中文摘要：

分别采用精细积分格式和Newmark-β积分格式推导了非平稳随机地震响应灵敏度的时域显式表达式.并分别将其应用于平面框架与平面桁架问题的灵敏度分析,研究了积分时间步长对两种积分格式的计算精度和效率的影响.发现：当结构主频处于地震主频范围内时,在同等精度条件下,基于精细积分的时域表达式效率更高;而在结构主频偏离地震荷载主频范围时,基于Newmark-β积分格式的时域表达式效率更高.该研究成果可以为在考虑非平稳随机振动的结构优化问题中的数值积分算法选择提供有效的参考和借鉴.

英文摘要：

In this paper, two time-domain explicit expressions of the non-stationary random seismic response sensi- tivity are derived respectively based on the precise integration format and the Newmark-β integral format, and they are respectively used to analyze the sensitivity of a plane frame and a plane truss structure. Then, the effects of the integral time step on the calculation accuracy and the efficiency of the two integral formats are investigated. It is found that, when the main frequency of the structure is within the range of the main load frequency, the time-do- main explicit expression based on the precise integration has a higher efficiency with the same accuracy, but when the main frequency of the structure deviates from the main load frequency range, the time-domain explicit expres- sion based on the Newmark-β integral format achieves a higher efficiency. The research achievements can provide an effective reference for the choice of the numerical integration algorithms used in the structure optimization consi- dering the non-stationary random vibration.