A periodically supported beam on a visco-elastic half-space is considered to model the vibration of railway tracks. The viscosity of the half-space is assumed to be of the Kelvin-Voigt type. Making use of the concept of equivalent dynamic stiffness, the reaction of the half-space to the sleepers is replaced by a system of identical spring located under each sleeper. The frequency-dependent equivalent stiffness of the springs is a function of the phase shift of vibrations of neighbouring supports. The equivalent stiffness is derived analytically employing the contour integration technique, resulting in a comprehensive expression for different phase velocities of the waves in the beam with respect to the wave speeds of the half-space. Apart from the Rayleigh type surface wave (quasi-elastic wave), an extra visco-elastic surface wave may exist in a visco-elastic half-space depending on the parameters of the half-space and the frequency range. The existence of this second surface wave has not been addressed within the field of train-induced ground vibration. The importance of this wave for the equivalent stiffness is analysed. An effective method to determine the frequency range for the visco-elastic surface wave to exist is proposed.

考虑使用粘弹性半空间上的周期性支撑梁来模拟铁路轨道的振动。假设半空间的粘度是开尔文-沃格特类型的。利用等效动态刚度的概念，半空间对轨枕的反作用由位于每个轨枕下方的相同弹簧系统代替。弹簧的频率相关等效刚度是相邻支座振动相移的函数。等效刚度是使用轮廓积分技术通过分析得出的，从而得出了光束中波相对于半空间波速的不同相位速度的综合表达式。除了瑞利型表面波（准弹性波）以外，取决于半空间的参数和频率范围，在粘弹性半空间中可能会存在额外的粘弹性表面波。在火车引起的地面振动领域中，还没有解决第二表面波的存在。分析了该波对于等效刚度的重要性。提出了一种确定粘弹性表面波存在频率范围的有效方法。