## 5 Conclusions  
The commonly used steel-spring floating slab track can effectively control environmental vibration in the frequency band higher than \(\sqrt{2}\) times its natural frequency, but the ground vibration is universally amplified at the natural frequency of the tracks, which has a significant negative impact on the normal use of precision instruments and other aspects. A novel ground vibration control method that considers frequency matching for environmental vibrations in combination with metro vibration source reduction and propagation path isolation was developed in this paper. Two types of periodic row piles were designed based on the Bloch-Floquet theory, and special FSTs, a 3D train-FST coupled model in the frequency domain established for the first time and a 3D track bed-soil-row-pile coupled FE model, were established to evaluate the effectiveness of the proposed vibration control method. This joint vibration control method not only solves the control problem of low-frequency vibration (especially the vibration around the natural frequency of the FST), but also achieves full-frequency ground vibration control, which could provide a solution to the difficult problem of train-induced ground vibration that is currently prevalent. The main conclusions of this study are as follows. 1. CFSTs can reduce the frequency vibration level by up to 40 dB, but vibration amplification occurs at 10 Hz, with an amplification of approximately 8 dB. After thickness adjustment, damping and FST stiffness reduction, the natural frequency of the FST shifts to a low frequency of 8 Hz, and the ground vibration decreases by approximately 5-8 dB in the frequency band near the natural frequency of the FST, but the vibration amplification does not be change. 2. The use of FST can significantly decrease the ground vibration acceleration, and the RMS value of vibration acceleration can be reduced by one order of magnitude. Adding row piles in FST lines can further reduce the RMS value of the ground vibration response by approximately 0.2 \(\times\) 10\({}^{-4}\) m/s\({}^{2}\). 3. The designed local resonance periodic row piles, whose bandgap range is adjusted to 7-9 Hz, can effectively reduce ground vibration at the natural frequency of the FST, with a decrease of 3-5 dB, which is lower than the ground vibration level under ordinary track conditions. 4. Replacing local resonance-type row piles with hollow pipe piles significantly decreases the ground vibration below 7 Hz, which can be reduced by 4-10 dB compared with  
Figure 17: Calculated ground vibrations under different working conditions. the conditions for local resonance row piles. This also decreases the ground vibration amplification at the natural vibration frequency of the FST, and the vibration level is lower than that of the ordinary track condition at this frequency. 5. The proposed comprehensive vibration control method that considers frequency matching and combines vibration reduction from the vibration source and propagation path solves the ground vibration amplification problem at the natural frequency of the FST in metro lines. Compared with ordinary tracks, the frequency vibration can be decreased by 4-12 dB in the frequency band below 20 Hz and by 10-35 dB in the frequency band above 20 Hz, realising ground vibration control in the full-frequency band. This study provides a new and effective method for vibration control in scenarios such as when using precision instruments. Conceptualization, B.J. and C.Q. ; methodology, J.L., M.M. and W.H. ; software, X.T. and B.J. ; validation, S.W. and X.T. ; formal analysis, C.Q. and X.T. ; investigation, X.T. and S.W. ; data curation, W.H. and S.W. ; writing--original draft preparation, X.T. ; writing--review and editing, X.T. and W.H. ; supervision, C.Q. and M.M. ; project administration, J.L. ; funding acquisition, B.J. and M.M. All authors have read and agreed to the published version of the manuscript.