基于直接模态摄动法的无阻尼线性随机结构的随机振动研究（II）

提出了基于数论选点的直接模态摄动法，用以求解无阻尼线性随机结构的随机动力反应。以数论选点的直接模态摄动法为基础，求出随机样本的特征值和特征向量，然后利用模态叠加法，求解样本结构在样本荷载作用下的动力反应，把所有的样本反应统计分析，即求得结构的随机反应。由于在计算过程中，没有将随机反应分解为均值部分和摄动部分，因此，采用直接模态摄动法求无阻尼复合随机振动系统的反应不存在久期项问题。算例分析表明，复合随机振动系统的随机反应均值比均值荷载作用下均值结构的确定性反应要小。

Study on Random Vibration of Un damping Linear Random Structure Based on Direct Modal Perturbation Method (II)

The direct modal perturbation based on selecting point by number theoretic method is proposed to find the random response of un damping linear random structures. Firstly, the direct modal perturbation based on selecting point by number theoretic method is used to find the random modes of random structures. Then, the dynamic response of the sampling structures under the sampling loads is studied with mode superposition method. Finally, the random response is found by statistic method. In calculation of the random response of un damping linear compound random vibration system, the secular term is avoided because the random response is divided into mean part and perturbation part. The results of calculation examples show that the mean values of the random response of compound random vibration system is less than the response of mean structures under mean loads.