壓電調諧質量阻尼器之研究

Study on Piezoelectric Tuned Mass Damper

周維苓(Wei-Ling Chou)

指導教授 ： 鍾立來

共同指導教授 ： 賴勇安

國立臺灣大學/工學院/土木工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801711

摘要

近年來能源的需求持續提高，且環保意識抬頭，如何將綠色能源再利用，成為各國目前的研究重點之一。由於土木結構與材料技術的發展，結構物建造越趨經濟，建築物及橋樑等外觀漸趨細長，結構週期也隨之延長，使得高樓建築物較易受風力振動，橋樑結構也較易受人行等活動激振，土木工程師為了降低振動量，遂以以加裝調諧質量阻尼器 （Tuned Mass Damper, TMD） 的方式，透過調諧質量阻尼器的振動頻率與結構自然頻率調諧，抑制結構的反應，並透過阻尼器來消散傳入之振動能。為了不要將振動能就此消散掉，本研究探討如何將這些能量收集起來再利用，故提出「壓電調諧質量阻尼器 (Piezoelectric Tuned Mass Damper, Piezo-TMD) 」，以壓電材料將機械振動能轉換為電能，再進行能量擷取。本文首先提出新型Piezo-TMD之模型，沒有加裝阻尼器，並將壓電材料與彈簧串聯，推導出Piezo-TMD系統加裝在單自由度結構之運動方程式，除了運動方程式，Piezo-TMD另有電路方程式，兩方程式互為耦合，且比傳統TMD多一電路振盪頻率，不論是運動方程式或是設計參數都比傳統的調諧質量阻尼器更多更複雜。本文之Piezo-TMD設計目標為能量擷取的平均功率最大化，遂以使電路功率的H2-norm最大化作為Piezo-TMD之最佳設計參數，並以台北101簡化為單自由度結構進行數值模擬，結果顯示Piezo-TMD具有與傳統TMD相近之結構減振效果，並可將風力所引致之振動能轉為可再利用之電能。本文藉由參數分析，掌握系統反應對參數之敏感度，顯示Piezo-TMD除其機械之自然頻率需與結構相調諧外，其電路之自然頻率也需與結構調諧，方可使結構之振動能量有效利用共振效應轉移至電路上。本研究釐清Piezo-TMD眾多設計參數之間的關係，簡化為四個無因次參數，並提出Piezo-TMD的設計公式，針對不同結構阻尼比和質量比的Piezo-TMD設計參數，利用曲線擬合與迴歸法提出單自由度結構加裝Piezo-TMD最佳化設計公式與查表法，並提出一套簡易的設計流程讓工程師可簡便、準確且快速地設計Piezo-TMD。最後利用一座人行橋作為案例，將其簡化為單自由度結構，透過最佳化設計公式與設計流程找出Piezo-TMD之最佳設計參數，進行歷時分析，確認其減振效果與能量擷取效果。

關鍵字

調諧質量阻尼器 ； 壓電材料 ； 能量擷取 ； 人行橋 ； 最佳化設計

並列摘要

Tuned mass damper (TMD) is an effective system to reduce the vibration of structures under wind load. The conventional tuned mass damper consists of proof mass, dampers and springs. The vibration energy is dissipated by dampers attached to the proof mass. We hope to restore the vibration energy instead of wasting it in vibration process. This study proposes a new type of tuned mass damper, piezoelectric tuned mass damper (Piezo-TMD), which uses a piezoelectric material device in replacement of the damper in the conventional TMD. Piezoelectric materials can convert the structural vibration energy to electricity. The Piezo-TMD consists of not only the proof mass, piezoelectric materials and resistance but also spring and inductor so that the mechanical and electrical frequencies of the Piezo-TMD can be adjusted to be tuned to the structure. The equation of motion of the Piezo-TMD mounted on SDOF structure is derived. By parametric study, the sensitivity of the system response toward the system parameters is able to comprehend. Taipei 101 is simplified to be a single degree of freedom structure. Implemented with the Piezo-TMD, it is analyzed when subjected to the design wind forces. The simulation results show that the Piezo-TMD can achieve the same performance as the conventional TMD in structural vibration reduction and transfer the absorbed energy to power for reuse. Different from the conventional TMD, the Piezo-TMD has more design parameters. We use four dimensionless parameters to simplify the design parameters of Piezo-TMD. The optimal dimensionless parameters of the Piezo-TMD for maximum energy harvesting are determined by using Matlab Direct Search toolbox. By applying curve fitting and regression method, the optimal design formulae for Piezo-TMD implemented in Taipei 101 are defined, and the optimal design procedures for Piezo-TMD are proposed. Finally, there is a case study of footbridge. The optimal design parameters are defined by using optimal design formulae derived from Taipei 101. After that, the footbridge implemented with the Piezo-TMD is analyzed when subjected to pedestrian loading and the performance is compared with the conventional TMD. The time history simulation results show that the Piezo-TMD can achieve vibration comfort of the footbridge and harvest more than a half of the structural vibration energy. The feasibility of optimal design formulae and optimal design procedures of Piezo-TMD is verified.

並列關鍵字

tuned mass damper ； piezoelectric material ； energy harvesting ； footbridge ； optimal design

參考文獻

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