中文摘要：

研究了Duffing单边约束系统在谐和与随机噪声联合激励下的响应问题.用谐波平衡法和摄动法分析了系统在确定性谐和激励和随机激励联合作用下的响应,用随机平均法讨论了随机扰动项对系统响应的影响.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.数值模拟表明该方法是有效的.

英文摘要：

The resonance of single-degree-of-freedom nonlinear impact oscillator to combined deterministic and random excitation is investigated.The method of harmonic balance,perturbation method and the method of stochastic averaging are used to determine the response of the system.The theoretical analyses are verified by numerical results.Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases,the nontrivial steady state solution may change form a limit cycle to a diffused limit cycle.Under some conditions the system may have two steady state responses,one is a non-impact response,the other an impact response.