中文摘要：

在随机振动及结构可靠性研究中，动力学系统的设计点激励有着不可替代的作用，但非线性动力学系统设计点激励的计算方法仍是当今研究者的焦点之一。该文利用振子自由振动响应的镜像激励，给出了高斯白噪声激励下非线性系统的设计点激励，并将其应用到首穿失效概率估计问题中，与原始的蒙特卡罗模拟相比较，两者体现了高度的一致性。为进一步说明该文方法的正确性，针对线性系统，利用解析方法获得设计点激励的准确值，利用镜像方法所得近似值，将其均应用到首穿失效概率的计算中，数值例子显示，两种方法所得设计点激励稍有不同，但在计算首穿失效概率时，展现出同样的有效性。

英文摘要：

For structural dynamic systems, the design-point excitation plays an important role in structural reliability assessment and random vibration. The calculation method of design-point excitation is still an important research focus today. This paper suggests a procedure to obtain the design-point excitation of non-linear systems based on mirror-image excitation of the flee-vibration response. It is shown that the design-point excitation thus obtained is effective in estimating excursion probabilities in non-linear dynamic systems when compared with the Monte Carlo method. In order to further illustrate the effectiveness of the method, the paper gives a numerical example of linear dynamic systems. We obtain the design-point excitation based on both the analytical method and mirror-image excitation. It is shown that the two methods have the same effectiveness when estimating excursion probabilities.