中文摘要：

复阻尼振动系统的瞬态响应通常只能在频域内求解。该文根据复阻尼理论应遵循对偶复化的原则,结合精细积分指数矩阵和高斯积分的运算方法,通过理论推导,给出了复阻尼结构动力方程的高斯精细时程积分法。分别采用Newmark-法和高斯精细时程积分法计算了复阻尼多自由度系统地震时程响应,并与频域法（视为精确解）的计算结果进行比较。结果表明：高斯精细时程积分法可用于复阻尼系统动力时程分析;且比Newmark-法有更高的精度和效率。

英文摘要：

The vibration analysis of complex damping systems is fulfilled mainly in frequency domain.Based on the dual principle of complex damping theory,a new time-history analysis method is proposed for complex damping systems,which combines the Gauss quadrature with the calculation technique of an exponential function matrix in the precise time-integration method.The responses of complex damping MDOF systems are calculated by Newmark-β method and Gauss precise time-integration method respectively,and compared with the frequency-domain solution.It is shown that Gauss precise time-integration method,having higher precision and efficiency than Newmark-β method,can be used to solve the complex damping vibration equation.