结合随机振动虚拟激励法、无穷周期链式结构的辛数学方法及有限元谐响应分析法,提出了考虑扣件胶垫刚度频变特性的车.线.隧垂向环境振动预测的辛模型。以南京地铁1号线为研究对象,利用等效线性动黏弹性模型之一的Martin—Davidenkov模型来描述土体加卸载对应的应力.应变非线性关系,将地表土层垂向振动加速度级的理论计算结果与实测数据进行对比,二者在整个频域内的吻合度较高,在中心频率为50Hz位置处两者的最大峰值结果仅相差0.6dB,表明实测线路上的轨道不平顺水平和计算条件较为接近,验证了车-线-隧垂向环境振动预测的辛模型及其参数选取方法合理,在频域范围内有较好的预测精度及效率。
By combining the random vibration Pseudo Excitation Method (PEM), symplectic mathematics of infinitely periodic sub-structures, and harmonic response finite element analysis, a prediction model of environment vertical vibration induced by a vehicle-track-tunnel coupled system is proposed which accounts for the frequency-dependent stiffness of the rail pad. Taking Nanjing's Metro Line 1 Project as the research object, a Martin-Davidenkov model, a type of equivalent linear visco-elastic model, was used to describe the relationship between soil loading and unloading and nonlinear stress-strain. Theoretical results of vertical acceleration of the surface soil are compared with the measured data, and they agree well in the whole frequency domain but have a maximum peak difference of 0.6 dB at the centre frequency of 50 Hz. The conclusion indicates that the track irregularity on the testing subway line is close to the calculated condition, and the prediction model for environment vertical vibration of the vehicle-track-tunnel coupled system has better predictive accuracy and efficiency in the frequency domain and its parameter selection method is reasonable.