Correspondence Between Alignment Wavelength and Vehicle Response Wavelength of High-Speed Rails

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The acceleration of the vehicle body is closely related to the wavelength components of the track, making the design of track alignments crucial for enhancing the comfort of high-speed rail travel. However, research on the effects of long-wavelength deformations on alignment design and their impact on vehicle dynamics remains limited, and existing methodologies fail to effectively calculate the wavelengths of traditional alignments, which consist of linear segments and vertical curves. This study introduces a novel approach for computing long-wavelength track alignments and vehicle response wavelengths using signal decomposition and the Hilbert transform. A comprehensive program is developed to analyze the relationship between alignment and vehicle response wavelengths through correlation coefficients and coherence functions. The results show that traditional alignments have predominant wavelengths exceeding 1 000[Formula: see text]m, which exhibit negligible correlation with vehicle response due to the dominant influence of alignment curvature. In contrast, Fourier series-designed alignments demonstrate a significant correlation with vehicle response, particularly under high-speed conditions. Quantitatively, vehicle response wavelengths are found to range from 1[Formula: see text]000[Formula: see text]m to 5[Formula: see text]000[Formula: see text]m, with Fourier series alignments effectively reducing dynamic impacts. These findings highlight the potential of the proposed approach in optimizing track design for challenging railway sections, providing valuable guidance for improving high-speed railway operations.