高铁连续梁桥横向变形与轨面几何形态变化的映射关系研究

为研究高速铁路桥梁结构横向变形与轨面变形间的映射关系，在考虑高速铁路桥梁-路基-无砟轨道系统层间相互作用的基础上，基于势能驻值原理，推导出连续梁桥横向变形与轨面变形的微分方程及边界条件，提出连续梁桥横向变形与轨面变形的映射解析模型。利用所提的解析方法及有限元方法分别求解连续梁桥横向变形下的钢轨变形，并研究横向变形幅值不确定性对轨面变形的影响。结果表明：两种方法求解结果吻合良好，验证了所提的解析模型的正确性；桥梁结构变形与轨面变形的映射系数随桥梁结构变形幅值的增加而非线性增大；钢轨变形具有明显的“跟随性”；钢轨变形及层间扣件内力随连续梁桥变形幅值的增大而增大；列车运行速度越快，钢轨变形引起的激励频率越大。

Mapping relationship between continuous girder bridge transverse deformation and rail geometric changes of high-speed railway

The mapping relationship between bridge structure transverse deformation and rail deformation of high-speed railway was studied. Based on the potential energy principle, differential equations and boundary conditions of continuous girder bridge transverse deformation and rail deformation were derived, and a mapping analytical model of continuous girder bridge transverse deformation and rail deformation was proposed considering the interaction between layers of bridge-subgrade-ballastless track system of high-speed railway. Analytical and finite element methods were used to solve the rail deformation under continuous girder bridge transverse deformation, and the influence of the uncertainty of transverse deformation amplitude on rail deformation was revealed. The results show that the two methods are in good agreement with each other, which proves the correctness of the analytical model. The mapping coefficient between bridge deformation and rail deformation increases nonlinearly with the increase of the deformation amplitude of continuous girder bridge. The rail deformation has obvious ‘following features’. The rail deformation and fastenings internal force increase with the increase of the deformation amplitude of continuous girder bridge. The faster the train runs, the greater the excitation frequency caused by rail deformation.