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中文摘要：
研究了单自由度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.在约束距离为0时,用矩方法给出了系统响应幅值二阶矩的解析表达式.在约束距离不为0时,近似地得到了系统响应幅值二阶矩的解析表达式.讨论了系统阻尼项、窄带随机噪声的带宽和中心频率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.数值模拟表明提出的方法是有效的.
英文摘要：
The subharmonic response of single-degree-of-freedom linear vibroimpact oscillator with a one-sided barrier to narrow-band random excitation was investigated. The analysis was 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 stochastic equations were solved exactly by the method of moments for the mean square response amplitude for the case of zero offset. A perturbation-based moment closure scheme was proposed for the case of non- zero offset. The effects of damping, detuning, bandwidth and magnitudes of random excita- tions were analyzed. The theoretical analyses were verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings.
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