模态叠加法计算地震加速度时程反应的几个问题

针对模态叠加法进行结构加速度时程反应分析,讨论了广义坐标积分步长、模态截断和离散位移时程求导三个问题对加速度时程反应误差的影响。并提出了振型加速度贡献系数的模态截断指标。以简谐荷载作用下单自由度体系的地震反应和三条地震波作用下的5层框架结构的地震反应为例进行数值计算。算例分析结果表明：当广义单自由度计算的离散时间步长小于1/32倍的自振周期时,加速度反应的误差小于5%；对于加速度时程反应而言,基于振型参与质量选取的模态数偏少,应基于振型加速度贡献系数作为模态截断的依据；由离散位移时程经中心差分法所得加速度的误差与直接由模态叠加法所得的基本相同,而FFT方法所得加速度时程存在虚假的高频振动而误差较大,采用低通滤波可有效降低误差。

Some problems in estimating acceleration time history response with modal superposition under seismic excitations

: To analyze the acceleration time history response with modal superposition, the effect of three problems, including the numerical integration step in generalized coordinates, the modal truncation and the numerical derivative of discrete displacement were discussed. Meantime, the modal contribution factor for acceleration was proposed as the basis of modal truncation. Numerical analyses performed on a single degree of freedom system under harmonic seismic excitation and a five-story building structure under three seismic waves excitation. The results showed that when the integration step of the generalized single degree of freedom was less than 1/32 times the natural vibration period, the errors of acceleration response was less than 5%. The modal number truncated with accumulated modal participating factor was not sufficient for acceleration time history response, and the accumulated modal contribution factor for acceleration could be used as the truncation basis. Furthermore, the acceleration errors estimated by central difference method based on discrete displacement time history were almost the same as the results by modal superposition. But the errors of results by FFT was lager due to the false high-frequency vibration of acceleration time history, which can be reduced with low-pass filtering.