     Improved Time Domain Calculation Method Based on Complex Damping Model

DOI：

 作者 单位 孙攀旭1，杨红1，2，刘庆林3 （1. 重庆大学 土木工程学院，重庆 400045； 2. 重庆大学 山地城镇建设与新技术教育部重点实验室，重庆400045； 3. 深圳信息职业技术学院 交通与环境学院，广东 深圳 518172）

针对复阻尼运动方程自由振动解中存在发散项，导致其不可计算结构自由振动响应，同时基于复阻尼模型的时域计算结果不能稳定收敛的问题，在复阻尼模型的基础上，利用时频域转换得到改进时域运动方程；引入地震加速度在时间步长内是线性变化的假定，利用改进时域运动方程的特点，提出地震作用下基于复阻尼模型的改进时域计算方法.算例分析表明：相比复阻尼模型的时域运动方程，改进的时域方程可适用于结构自由振动响应的时域计算，且计算得到的地震作用下结构动力响应是稳定收敛的；相比基于改进时域运动方程的傅里叶级数法，本文提出的改进时域计算方法计算量更少，计算效率更高. 随着阻尼比的增大，复阻尼模型的改进时域方法和黏性阻尼模型的时域方法计算结果差异逐渐增大.当结构阻尼比为0.5时，在部分地震波作用下两种方法计算得到的加速度峰值相对误差可达到20%以上.

There are divergent items in the free vibration solution of complex damping vibration equation. The structural free vibration responses cannot be calculated based on complex damping model, and the structural time domain calculation results are not stably convergent. On the basis of the complex damping model, the improved time domain motion equation can be obtained by time and frequency domain transformation. In the time step, it is assumed that the relationship of earthquake acceleration is linear. By the characteristics of the improved motion equation, the improved time domain calculation method under earthquake action is put forward. The cases show that， compared with the time domain motion equation of complex damping model, the improved time domain motion equation can be applied to the time domain calculation of structural free vibration responses. The structural time domain calculation results are stably convergent under earthquake action. Compared with the Fourier series method, the calculation amount of the proposed method is less and the computational efficiency of the proposed method is higher. With the increase of damping ratio, the difference between the improved time domain calculation method of complex damping model and the time domain calculation method of viscous damping model is increasing gradually. When the damping ratio is 0.5, the biggest relative error of structural acceleration peak values which are calculated by the two methods is over 20% under some seismic wave.