基于滞变阻尼模型的时域计算方法

复阻尼时域运动方程的自由振动解中包含发散项,导致时域数值计算结果不能稳定收敛。在复阻尼模型的频域运动方程基础上可得到滞变阻尼模型的时域运动方程。针对滞变阻尼模型的特点,依据复平面法和地震加速度的三角级数表达式,该文提出了滞变阻尼模型的时域理论计算方法;假定时间步长内结构的振动响应为简谐振动响应,同时借助于常平均加速度法,提出了滞变阻尼模型的时域数值计算方法。算例分析表明,与复阻尼模型的时域数值计算方法相比,滞变阻尼模型的时域理论计算方法和时域数值计算方法可有效避免时域发散现象;滞变阻尼模型的时域理论计算结果和时域数值计算结果与复阻尼模型的频域计算结果近似相等,进一步证明了该文方法的正确性。

TIME DOMAIN CALCULATION METHOD BASED ON HYSTERETIC DAMPING MODEL

The free vibration solution of a complex damping time domain motion equation contains divergent items which make the numerical results of the time domain divergent. Based on the frequency domain motion equation of a complex damping model, the hysteretic damping time domain motion equation can be obtained. According to the characteristics of a hysteretic damping model, the time domain theoretical calculation method of the hysteretic damping model is proposed based on the complex plane method and trigonometric series expression of earthquake acceleration records. It is assumed that the structural vibration response is a harmonic vibration response in a short time step. Based on the average acceleration method, the time domain numerical calculation method of the hysteretic damping model is proposed. The analysis results show that: compared with the time domain numerical method of a complex damping model, the two proposed methods can avoid the time domain divergence phenomena effectively. The time domain calculation results of the two proposed methods are approximately equal to the frequency domain calculation results of a complex damping model. The correctness of the two proposed methods is verified.