本研究旨在探討顆粒調諧質量阻尼器(Particle Tuned Mass Damper, PTMD)在軌道系統之減振應用。首先，提出顆粒調諧質量阻尼器耦合軌道系統的理論數學模型，並推導其動力運動方程式。接著，推導該系統之加速度頻率響應函數及目標函數，利用 最佳化方法最小化隨機激勵下結構相對位移的均方響應。根據頻率響應函數及目標函數，推導出PTMD的最佳設計參數解析解。並通過衝擊實驗數據擬合和分析PTMD耦合軌道模型的動力行為，比對PTMD填充不同填充材料、尺寸及填充率的實驗結果，以確保模型的準確性。結果顯示，數學模型與實驗數據高度一致。此外，藉由調整PTMD參數，利用分析數值模型在不同PTMD配置下對軌道減振效益的影響，並找出最佳參數組合。最後，考量軌道不平順度，並加載不同列車車速的垂向輪軌接觸力於軌道系統，探討不同PTMD參數下之減振效益。結果表明，應用PTMD於高頻軌道系統能顯著降低其振動響應，從而為軌道系統設計和列車激振力作用下之結構穩定性提供有效的應對策略。;This study aims to investigate the application of a Particle Tuned Mass Damper (PTMD) in vibration reduction for railway systems. Firstly, a theoretical mathematical model coupling the PTMD with the railway system is proposed, and the dynamic equations of motion are derived. Subsequently, the acceleration frequency response function and the objective function of the system are derived. optimization method is utilized to minimize the mean square response of the structure’s relative displacement under random excitation. Based on the frequency response function and objective function, the optimal design parameters of the PTMD are analytically derived. The dynamic behavior of the PTMD-coupled railway model is analyzed and fitted using impact test data. Experimental results with different filling materials, sizes, and filling ratios are compared to ensure model accuracy. The results show a high consistency between the mathematical model and experimental data. Additionally, by adjusting the PTMD parameters, the effect of different PTMD configurations on the vibration reduction of the railway is analyzed using a numerical model to find the optimal parameter combination. Finally, considering track irregularities and applying vertical wheel-rail contact forces at different train speeds to the railway system, the vibration reduction effect under various PTMD parameters is explored. The results indicate that applying PTMD to high-frequency railway systems can significantly reduce their vibration response, thereby providing an effective strategy for the design of railway systems and the structural stability under train-induced excitation forces.
