Modelling dynamic interaction of maglev train–controller–rail–bridge system by vector mechanics

The dynamic coupling interaction of maglev train–controller–rail–bridge (TCRB) system has the potential to induce instability of travelling maglev trains. The conventional contact-type finite element model (FEM) method is difficult in modelling the TCRB system in the presence of non-contact levitation between the maglev vehicle and guideway and in incorporating the time-variant mechanism of suspension controllers in a high-dimensional FEM. In this study, we develop a new method, which endeavours to overcome the above difficulties, for modelling the maglev TCRB system and its dynamic interaction in the context of vector mechanics (VM). The VM underlies the principles on formulating vector form intrinsic finite elements (VFIFEs) to solve problems such as large deformation, large displacement, structural discontinuity, and non-contact mechanisms. In the VM formulation, we model the vehicle bodies, suspension bogies, and electromagnets as a collection of mass particles rigidly connected or linked by spring–dashpot units, with the levitation forces between the F-type rail and electromagnets being commanded by feedback controllers. Meanwhile, the guideway, including rail and bridge, is modelled as a group of mass particles linked by VFIFEs. The equations of motion for each mass particle are solved individually without need of assembling a global stiffness matrix, thereby eliminating the problems of ill-conditioning and numerical divergence. The proposed modelling method is validated by comparing the measured vehicle and bridge responses from a full-scale maglev train during its running on a test line with the computed results by the proposed method. After validation, the vertical and pitching resonant characteristics of the maglev system and the condition to invoke levitation gap resonance are evaluated.