列车荷载作用下黏弹性半空间体的随机动力响应Dynamic response of viscoelastic half-space subjected to train loads

针对列车荷载作用下黏弹性半空间体响应的问题，利用虚拟激励法将系统的随机分析转化为确定性分析。根据列车荷载构造了相应的虚拟激励形式，通过傅里叶积分变换法把半空间体控制方程转入波数‐频率域，并推导获得了系统虚拟响应的积分形式解。当相速度接近或大于瑞利波速时，积分形式解中被积函数往往具有奇异性和高振荡性，使得数值计算相当困难。对此，将被积函数图形化以确定函数的积分限，并通过自适应数值积分算法解决被积函数的振荡性。数值算例中，进行了随机列车荷载作用下半空间体的响应分析，讨论了荷载移动速度及频率等参数变化对响应的影响，给出了响应的时间和空间分布规律。本文方法可进一步推广至移动矩形荷载等载荷模型，对移动荷载作用下环境振动行为预测具有很好的借鉴意义。

Dynamic response of viscoelastic half-space subjected to train loads

To study the response of visco-elastic half-space induced by train loads is an important work.Using the pseudo-excitation method,the stochastic analysis of the system is transformed into deterministic analysis.First,the pseudo-excitation is made up according to train loads,and then the equations of the half-space are transformed into wave number and frequency domain,finally the virtual response is achieved in integral form.Although the response in integral form is quite sure,the evaluation of these integrals is a formidable task due to the high oscillatory and singularity when the phase speed approaches or exceeds Rayleigh-wave speed.The integration interval is confirmed by visualizing the integrand,and the oscillatory of the integrand can be overcome by adopting adaptive numerically integration algorithm,the numerical results is given.For the purpose of verification,the response of viscoelastic half-space subjected to moving deterministic loads is also evaluated,and the numerical results are good with the results in literature.Based on the numerical method,the response of viscoelastic half-space under train loads have been calculated.The contribution of different moving loads'' speeds and loads'' frequency is analyzed,as well as the response'' s distribution in time and space.