多点激励下绝对位移直接求解算法的误差频域分析

多点激励地震响应分析时，相对运动法将结构内部节点绝对位移分解成拟静位移和动态位移两部分分别进行求解，而绝对位移直接求解法直接对内部节点绝对位移进行求解，在两种求解算法中，阻尼分别假定与内部结点相对速度、绝对速度成比例。两种算法的阻尼假定不同可能会引起计算结果误差，在瑞利阻尼、单元阻尼模型下，采用随机振动方法对两种算法计算结果误差在频域内进行了理论分析，指出了瑞利阻尼模型下两种算法求得的结构动态内力功率谱密度误差主要受结构阻尼比、激励频率与结构基频率比值影响，但单元阻尼模型下两种算法得出的动态内力功率谱密度不存在误差。最后从概率意义上指出：瑞利阻尼模型下，两种算法得出的结构内力响应方差的误差随结构阻尼比的增大而增大，当结构阻尼比不大于5%时，两种算法计算结果误差很小。

Error analysis of seismic response obtained by directly solving absolute displacement in frequency domain under multi-support earthquake excitations

Under multi-support earthquake excitations,nodal displacements were decomposed into pseudo-static and dynamic parts,respectively with the relative motion method,while the nodal displacements were solved directly with the absolute displacement solving method.The damping was proportional to the relative velocity in relative motion method,but the damping was proportional to the absolute velocity in the method of directly solving absolute displacement.The different damping assumptions may cause calculation errors on structural responses.The theoretical analysis based on random vibration showed that the structural response power spectral density errors obtained with the two solving methods are caused by mass damping,and affected by damping ratio and the ratio between excitation frequency and fundamental frequency of the structures with Rayleigh damping.The damping forces are determined by the nodal velocity difference with element damping model,and the nodal velocity difference are equal in the two solving method,so the calculation errors don’t exist using element damping model.