Lateral-vertical coupled nonlinear vibration characteristics of HTS maglev based on multiscale method and experimental test

High-temperature superconducting (HTS) maglev systems provide inherently stable, non-contact levitation and low energy consumption, making them attractive for high-speed transportation applications. However, the nonlinear dependence of levitation and guidance forces with lateral and vertical displacements leads to pronounced lateral-vertical coupling effects. These coupled vibrations, especially under external perturbations, can activate a broad range of resonant frequencies, thereby potentially affecting ride stability and operational safety. In this study, the nonlinear lateral-vertical coupled vibration responses of an HTS maglev system are investigated through integrated theoretical analysis, numerical simulations, and experimental validation. A coupled levitation/guidance force model is established via numerical simulations, quasi-static measurements, and dynamic experiments. The multiscale method is applied to derive analytical solutions for the coupled dynamics, under free vibration, lateral primary resonance, and forced vibration at critical frequencies. Theoretical analysis and numerical simulations reveal that lateral disturbances not only induce significant vertical responses but also excite a rich spectrum of resonant modes, including sum and difference frequencies between the lateral and vertical natural frequencies. These phenomena are confirmed by dedicated forced vibration experiments over a wide frequency range. Comparisons demonstrate strong agreement between theoretical predictions, simulations, and experimental data. Importantly, the study identifies specific frequency regions where the external excitation matches the sum or difference of the system’s natural frequencies, which are critical for system stability and result in substantial amplification of coupled vibration amplitudes. The combined theoretical and experimental framework based on the multiscale method enables accurate prediction of the nonlinear lateral-vertical coupled dynamics in HTS maglev systems and clearly identifies the critical frequency regions that need to be avoided in design and operation. These findings are of great significance for ensuring the stability and safety of HTS maglev systems at high speeds and are essential for maintaining overall system reliability.