改良之壓電調諧質量阻尼器及其應用於台北101之最佳化概念設計

Improved Piezoelectric Tuned Mass Damper and Its Optimal Conceptual Design for Taipei 101

何彥葳(Yen-Wei Ho)

指導教授 ： 鍾立來

共同指導教授 ： 賴勇安(Yong-An Lai)

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202000422

摘要

結構可藉由加裝調諧質量阻尼器（Tuned Mass Damper, TMD）透過阻尼器來消散能量以降低振動量，而壓電調諧質量阻尼器（Piezoelectric Tuned Mass Damper, Piezo-TMD）則以壓電材料將振動能轉換為電能做利用，既減少振動又能擷取能量，可是就過去壓電調諧質量阻尼器之組成，在極限狀況下，壓電材料之破壞會導致質量塊失控，此外，該組成也並不適用於台北101之懸吊系統，且過去Piezo-TMD曾以平均功率最大化做最佳設計，但其中引用以結構位移均方最小化做TMD之最佳設計所得到之最佳頻率比，使得Piezo-TMD之最佳設計依賴於TMD之最佳設計，因此，本文提出新Piezo-TMD之模型及Piezo-TMD之機械頻率比與電路頻率比以改善上述問題。
新Piezo-TMD模型之控制方程式首先被推導出，其中顯示Piezo-TMD有機械頻率與電路頻率，單自由度結構加裝Piezo-TMD受外力之控制方程式接著被推導出以做分析與設計。由於Piezo-TMD之兩作用為擷取能量及減少振動，因而以平均功率最大化與結構位移最小化做Piezo-TMD之最佳設計，為使最佳設計適用於各種不同結構，四個無因次參數被提出並應用於設計，設計參數之最佳值即透過使電路功率的H2-norm最大化及結構位移的H2-norm最小化藉由直接搜尋法得到。不同質量比和結構阻尼比的最佳設計參數被整理成表格供查表法之用，而因平均功率最大化近乎確保結構位移最小化，僅利用曲線擬合與迴歸分析提出Piezo-TMD之平均功率最大化設計公式，隨後，一套設計流程被提出，而後以台北101作為案例簡化為單自由度結構，設計出Piezo-TMD之參數，並進行風力歷時分析，確認其符合減振與能量擷取之需求後，完成Piezo-TMD構件之概念設計，其令實際組裝Piezo-TMD更趨實現，最後於數值上驗證概念設計之Piezo-TMD之減振及擷能效果。

關鍵字

壓電調諧質量阻尼器 ； 最佳設計 ； 台北101 ； 概念設計

並列摘要

Structural vibration can be reduced by installing a tuned mass damper (TMD), which dissipates the vibration energy through dampers, whereas a piezoelectric tuned mass damper (Piezo-TMD), which converts the vibration energy into electric energy to use, not only reduces structural vibration but also harvests energy. However, with the previous configuration, in extreme states, failure of the piezoelectric material leads to out of control of the mass block. Besides, that configuration is not applicable for the pendulum system in Taipei 101, and previous Piezo-TMD was optimally designed by maximizing mean power yet with the citation of optimal frequency ratio emanated from the optimal design of TMD by minimizing mean square of structural displacement, which makes the optimal design of Piezo-TMD dependent on the optimal design of TMD. Therefore, a new model of Piezo-TMD, mechanical frequency ratio, and electrical frequency ratio are proposed to account for the defects.
Governing equations of the new Piezo-TMD model, which reveals the existence of mechanical frequency and electrical frequency of Piezo-TMD, are first derived. Governing equations of a single-degree-of-freedom (SDOF) structure subjected to external loading with installation of Piezo-TMD are subsequently derived to analyze and design. Because two purposes of Piezo-TMD are to harvest energy and reduce vibration, Piezo-TMD is optimally designed by either maximizing mean power or minimizing mean structural displacement. To let the optimal design be applicable for various structures, four dimensionless parameters are proposed and utilized in the design. Optima of the design parameters are obtained through Direct Search Method by either maximizing H2-norm of power of the circuit or minimizing H2-norm of structural displacement. Optimal design parameters with different mass ratios and structural damping ratios are organized into tables for table method. Since minimization of mean structural displacement is approximately ensured by maximization of mean power, only optimal design formulas for maximal mean power are suggested by regression analysis. An optimal design procedure is proposed thereafter. Taipei 101 is taken as a case to be simplified to a SDOF structure. Parameters of Piezo-TMD are designed. Time history analysis of wind is conducted to confirm the requirement of vibration reduction and energy harvesting is satisfied. Conceptual design of each component of Piezo-TMD is then completed, which makes assemblage of a Piezo-TMD in reality feasible. Eventually, the effect of vibration reduction and energy harvesting of the conceptually designed Piezo-TMD is verified numerically.

並列關鍵字

piezoelectric tuned mass damper ； optimal design ； Taipei 101 ； conceptual design

參考文獻

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