窄带随机噪声参数激励下非线性碰撞系统的响应

Response of a single-degree-of-freedom nonlinear vibroimpact system to a narrow-band random parametric excitation

研究了单自由度非线性单边约束碰撞系统在窄带随机噪声参数激励下的响应问题,窄带噪声采用有界随机噪声模型。用Zhurav lev变换将碰撞系统转化为连续的非碰撞系统,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,给出了系统响应幅值满足的代数方程;在有随机扰动情形,结合线性化方法和矩方法给出了系统响应幅值二阶矩近似解的解析表达式。讨论了系统阻尼项、非线性项、窄带随机噪声的带宽、中心频率和振幅以及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,系统响应将随激励频率和振幅的增大而增大,而随系统阻尼和非线性强度的增大而减少。并发现了随机跳跃现象,即当随机激励的振幅超过某个阈值时,系统的稳态响应将从零解跳跃为一个较大的非零解;而当随机扰动的强度超过某个阈值时,系统的稳态响应将从一个较大的非零解跳跃为零解。

The resonance response of single-degree-of-freedom nonlinear vibroimpact oscillator with a one-sided barrier to narrow-band random parametric excitation is investigated.The narrow-band random excitation used here is a boundary random noise.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 asymptotic averaging over the period for slowly varying inphase and quadrature responses.The averaged equations are solved exactly and algebraic equation of the amplitude of the response is obtained in the case without random disorder.The methods of linearization and moment are used to obtain the formula of the mean square amplitude approximately for the case with random disorder.The effects of damping,detuning,restitution factor,nonlinear intensity,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 response amplitudes will be reduced at large damping or large nonlinear intensity,and will be increased with large amplitudes or frequencies of the random excitations.The phenomena of stochastic jump is observed,i.e.the steady response of the system will jump from trivial solution to a large non-trivial one when the amplitude of the random excitation exceed the threshold value,or will jump from the a large non-trivial solution to trivial one when the intensity of the random disorder of the random excitation exceed the threshold value.