轨道随机不平顺影响下高速铁路地基动力分析模型

考虑轨道随机不平顺影响，建立了移动车辆-有砟轨道-路基-层状地基垂向耦合振动解析模型。模型中，将虚拟激励法和解析的波数-频率域法有效结合起来，直接由轨道不平顺的功率谱密度得到准确的动态轮轨力功率谱。将移动列车轴荷载和轨道随机不平顺引起的动态轮轨力考虑为傅里叶级数表示的谐波叠加形式，根据线性系统叠加原理，求得地基动力响应功率谱估计值与时程结果。利用在波数域内直接计算位移频谱、划分合适谐波区间等技术，显著提高了随机振动响应功率谱和时程的计算效率。对比分析了地基表面测点垂向振动加速度时程与频谱的理论计算与现场实测结果，证明了本文模型的合理性。

A dynamic model of ground for high-speed railway with track random irregularities

An analytical model for vertical vibration of the moving vehicle-ballasted track-subgrade-layered ground coupling system is established with taking into consideration of track random irregularities. The pseudo-excitation method and the analytical method of wavenumber-frequency domain are effectively combined to derive the accurate dynamic wheel-rail force power spectrum by directly employing the power spectral density of track irregularity.Based on supposing that both the moving axle loads and the dynamic wheel-rail forces induced by track random irregularities can be expressed in form of Fourier series, the power spectral density estimates and time histories of ground vibration are obtained according to the superposition principle of linear systems. The computation efficiency of power spectrum and time history of random vibration is remarkbly improved by using such techniques as directly computing the displacement spectrum in wavenumber domain and properly dividing the adaptive interval of harmonic wave. The proposed analytical model is validated by conducting camparison between the theoretical calculation results and the experimental results of the time histories and spectra of vertical acceleration of ground surface points.