弹性长枕无砟轨道动刚度垂向耦合动力及能量分析

本文探索弹性长枕无砟轨道动刚度的变化规律、轨道动力刚度改变对车辆-轨道耦合系统中各构件动力响应及其与车辆、轨道子系统中能量(动能、势能)变化的关系。利用车辆-轨道耦合及哈密顿原理,列出耦合系统总动能、势能和阻尼做功方程并作一阶变分,按对号入座法得出耦合系统总质量矩阵、刚度矩阵和阻尼矩阵,再用Wilson-θ法求解微分方程。通过计算结果分析得出:轨道垂向动刚度与车速的变化规律;扣件刚度、枕下支撑刚度、道床板下(路基)支撑刚度各自对轨道动刚度的影响程度及其与耦合系统中各构件垂向位移、加速度之间的关系;车辆、轨道子系统势能(动能)与轨道动刚度之间的关系,势能(动能)也可作为评价轨道振动的依据。

Analysis on Coupling Dynamic Stiffness and Energy of Elastic Supporting Long-pillow Unballasted Track

The changing law of dynamic stiffness of the unballasted track with the elastic supporting long-pillow,and the relationship between changes of dynamic stiffness of track and dynamic responses of respective coupling system components and changes of energy(potential energy & kinetic energy) of vehicle and track sub-systems were sludied.The equations of total kinetic energy,potential energy and damping action work were written on the basis of the vehicle-track coupling principle and Hamilton’s principle,and first-order variation was made with the above equations.The total mass matrix,stiffness matrix and damping matrix of the coupling system were found,then the differential equations were solved by the wilson-θ method.The following conclusions are drawn through calculation and analysis:The relationship between the changes of vertical dynamic stiffness of track and the speed changes of vehicle;the degree of respective influence of fastening stiffness,under-sleeper support stiffnesss and under-slab support stiffness,on dynamic track stiffness and their relationship with the vertical displacement and acceleration of each coupling system component;the relationship between the potential energy(kinetic energy) of subsystems of vehicle & track and the dynamic stiffness of track,the potential energy(kinetic energy)being used as the criteria for evaluation of track vibration.