To make it mathematically easy to solve, various practical time history analysis methods are all based on the viscous damping assumption to establish the dynamic equations of the system. From the viscous damping assumption, the conclusion that the damping force or its energy dissipation of the system is proportional to the frequency of the system can be deduced, which is not consistent with the experimental results. When the classical mode superposition method based on the viscous damping assumption is used to calculate the dynamic response of a hybrid structure under an earthquake, how to calculate the modal damping ratio or how to determine a number of significant frequencies of the response to calculate the damping matrix has always been an urgent problem to be resolved in the engineering community. Since the hysteretic damping assumption is consistent with the experimental results, the mode superposition method based on the hysteretic damping assumption is explored in this paper to solve the above problems. The mode superposition method based on the hysteretic damping assumption can avoid the modal damping ratio trouble of the classical mode superposition method based on the viscous damping assumption, and its damping matrix has advantages of simple construction method and small construction workload and clear physical meaning. In this paper, the complex mode superposition method and the real mode superposition method based on the hysteretic damping assumption are studied, the calculation results and calculation efficiency of the two methods are analyzed and compared, and the conclusion is drawn that the real mode superposition method is better than the complex mode superposition method.

为使数学上易于求解，各种实用的时程分析方法均基于粘性阻尼假设来建立系统的动力学方程。从粘性阻尼假设可以推导出系统的阻尼力或其耗散的能量与系统的频率成正比的结论，这与实验结果不一致。当基于粘性阻尼假设的经典模态叠加法计算地震作用下混合结构的动力响应时，如何计算模态阻尼比或如何确定响应的若干有效频率来计算阻尼矩阵一直是工程界亟待解决的问题。由于滞后阻尼假设与实验结果一致，本文探索了基于滞后阻尼假设的模态叠加方法来解决上述问题。基于滞回阻尼假设的模态叠加法可以避免基于粘性阻尼假设的经典模态叠加法的模态阻尼比问题，其阻尼矩阵构造方法简单，施工工作量小，物理意义明确。本文对复模态叠加法和基于滞回阻尼假设的实模态叠加法进行了研究，对两种方法的计算结果和计算效率进行了分析比较，