A Non-Iterative Integration Scheme Enriching the Solution to the Coupled Maglev Vehicle–Bridge System

Abstract

A non-iterative integration scheme is presented in this study to enrich the solutions to the coupled equations of the maglev vehicle–bridge system. The proposed integration scheme is composed of two integration methods aiming at providing the solutions to equation of motion and state-space equation. First, the equation of motion of the simply supported girder bridge is transformed by the modal superposition method. Then the state-space equation is used to describe the motions of both the vehicle and the suspension control system, with the associated matrices assembled using the fully computerized approach. By adopting this integration scheme, only pure vector calculations arise in the solution process, regardless of the existence of time-dependent displacement and velocity on the right-hand sides of the two coupled equations. The proposed integration method is of the second-order accuracy with and without damping. Being equipped with adequate numerical dissipation and dispersion, the method also possesses the characteristic of little computing errors, as can be achieved through the use of different pairs of parameters. Finally, numerical simulations have been conducted to assess the influence of different feedback gains, three types of bridges with different lengths, and guideway irregularity on the maglev vehicle–bridge system.