基于对称性的三维车辆轨道耦合系统随机振动虚拟激励方法

Efficient random vibration analysis of 3D-coupled vehicle-track systems based on symmetry principle

基于结构的对称性提出了用于三维车辆轨道耦合系统高效随机动力响应分析的虚拟激励方法。车辆采用刚体动力学模型,轨道结构利用三维轨道广义单元建模,车辆与轨道通过线性轮轨关系耦合。采用虚拟激励法将高低、方向和水平三类轨道不平顺转化为一系列简谐的虚拟不平顺;考虑车辆及轨道结构的对称性,分别推导了耦合系统的对称和反对称凝聚矩阵,提出了用于车辆轨道耦合系统动力响应计算的自由度凝聚方法,将耦合系统的自由度缩减至原来的一半以下,并在此基础上实现了耦合系统随机振动的高效分析。数值算例将本文方法与传统有限元方法进行对比,验证了本文方法的正确性和有效性。

An efficient method for random vibration analysis of 3D-coupled vehicle-track systems based on pseudo-excitation method （PEM） and symmetry principle is developed. The vehicle is regarded as a spring-mass-damper system and the track is modeled by the generalized finite element method, they are coupled via linear rail-wheel relationship. Initially the PEM is used to transform the complicated random vibration analysis into the simple pseudo response analysis by transforming the three types of rail irregu- larities into deterministic harmonic excitations. Considering the symmetry of the vehicle and the track, the symmetric and anti-symmetric condensation matrices are then established. The symmetric condensation method for analyzing the random vibration of the coupled vehicle-track system is developed accordingly. More than half of the degrees of freedom of the coupled system are condensed in this way, which considerably reduces the computational effort. The proposed method is justified by comparison with the conventional finite element method.