Superconducting electrodynamic suspension (EDS) trains promise very high-speed transport, yet electromechanical coupling can induce vibrations because of low or even negative damping, aggravated by track irregularities and high-frequency harmonics from discrete levitation and guidance coils (LGCs). An electromechanical coupling framework is developed together with an electromagnetic shunt damper (EMSD) for vibration suppression. An EDS train model integrates dynamic circuit representations of LGCs and damping coils with vehicle motion equations. The electromagnetic force module is validated against finite element simulations and experiments. A speed-based stepping window algorithm enables long-track simulation with reduced computational burden for mutual inductance and circuit matrices. Using fixed point theory, geometric and electrical parameters of the electromagnetic damper (EMD) and EMSD are optimized, and parameter sensitivity analysis examines how deviations in electromagnetic quantities affect attenuation across frequency bands. Simulations of suspension bogie system under random track irregularities show clear suppression by both an EMD and the EMSD; relative to EMD, EMSD reduces lateral acceleration RMS by 27.3% and vertical acceleration RMS by 17.5%. For a full train system at 600 km/h, EMSD reduces lateral acceleration RMS by 28.9% to 38.0% and vertical acceleration RMS by 2.4% to 7.4%, and lowers the vehicle body Sperling ride comfort index. By aligning electromagnetic and mechanical resonances, the optimized EMSD provides strong damping, most of all in the lateral direction. The framework offers a practical and scalable route to improve the dynamic stability of superconducting EDS trains, and future work will explore adaptive parameter tuning and intelligent control to coordinate damping across multiple vibration modes.
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