可變擺長單擺式調諧質塊阻尼器之半主動控制

Semi-active control of pendulum-like TMD with variable length

連冠華(Kuan-Hua Lien)

指導教授 ： 鍾立來

共同指導教授 ： 吳賴雲(Lai-Yun Wu)

國立臺灣大學/工學院/土木工程學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.01770

摘要

現今對於調諧質塊阻尼器的研究已趨於成熟，且其應用已相當廣泛。但因其不具有適應性，且對於結構頻率波動相當敏感，再加上若非設計地震力及設計風力，則無法充分發揮原設計之下的減振效果。因此進一步發展出主動調諧質塊阻尼器，在外力作用下，可藉由量測系統反應並即時回饋給控制系統，進而進行控制。主動調諧質塊阻尼器雖具有適應性，然而其耗能較大，更有穩定性的疑慮。近年來半主動調諧質塊阻尼器逐漸受到重視，藉由調整系統結構參數，如勁度、阻尼或摩擦力來間接達到控制的效果，即其綜合了調諧質塊阻尼器的穩定性與主動調諧質塊阻尼器的適應性。有鑑於此，本文除了探討可變擺長單擺式調諧質塊阻尼器之半主動控制外；且亦提出單擺式調諧質塊阻尼器之最佳化理論，以進行最佳化單擺式調諧質塊阻尼器與可變擺長單擺式調諧質塊阻尼器之比較。針對消能不足，提出最佳化勁度控制法則，藉由此控制變化擺長，可提供可控回復力，以進行消能；針對離頻效應，提出適應性勁度控制法則，藉由兩種識別方法，一為Hilbert轉換及多項式擬合；二為結構最大反應之關係，可各自分別識別結構之瞬時頻率，進而調整擺長，以維持最佳頻率比；針對消能不足及離頻效應，藉由組合適應性及最佳化勁度之控制法則，以克服之。分別以多自由度結構及其經單自由度化之結構為例，於白噪音風力作用下，進行三種勁度控制法則之數值模擬及參數分析。依據數值結果，不論多自由度結構或其經單自由度化之結構，可變擺長單擺式調諧質塊阻尼器採用最佳化勁度控制法則，均可補足消能不足且亦可完全取代單擺式調諧質塊阻尼器之黏滯消能；採用適應性勁度控制法則，均可克服離頻效應；更進一步驗證，藉由組合勁度控制法則，均可同時克服消能不足及離頻效應。並由參數分析可知，可變擺長單擺式調諧質塊阻尼器採用最佳化勁度控制法則，在結構減振效果方面，均對於頻率比相當靈敏，而對阻尼係數則不靈敏；採用適應性勁度或組合勁度控制法則，均對於頻率比及阻尼係數則不甚靈敏。另於正弦外力下，對應三種勁度控制法則之特性下改變外力振幅或頻率，可知三種勁度法則之強健性均優於單擺式調諧質塊阻尼器。最後採用經單自由度化之台北101大樓作為實際案例，於設計風力下，進行可變擺長單擺式調諧質塊阻尼器採用三種勁度控制法則之可行性驗證。經數值分析之驗證，確實發揮減振效果，符合舒適度之要求。

關鍵字

單擺式調諧質塊阻尼器 ； 最佳化設計理論 ； 可變擺長 ； 可變勁度 ； 半主動控制 ； 最佳化勁度控制 ； 適應性勁度控制 ； 組合勁度控制

並列摘要

The tuned mass damper has been well developed and widely applied in vibration reduction for buildings today. However, it is very sensitive to frequency ratio and not adaptive under winds which are different from the design ones. For this reason, an active tuned mass damper was developed. Although active tuned mass damper possesses adaptive function, it must have control algorithms, sensors and external power. Stability may also be a problem. In recent years, the semi-active tuned mass damper is widely studied because it combines the stability of passive tuned mass damper with adaptability of active tuned mass damper. Its adaptive function is realized only by changing system parameters to reach the control effect indirectly.
In view of this, the semi-active control of pendulum-like tuned mass damper (SAPTMD) with variable pendulum length is investigated. In addition to the optimal design theory for the pendulum-like tuned mass damper (PTMD) with nonlinear viscous damper, the optimal, adaptive and combined stiffness control algorithms for SAPTMD are proposed and compared in this study. When the dissipated energy is insufficient for the demand of SAPTMD, the controllable restoring force is provided by variable pendulum length based on optimal stiffness control algorithm to dissipate energy. For the detuning effect, the adaptive stiffness control algorithms through two identified methods which are Hilbert transform-polynomial fitting and relation of maximum structural responses to track the instantaneous frequency of structure to keep the optimal frequency ratio by variable pendulum length. When the inadequate energy dissipation and the detuning effect occur simultaneously, it can be overcome through the combination of optimal and adaptive stiffness control control algorithms.
The multi-degree-of-freedom (MDOF) and single-degree-of-freedom (SDOF) structures implemented with the SAPTMD using three stiffness control algorithms under the white-noise wind, respectively, are taken as examples to conduct the numerical simulation and parameter analysis. Based on numerical results, no matter the structure is MDOF or SDOF, the functions of the SAPTMD using three stiffness control algorithms can be achieved, respectively. By the parameter analysis results, the effectiveness of the SAPTMD using optimal stiffness control algorithm is sensitive to the frequency ratio but not that sensitive to the damping coefficient; the SAPTMD using adaptive stiffness control algorithms or combined stiffness control algorithms are not sensitive to both frequency ratio and damping coefficient. The robustness of the SAPTMD using three stiffness control algorithms are better than that of the PTMD under sinusoidal wind force, respectively. Finally, the feasibility of the SAPTMD using the three stiffness control algorithms is illustrated numerically by using the Taipei 101 subjected to the design wind force. From the numerical verification, SAPTMD using the three stiffness control algorithms are so effective that the requirement of serviceability of the buildings can be met.

並列關鍵字

pendulum-like tuned mass damper ； optimal design theory ； variable pendulum length ； variable stiffness ； semi-active control ； optimal stiffness control ； adaptive stiffness control ； combined stiffness control

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