Time-history Calculation Method of Improved Frequency Dependent Viscous Damping Model

DOI：

 作者 单位 孙攀旭1，杨红1，2，赵雯桐1，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，深圳 518172）

复阻尼模型的时域计算结果不能稳定收敛. 迟滞阻尼模型存在能量耗散与实际不符以及非线性的缺陷. 针对复阻尼模型和迟滞阻尼模型的缺陷，本文依据频域转化原则得到了频率相关黏性阻尼模型. 为实现结构体系的时程计算，基于加速度与位移的关系假定，进一步得到了改进频率相关黏性阻尼模型.改进频率相关黏性模型保留了结构每周期耗散能量与外激励频率无关的优点，同时克服了迟滞阻尼模型中能量耗散与实际不符的缺陷，还保证了单一振动频率下单自由度结构的线性特征.假定时间步长内结构处于单一频率的简谐振动，引入常平均加速度法，提出了单自由度体系的时程计算方法. 在此基础上，结合模态叠加法，推导了多自由度体系的时程计算公式. 算例结果表明，改进频率相关黏性阻尼模型可克服复阻尼模型频域法的缺陷，同时有效避免复阻尼模型时域法计算结果的发散现象.

There is divergent phenomenon existing in time-domain calculation results based on complex damping model. Hysteretic damping model has the shortcomings that energy dissipation is not consistent with the practical case and a defect of nonlinearity in linear elastic stage. To overcome the above shortcomings of complex damping model and hysteretic damping model, a frequency dependent viscous damping model is obtained based on the principles of frequency domain transformation in this paper. For the realization of structural time-history calculation method, an improved frequency dependent viscous damping model is obtained based on the assumption of the relationship between acceleration and displacement. The improved frequency dependent viscous damping model has the advantage that energy consumption is independent of external excitation frequencies. At the same time, the energy consumption in the proposed model is consistent with the practical case, and it maintains linear characteristic of single-degree-of-freedom structure with a single vibration frequency. It is assumed that structural response is harmonic vibration response in every time step. It contains the single frequency. By introducing the constant average acceleration method, a time-history calculation method of single degree of freedom system can be put forward. On this basis, combined with the modal superposition method, the time-history calculation formulas of multi-degree of freedom system are obtained. The analysis results of the cases show that improved frequency viscous damping model can overcome the shortcoming of the frequency-domain method based on complex damping model. It can also avoid the divergent phenomenon in calculation results of time-domain method based on the complex damping model.