本研究針對被動式調諧質量阻尼器(Tuned Mass Damper, TMD)，以主動控制理論，提出最佳化設計方法，進行數值模擬分析，驗證此設計方法可通用於單自由度與多自由度結構，且不限於無阻尼或有阻尼結構，當結構遭受外力為風力或地震力時皆可適用。將運動方程式中之TMD設計參數移項配置，轉換TMD之回復力與阻尼力為控制力，使TMD最佳化參數設計問題，變為增益矩陣最佳化問題，並利用主動控制理論之直接輸出回饋方法，求解最佳增益矩陣。然而，設計出之最佳增益矩陣並非即為最佳TMD參數，無法一次求解出最佳TMD參數。對此，本研究進一步提出參數更新迭代之方法，將直接輸出回饋求得之最佳增益矩陣進行參數更新迭代，如此即可完成最佳TMD設計。不僅如此，針對不同減振需求之TMD設計目標，僅需選擇不同之輸出向量，組合出對應之權重矩陣求解即可，如此設計流程，既能應對不同減振需求之TMD設計問題，求解過程也十分直觀簡便。除此之外，本研究也將多元調諧質量阻尼器(Multiple Tuned Mass Dampers, MTMDs)最佳參數設計問題轉換為多個控制力輸入問題，再利用重新推導之多輸入控制力直接輸出回饋方法，同時求解多組增益矩陣，使MTMDs也能適用於本研究所提之設計方法。經由數值模擬，所求出之TMD最佳設計參數，可與隨機振動理論下之解析解相等，並優於近似解，驗證所提之設計方法之可行性。將分析結構擴展為多自由度，也確認可直接進行設計，使TMD設計能更接近真實情況。針對MTMDs設計，本研究之設計結果亦能使系統之均方反應能夠同等或優於參考文獻之MTMDs設計結果。;In this study, an optimal design method of passive tuned mass damper (TMD) based on active control theory is proposed. The numerical simulation analysis verifies that the design method can be applied to single-degree-of-freedom (SDOF) or multi-degree-of-freedom (MDOF) structures. Either undamped or damped structures are applicable. The proposed method also can be applied when the structure is subjected to external force such as wind forces or earthquake forces. In the equation of motion, the partial TMD parameters are shifted to the control term. Therefore, the restoring force and damping force of TMD are transformed into the control force. The optimization of TMD parameters design problem is therefore transformed into the gain matrix optimization problem. And the direct output feedback algorithm is used to solve the optimal gain matrix. However, the gain matrix obtained by solving direct output feedback algorithm is a conditional weight balanced optimal solution of system response and control force. The obtained gain matrix is not just the optimal TMD parameters which can minimize the mean square response of the main structure. In this regard, the present study further proposes a parameter updating iterative procedure. The optimal gain matrix obtained by solving direct output feedback is used for parameter updating iteration, so that the optimal TMD design parameters can be obtained. The proposed TMD optimization design method is a general method for different structures. For the reduction objective of various structural vibrations, the proposed method only requires to select the corresponding output matrices to cast the weighting matrix and quadratic initial condition matrix for computation. Such a design process can deal with the TMD design problems with different vibration reduction requirements intuitively and simply. In addition, this study also transforms the optimal parameters design problem of Multiple Tuned Mass Dampers (MTMDs) into multiple control force input problems. And the re-derived multi-input control force direct output feedback algorithm is used to solve multiple gain matrices. Therefore, the design of MTMDs can also be applied by the proposed method in this study. After numerical simulation results verification, the obtained optimal design parameters of the passive TMD are found to be equal to the analytic solution obtained by random vibration theory. Moreover, the obtained optimal TMD parameters are even better than the approximate solution. The verification results confirm that the proposed design method is accurate and feasible. Furthermore, expanding the analysis structure to the MDOF structure also confirms that the proposed design method can be carried out directly. So the TMD design can be much suitable for the real application. For the design of MTMDs, the verification results also show that the mean square response of the system is better than the design results of the MTMDs in the reference.
