Response of a maglev vehicle moving on a series of guideways with differential settlement

The objective of this study is to investigate the dynamic response of a maglev (magnetically levitated) vehicle traveling over a series of guideway girders undergoing ground support settlement. The maglev vehicle is simulated as a rigid car body supported by a rigid levitation frame using a uniformly distributed spring–dashpot system, and the guideway unit is modeled as a series of simple beams with identical span. To carry out the interaction dynamics of maglev vehicle/guideway system, this study adopts a PI (proportional-integral) controller with constant tuning gains based on Ziegler–Nicholas (Z–N) method to regulate the electromagnetic forces between the magnetic-wheels and guide-rail. For the inclusion of support movements, the total response of the simple beam is decomposed into two parts: the static response due to support settlement and the dynamic component caused by inertia effect of beam vibration. Once the static displacement for a simple beam undergoing vertical support movements is derived, the remaining dynamic response of the maglev vehicle/guideway system is solved by Galerkinʹs method and computed by an iterative approach using Newmarkʹs finite difference formulas. Numerical studies indicate that the increase in levitation gap for a maglev vehicle may result in larger vehicleʹs response, but the response of the maglev vehicle with smaller air gap will be significantly amplified at higher speeds once ground settlement appears at the guideway supports.