车辆-轨道非线性耦合动力学的精细积分法及其应用

提出精细积分法求解移动质量与结构相互作用的新的计算方法。分析焊接接头不平顺和轨枕悬空对轮轨力和轨道部件之间相互作用力的影响。该方法采用非齐次项的Duhamel积分的精细积分算法，避免状态空间下系统矩阵求逆。通过Lagrange插值多项式获得移动质量与结构相互作用的载荷项外插公式，无需迭代求解移动质量和结构非线性相互的动态响应。系统矩阵具有时不变性，无需反复计算指数矩阵。在每个积分步内，利用Euler梁的形函数分解移动载荷项，获得移动载荷与结构相互作用时间和空间连续变化的情况。计算结果表明，轮轨力的第一个峰值主要由于焊接接头不平顺造成，轨枕悬空主要影响轮轨力第二峰值。焊接接头不平顺区易出现轨枕悬空。轨枕悬空出现后，悬空区有扩大的趋势。

A precise integration method for vehicle-track nonlinear coupling dynamics and its application

A new method for solving interaction between a moving mass and a structure with the explicit precise integration method was proposed.When a vehicle ran on a track with weld irregularity and sleeper hanging,the wheel/rail force and the interaction force among the track parts were analyzed.The Duhamel integral of the inhomogeneous terms was calculated with the precise integration to avoid inversing the state-space system matrix.The extrapolation formula for the interaction load between the moving mass and the structure was obtained with Lagrange interpolation polynomial.The dynamic response to the nonlinear interaction between the moving mass and the structure was solved without iteration.The repeated calculation of the exponential matrix was not required due to the time-invariant system matrix generated.In each integration step,the moving load term was decomposed with the shape functions of an Euler beam to represent the continuous movement of the load.The results indicated that the first peak of the wheel/rail force is induced by weld irregularity;sleeper hanging influences the second peak of the wheel/rail force;hanging sleeper appears easily at rail weld;once there is one unsupported sleeper,the adjacent sleeper may hang.