樓版振動舒適度評估及採壓電調諧質量阻尼器作減振及能量擷取

Floor Vibration Serviceability and Using Piezoelectric Tuned Mass Damper for Vibration Reduction and Energy Harvesting

鄧彥甫(Yan-Fu Deng)

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/NTU202003305

摘要

長跨度或輕質的樓板常被用於體育場館、舞廳和購物中心等。此類樓版常有低振動頻率與低阻尼的特性，而低頻的人行外力可能與樓板產生共振。過量的振動會對行人產生不舒適感，因此工程師及設計者應考慮到人行外力下樓板的舒適度。本研究主要重點為樓板在人行外力下的舒適度評估，且當加速度超出所設定之限制，可採用調諧質量阻尼器減振。而壓電調諧質量阻尼器亦在文章中被介紹且作為減振策略。壓電調諧質量阻尼器利用壓電材料使於傳統調諧質量阻尼器中阻尼器所消散的振動能，轉為電能而被擷取。本文提出新的壓電調諧質量阻尼器機構，其中加入了縮放儀的機構。在縮放儀的調整下，壓電塊可不必再是細長狀，而能在壓電塊總數決定後任意調整其橫縱向的比例，使其在施工、安裝上及防止挫曲上更容易達成。
樓板舒適度評估及相關的分析皆在示範案例中展示。利用SAP2000所建立的模型作為多自由度結構，也將其簡化為單自由度結構，比較兩者的振動下加速度反應，確認單自由度結構之反應結果仍具一定代表性，可作為分析依據。在示範案例中，原結構在人行外力下之加速度過大，因此透過傳統調諧質量阻尼器及壓電調諧質量阻尼器將加速度降低，使其滿足舒適度需求。將壓電調諧質量阻尼器加裝於簡化之單自由度樓板中進行設計及分析，以平均功率最大化為最佳化目標設計，並利用時域及頻域之數值模擬分析安裝後之效果。模擬結果顯示，壓電調諧質量阻尼器不僅能使樓板在減振後滿足舒適度需求，亦能有效將振動能轉為電能進行擷取。

關鍵字

樓版 ； 舒適度評估 ； 壓電調諧質量阻尼器 ； 人行外力 ； 垂直振動 ； 最佳化設計

並列摘要

Lightweight or long-span floors are common in structures like sports stadiums, gymnasiums, aerobic dance studios, and shopping malls. These floor structures may lead to low vibrational frequency and low damping behavior. Human-induced vibrations with low movement frequencies are likely to cause resonance with the floor structure. Excessive vibrations may result in discomfort and intolerance for occupants. Therefore, it is important for engineers or designers to consider the serviceability of floor structures under human-induced excitation. In this study, the main objective is to assess vibration serviceability of floor structures under human walking force. Dealing with excessive vibration issues, Tuned Mass Dampers (TMD) can be utilized for vibration reduction. A Piezoelectric Tuned Mass Damper (Piezo-TMD) is also introduced and applied in the example case. Piezo-TMD makes use of piezoelectric materials to harvest the vibration energy rather than dissipating the energy through dampers. In the new configuration of Piezo-TMD, the pantograph mechanism is employed. With the pantograph mechanism, the dimension of the piezoelectric stacks which used to be in a slender shape is then free to be determined after the total number of the stacks is decided. The dimension of the Piezo-TMD is therefore more realistic to add on to the structures, and the construction is easier to be carried out.
The assessment and analyses of an example floor used in gymnasiums are demonstrated. The finite element model in the SAP2000 software is considered as a MDOF structure. It is also simplified to a SDOF structure. Acceleration responses of both structures are compared. The results of SDOF structure are shown to be acceptable for the acceleration assessment. In the example case, the acceleration of the initial floor structure under human-induced force exceeds the acceleration limit. Therefore, conventional TMD and Piezo-TMD are added to the structure to decrease the acceleration to a value that meets the vibration serviceability. The case of SDOF floor applied with Piezo-TMD is also shown. The optimal Piezo-TMD is designed with the objective of maximal mean power. Numerical analyses under time-domain and frequency-domain are conducted to examine the effectiveness of Piezo-TMD. The simulation shows that the Piezo-TMD can not only reduce the excessive vibration but also harvest the energy by converting the vibration energy to electrical energy.

並列關鍵字

floor structures ； vibration serviceability ； piezoelectric tuned mass damper ； human-induced vibration ； vertical vibration ； optimal design

參考文獻

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