基于谐响应的三维场地地震动频域研究

刘爽，闫少敏^*，裴旺

天津市交通科学研究院，天津  300300

摘要：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。

关键词：地震动频域；频域分析；局部场地效应；谐响应分析

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

LIU Shuang, YAN Shaomin^*, PEI Wang

Tianjin Transportation Research Institute, Tianjin 300300, China

Abstract: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.

Keywords:seismic motion in the frequency domain; frequency domain analysis; local site effect; harmonic response analysis