| 摘要: | 本研究主要針對壓電懸臂梁形式之壓電調諧質量阻尼器(Piezoelectric-Tuned Mass Damper, Piezo-TMD)，進行數值模擬分析與最佳化設計。本研究首先推導壓電懸臂梁力學與電路之運動方程式，並且將壓電懸臂梁之運動方程式引入多項式形狀函數以單自由度化其運動方程式，並且跟分布參數之形狀函數進行頻率反應函數異同的比較。對於壓電調諧質量阻尼器而言，在具備一定減振效果上，如何能有較佳的發電效率為其重點，而最大壓電阻尼比可以是判斷其發電效率的關鍵因素。因此本研究針對了壓電懸臂梁的寬度、長度、壓電層和基底層為相同厚度比例下之總厚度、以及外接質量塊質量，上述四項進行敏感度分析，可以知道它們的改變並不會影響最大壓電阻尼比的數值，也因此了解壓電調諧質量阻尼器之壓電阻尼比會有其極限，無法僅靠著增加壓電材料的使用量而輕易改變其最大壓電阻尼比，也就是不能單純藉由增加壓電材料而增加發電效率。故在壓電調諧質量阻尼器設計上，針對壓電懸臂梁的部分，其各項尺寸可預設一個初步的數值，靠著其初步數值便可以計算出其最大壓電阻尼比，而有了最大壓電阻尼比之後，便可以利用傳統調諧質量阻尼器最佳阻尼比設計公式推算出其質量比，在此情況下就可以再藉著外接質量塊來調整整個壓電調諧質量阻尼器的總質量。壓電調諧質量阻尼器之自然頻率與電路頻率和結構頻率相調諧時，結構振動能轉為電能之效率為最佳，因此利用傳統調諧質量阻尼器最佳頻率比設計公式來找出其最佳頻率比，接著就可利用調整長度和寬度來調諧機械頻率，並調整電阻來匹配電路進而找到其最佳電阻。利用設計出來之壓電調諧質量阻尼器進行數值分析繪出其頻率反應函數圖，並做動力分析，可知在隨機風力作用下，若在氣彈模型上有加裝壓電調諧質量阻尼器時可有效減振，並同時具備不錯的發電效率。;This research focuses on numerical analysis and optimal design of the cantilever-type piezoelectric tuned mass damper (Piezo-TMD). At first, this research derives the mechanical and electrical of equations of motion of piezoelectric cantilever beam, and then the polynomial shape function is introduced to obtain the generalized single-degree-of-freedom equations of motion. The frequency response function is further derived to compare with the one derived by distributed parametric shape function. For the cantilever-type Piezo-TMD, in terms of having a certain vibration reduction effect, to have a better power generation efficiency is the key point, and the maximum piezoelectric damping ratio can be used to evaluate the power generation efficiency. Therefore, the research had tested four key parameters for sensitivity analysis, including the width and length of the piezoelectric cantilever beam, the total thickness of the piezoelectric layer and the base layer at the same thickness ratio, and the mass of the external proof mass. The results show that these four terms are not affecting the value of the maximum piezoelectric damping ratio, so just trying to add the amount of piezoelectric material will not lead to a higher power generation. In view of this, when designing the cantilever-type Piezo-TMD, a proper size of piezoelectric cantilever beam can be firstly chosen to realize the maximum piezoelectric damping ratio, then the optimal TMD mass ratio could be found by using the optimal damping ratio design formula of traditional tuned mass damper. Accordingly, the external proof mass is designed to match the optimal TMD mass ratio. For the best power generation and vibration reduction, the cantilever-type piezo-TMD have to tune to the main structure according to the design formula of optimal frequency ratio of traditional tuned mass damper. Thus, the length and width of piezoelectric beam can then be adjusted for the mechanical tuning, the resistance can also be adjusted for electrical matching. Use the aeroelastic model structure implemented with designed cantilever-type piezo-TMD to perform numerical analysis of frequency response function and time history analysis, the result shows that the cantilever-type piezo-TMD can effectively reduce the structural vibration and have great power generation simultaneously. |
