多点激励地震响应分析过程中,相对运动法和绝对位移直接求解法分别假定阻尼与内部节点相对速度、绝对速度成比例,由于阻尼假定的不一致,计算结果可能存在误差.采用随机振动分析方法对瑞利阻尼模型下2种求解方法计算结果之间的误差进行了理论分析,得出了2种算法下结构动态响应功率谱密度误差主要受激励频率与结构基频的比值、结构阻尼比影响的结论,然后从概率统计意义上得出了2种算法下结构动态响应方差误差与结构阻尼比的关系,并进行了相关算例数值论证.最后得出如下结论:2种算法计算结果误差随阻尼比的减小而减小,当结构阻尼比不大于5％时,2种算法计算结果误差基本可忽略.%Under multi-support earthquake excitation, the damping is proportional to the relative velocity in relative motion method, While the damping is proportional to the absolute velocity in method of direct solving absolute displacement, and the damping assuming difference may cause the calculation errors on structural responses. The structural response errors of the dynamic component of power spectral density between the two solving methods are derived by random vibration theoretical analysis in Rayleigh damping model, which include damping ratio and the ratio between excitation frequency and fundamental frequency of the structures. Based on probability theory, the variation errors of dynamic component response between the two solving methods are also derived by theoretical analysis, and some numerical examples are provided to verify the error analysis. At last, it is pointed out that the calculation errors between the two solving methods decrease with damping ratio, and it is negligible when the damping ratio of structure is less than 5%.
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