鐵道道岔岔心區因斷面幾何與基礎剛度存在高度不連續性，列車通過時會激發複雜的輪軌動力相互作用，若發生軌枕下道碴掏空，將嚴重威脅行車安全。傳統三維有限元素模型計算成本龐大，有鑑於此，本研究基於車輛—軌道耦合動力學理論，結合 SolidWorks 三維斷面切分，建置了高效且準確的二維縱向平面耦合動力學數值模型，其垂直加速度模擬結果與現地實測數據高度吻合。隨後，針對多組車速、掏空範圍及掏空深度規劃了全面的參數化敏感度分析。
時域分析顯示，枕下掏空會顯著放大系統振動幅值，但當深度超越系統的「動態垂向位移極限」時，響應會呈現封頂的動力飽和鈍化現象。此外，當掏空深度適中且列車高速通過時，軌枕會與道碴床發生劇烈的撞擊，導致正向加速度峰值反常地飆升至負向峰值多倍，成為判定軌枕實質觸底衝擊的核心指標。
頻域分析部分，本研究透過 1/3 倍頻帶深度分析，成功篩選出具備高敏感度的特徵指紋頻率：
1. 掏空範圍判別：中心頻率 16 Hz、20 Hz與25 Hz（負相關指標）可作為判定「掏空軌枕數量」的黃金頻率組合，16 Hz約至良好狀態下之3至4倍，20 Hz約4至5倍，25 Hz約5至6倍便需要特別注意。
2. 掏空程度診斷：中心頻率 80 Hz（負相關）可做為判斷掏空深度的指標，在良好狀態的0.75倍左右便需要特別注意；160 Hz（正相關）則須在良好程度的3至4倍便需要特別注意維護。
綜上所述，本研究提出「低頻看剛度、高頻看衝擊」的多頻率交叉驗證機制，為特殊道岔結構的健康監測與預防性維修養護提供了高信賴度的理論依據。

The railway turnout frog zone experiences severe wheel-rail dynamic interactions due to structural discontinuities, which are exacerbated by sub-sleeper ballast voids. To overcome the high computational costs of 3D models, this study establishes an efficient 2D vehicle-track coupled dynamics model. The model's vertical acceleration predictions demonstrate high agreement with field measurements.
Parametric analyses across various train speeds, void numbers, and void depths reveal key dynamic indicators:
• Time-Domain Behavior: Ballast voids amplify accelerations up to a saturation limit set by vertical displacements. At high speeds and moderate depths, severe sleeper-ballast impacts cause positive acceleration peaks to abnormally exceed negative peaks by up to 1.7×.
• Frequency-Domain Diagnosis (1/3-Octave): Center frequencies at 16, 20, and 25 Hz correlate strongly with the number of unsupported sleepers, surging 3–6× above baseline. Meanwhile, the 80 Hz band drops below 0.75× baseline and the 160 Hz band surges 3–4× under deep voids (≥3 mm), providing a complementary metric for void depth assessment.
In conclusion, this research provides a multi-frequency framework—"low frequencies reflect stiffness, high frequencies reflect impacts"—for the structural health monitoring and maintenance of turnout frogs.

[1] D. Milne, L. L. Pen, D. Thompson and W. Powrie, "Properties of train load frequencies and their applications," Journal of Sound and Vibration, vol. 397, pp. 123-140, 2017.
[2] M. Sysyn, O. Nabochenko and V. Kovalchuk, "Experimental investigation of the dynamic behavior of railway track with sleeper voids," Railway Engineering Science, vol. 28, no. 3, pp. 290-304, 2020.
[3] J.-Y. Shih, D. Kostovasilis, Y. Bezin and D. J. Thompson, "MODELLING OPTIONS FOR BALLAST TRACK DYNAMICS," in 24th International Congress on Sound and Vibration, London, 2017.
[4] J.-Y. Shih, Models of vehicle/track/ground interaction in the time domain, Southampton: University of Southampton, 2017.
[5] V. Markine, M. Steenbergen and I. Shevtsov, "Combatting RCF on switch points by tuning elastic track properties," Wear, vol. 271, pp. 158-167, 2011.
[6] C. Wan, V. L. Markine and I. Y. Shevtsov, "Analysis of train/turnout vertical interaction using a fast numerical model and validation of that model," Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, vol. 228, no. 7, pp. 730-743, 2013.
[7] Network Rail, “Inspection and Maintenance of Permanent Way,” Network Rail, London, 2012.
[8] 黃冠瑜, 枕間距對軌道承載力之影響分析, 台南市: 國立成功大學土木工程研究所碩士論文, 2024.
[9] 曾庭峰, “軌道支承掏空對岔心結構疲勞壽命影響之數值模擬,” 國立成功大學土木工程研究所碩士論文, 台南市, 2026.