freedom nonlinear vibroimpact oscillator with a one-sided barrier to narrow-band random excitation is investigated.The analysis is based on a special Zhuravlev transformation,which reduces the system to one without impacts,or velocity jumps,thereby permitting the applications of random averaging method.The averaged equations are solved exactly and the algebra equation of the amplitude of the response is obtained in the case without random perturbation.A perturbation-based moment closure scheme is proposed and an iterative calculation equation for the mean square response amplitude is derived for the case with random perturbation.The effects of damping,nonlinear intensity,detuning,bandwidth,and magnitudes of random excitations are analyzed.The theoretical analyses are verified by numerical results.Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detuning,and when the intensity of the random excitation increases,the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle,even to a chaotic one.