運用結構合成法推導獵能器之振動及電壓方程式

A Synthesis Method to the Vibration Analyses of Power Harvester

蔡朝洋(Chao-Yang Tsai) ； 黃世欽(Shyh-Chin Huang)

《中華民國振動與噪音工程學會論文集》 2015 (2015/06) Pp. 287-294

摘要

本研究採用具有力電轉換特性的壓電材料（PZT）懸臂樑作為振能回收之媒介，並結合多重彈性支撐，期能藉由多重支撐勁度之大小改變，使獵能器－壓電樑振動能量擷取系統（Piezoelectric vibration power harvestingsystems）之頻率與激振頻率一致而形成共振，達到最大振能回收之功效。吾人首先分析壓電懸臂樑獨立之機械特性，並加入力電耦合效應，以假設模態法（Assumedmode method）及漢彌爾頓定理（Hamillton's principle）求得系統的運動方程式，續應用接納法將壓電懸臂樑與中間支撐結合，得到整體能量擷取系統之頻率及電壓方程式。接著再利用接納度矩陣中共振頻率對於支撐位置及支撐勁度等相關設計參數之敏感度，作為支撐勁度調整之依據，有效率的調整系統頻率達到所欲調整之共振頻率，並建立一方便的數值解析程序。文中以三個彈性支撐為例，由數值結果顯示，獵能器可調整的頻率範圍約 ± 30%，且於系統之激振頻率變化值達15%之情況下，僅需5個步驟就能將頻率調整至重新設定的激振頻率，進而獲得另一較佳的電壓輸出值。對於一結構複雜的振能擷取系統而言，此設計概念頗具創新性，經由理論的模擬分析與簡易的實體量測比較，二者具有相近之電壓值且誤差亦於合理範圍內，此一研究成果可提供振能擷取系統之設計人員一參考方向。

關鍵字

壓電能量擷取 ； 振能回收 ； 結構合成 ； 接納法

並列摘要

A frequency-tunable PZT beam for vibration energy harvesting was presented. The tunability was achieved by adjusting inter-multiple supports' stiffness. Theoretical derivation began with the Hamilton's principle and the assumed-mode method for the PZT beam. Receptance method followed to connect the inter-multiple supports with the beam and yielded the frequency equation of the harvester. The resultant receptance matrix also provided the sensitivities of harvester’s resonance frequencies to supports' stiffness (design variables). This information is helpful in guiding the direction of stiffness adjustment so as to tune the harvester to a desired frequency. Vibration response and voltage output equations of such a complex beam harvester were, for the first time, derived and experimentally verified. Examples of adjusting three-support stiffness to tune the harvester's first resonance matching the ambient frequency were illustrated and a computing algorithm was introduced. The tunable range of harvester's resonance frequency could be up to ±30%, as illustrated in the numerical results of three discrete supports. This is apparently significant from a comparison with the existing literature. Simulation of a sudden change of 15% excitation frequency was demonstrated and it took only five steps of adjustment to regain a maximum voltage output. The harvester's voltage output equations were finally verified by a simple experiment and satisfactory agreement was obtained.

並列關鍵字

vibration harvester ； tuneable beam ； PZT beam