Viscous damping theory has some disadvantages,one of which is that energy consumption per cycle is related to external excitation frequencies. The general solution to the complex damping theory's motion equation contains divergent items. Here,with the principle of frequency domain conversion,the complex damping motion equation was equivalently converted into a frequency dependent viscous damping motion equation to overcome the disadvantage of the complex damping theory having instability in time domain,and guarantee energy consumption per cycle being independent upon external excitation frequencies. Using the relationship assumption of velocity and displacement and the principle of energy conservation,the frequency dependent viscous damping motion equation being suitable for time history calculation was built. Combining with the constant average acceleration method,the recursion expression for time history integration calculation of the frequency dependent viscous damping motion equation was derived. The calculation examples showed that the time history integration calculation results of the frequency dependent viscous damping theory are stably convergent to effectively avoid divergent problems in time history integration calculation of complex damping theory.%黏性阻尼理论存在每循环消耗能量与外激励频率相关的缺陷,而复阻尼理论的运动方程通解中包含有发散项.依据频域转化原则,将复阻尼运动方程等价转化为频率相关黏性阻尼运动方程,克服复阻尼理论时域不稳定性的缺点,同时保证了每循环消耗能量与外激励频率无关.在此基础上,基于速度与位移关系假定和能量守恒准则,构建了适用于时程计算的频率相关黏性阻尼运动方程.结合常平均加速度法,给出了频率相关黏性阻尼运动方程时程积分计算的递推表达式.算例分析表明,频率相关黏性阻尼理论时程计算结果稳定收敛,可有效避免复阻尼理论时程计算中的发散问题.
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