| 摘要: | 調諧質量阻尼器(Tuned Mass Damper, TMD)為一種被動式振動控制裝置，廣泛應用於抑制結構物於風力、地震或外力激振下之動態反應。然而，傳統TMD設計易受限於附加質量較高、頻率調整困難、安裝空間需求大及阻尼元件易劣化等問題，使其於高層建築、長跨橋梁及離岸設施等結構中之實務應用產生限制。為提升其工程可行性與穩定性，本研究提出電磁式慣質調諧質量阻尼器(Electromagnetic Inerter-based Tuned Mass Damper, EMI-TMD)系統，整合電磁式慣質阻尼器(Electromagnetic Inerter-based Damper, EMID)取代傳統黏滯性阻尼(Viscous Damper, VD)元件，進一步強化系統之阻尼調控能力。EMID利用滾珠螺桿轉換直線運動為旋轉運動，結合飛輪發電機構進而放大慣質與可變阻尼特性，並同時有效克服離頻效應及滿足維修需求，增強振動控制的穩定性及適應性。
本研究建立結構裝設EMI-TMD系統之耦合數學模型，推導其動態平衡方程式以得到在地震與外力激振條件下之轉換函數。為進一步探討慣質與阻尼參數對系統動態行為之影響，採用結構系統反應之均方反應值作為性能指標，透過應用H2範數於頻率範圍內量化振動反應量，並針對無阻尼主結構裝設EMI-TMD系統進行最佳參數設計。接著，利用最佳參數迭代法推導具阻尼主結構裝設EMI-TMD系統之最佳參數迴歸設計公式。最後，透過數值模擬驗證EMI-TMD系統於地震力與掃頻激振下之減振效能，並與傳統TMD進行性能比較。分析結果顯示，在附加質量減少超過20%之情況下，EMI-TMD仍能維持良好之減振效能，展現其於輕量化應用上之顯著潛力，對未來結構系統之減振設計具高度發展性與實用價值。
;The Tuned Mass Damper (TMD) is a passive vibration control device widely used to suppress the dynamic responses of structures under wind, seismic, or external excitations. However, traditional TMDs face several limitations, including high additional mass, difficulty in frequency tuning, large installation space requirements, and degradation of damping components over time, which restrict their practical application in high-rise buildings, long-span bridges, and offshore structures. To enhance engineering feasibility and long-term stability, this study proposes an Electromagnetic Inerter-based Tuned Mass Damper (EMI-TMD) system that integrates an Electromagnetic Inerter-based Damper (EMID) in place of the conventional Viscous Damper (VD), thereby enhancing damping control capabilities. The EMID converts linear motion into rotational motion via a ball screw, using a flywheel-generator mechanism to amplify inertia and provide variable damping, effectively addressing detuning effects while offering easier maintenance and greater adaptability.
A coupled mathematical model of the structure with the EMI-TMD system is developed, and its dynamic equilibrium equations are derived to obtain transfer functions under seismic and external excitation. To evaluate the effects of inertance and damping parameters on system behavior, the mean-square response of the structural system is adopted as the performance index. The H2 norm is applied in the frequency domain to quantify vibration energy, and optimal parameter design is conducted for the undamped primary structure equipped with EMI-TMD. Subsequently, a regression-based optimal parameter formulation is derived for damped structures using an iterative optimization approach. Finally, numerical simulations are carried out to evaluate the vibration mitigation performance of the EMI-TMD system under seismic and sweep-frequency excitations and compared with that of the traditional TMD. Results demonstrate that the EMI-TMD achieves comparable or superior control performance even with over 20% reduction in additional mass, highlighting its significant potential for lightweight vibration control applications and practical structural implementation in the future. |
