基于谐响应的三维场地地震动频域研究

Research on seismic motion in the frequency domain in three-dimensional site based on harmonic response

为提高三维场地地震动响应的频域计算效率,基于工程波动理论,推导三维P波、SV波、SH波垂直入射的时域等效节点力公式,采用频域分析相关理论与快速傅里叶算法,将时域等效节点力公式转换为频域计算公式,提高三维频域计算求解效率;同时基于软件ANSYS谐响应分析模块,编写局部场地效应频域分析的核心计算程序,分别验证自由场地、沉积场地、凹陷场地的频域计算结果。研究结果表明:采用谐响应分析能显著提高场地地震动频域的计算效率,计算结果的准确度较高。

To improve the computational efficiency of frequency-domain calculations for seismic response in three-dimensional(3D) sites,an equivalent nodal force formula is derived based on the engineering wave motion theory for vertical incidents of P-waves,SV-waves,and SH-waves.By utilizing frequency-domain analysis theory and fast Fourier transform algorithms,the time-domain equivalent nodal force formula is transformed into a frequency-domain calculation formula,to enhance the efficiency of 3D frequency-domain calculations.Additionally,a core calculation program for frequency-domain analysis of local site effects is developed using the ANSYS harmonic response analysis module.The frequency-domain calculation results for free-field sites,sedimentary basins,and subsided sites are separately validated.The research findings demonstrate that utilizing harmonic response analysis significantly improves the computational efficiency of seismic response frequency-domain results,while maintaining a high level of accuracy.