车轨系统随机响应周期性拟稳态分析

提出用于三维车轨耦合系统随机动力响应高效求解的周期性拟稳态分析方法. 车辆采用三维刚体动力学模型,轨道结构利用三维轨道广义单元建模. 假定轨枕间距均匀,则列车在轨道上行驶过程中,车轨耦合系统动力学方程具有典型周期时变特征. 应用虚拟激励方法将轨道随机不平顺转化为虚拟简谐不平顺,在状态空间下运用周期系数微分方程的性质和Schur分解技巧将上述问题的求解转化为周期性拟稳态响应分析,只需通过求解系数矩阵为上三角的线性方程组即可代替以往时变系统虚拟响应求解过程中的逐步积分过程,计算效率获得较大提高. 采用该方法进行了三维车轨耦合系统的随机动力响应分析,并进行了不平顺随机载荷在车体、转向架、轮对和轨道等部件中传递机理分析,获得了一些有价值结论. 

A PSEUDO-STEADY STATE METHOD FOR' ANALYZING RANDOM RESPONSES OF COUPLED VEHICLE-TRACK SYSTEMS

A pseudo-steady state method for analyzing random responses of coupled vehicle-track systems subjected to track irregularities is developed. The vehicle is simplified as a three dimensional multi-rigid body dynamic system and the track is modeled by the generalized finite element method. Assume that the sleeper spans are uniform, and then the equation of motion of the coupled system is periodically time-varying. Pseudo-excitation method (PEM) is used to transform the three types of rail irregularities into harmonic pseudo-excitations; the differential equations theory and the Schur decomposition scheme are then applied to develop a pseudo-steady state method for solving the above equation of motion. In this method, a linear equation set with an upper triangular coefficient matrix is established to replace the conventional step-by-step integration process when calculating the pseudo-responses of PEM which considerably reduces the computational effort. The random response of a three-dimensional coupled vehicle-track system is analyzed in the numerical example and the transmission mechanism of random vibration in the coupled system is investigated.