微壓電振動子應用於能量擷取之理論與實驗驗證

Theory and Experiment of Micro-Piezoelectric Oscillator Applied in Energy Harvesting

黃亭瑋(Ting-Wei Huang)

指導教授 ： 舒貽忠

國立臺灣大學/工學院/應用力學研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.02417

摘要

本研究之目的為探討懸臂樑型式的微型壓電振動子之非線性現象，希望以適當的數學模型，描述其運作特性。首先，本文假設壓電力學的組成律維持線性，以尤拉－柏努利樑理論，考慮質點位移的幾何非線性，結合Rayleigh-Ritz法近似，透過漢米爾頓定理，推導出系統的非線性常微分方程式。
接著，為了分析此非線性常微分方程式的特性，以諧波平衡法，解出系統在穩態下的近似解，以描繪在懸臂樑在不同的環境加速度，不同負載電阻下的頻率響應，解釋微型振動子的非線性現象，並以實際的參數代入做驗證。由近似解的模擬結果推論，系統應屬於硬性的非線性振動子。為了驗證模型的可行性，我們以實際的微型振動子做實驗測試，觀察到硬性的頻率響應，確立推導出之非線性數學模型，定性上與實驗結果符合。由實驗試樣的結果，在不同阻抗下，跌跳點發生的頻率沒有明顯差異，應屬於弱力電耦合的壓電振動子。
　　為了進一步驗證，以另一組試樣重複試驗，得到的頻率響應卻是性質相反，軟性的非線性現象。然而以不含壓電層之相同基板做測試，結果卻呈現硬性現象，因此推測造成壓電複合樑軟性的原因可能為製程產生之內應力影響，未來可進一部探討內應力之效應。

關鍵字

壓電振動能量擷取 ； 微型壓電振動子 ； 非線性振動 ； 懸臂樑 ； 諧波平衡法

並列摘要

This thesis studies the nonlinear response of piezoelectric MEMS energy harvesters. The analysis is based on several assumptions including linear piezoelectric constitutive relation, Euler-Bernoulli beam theory considering geometric nonlinearity, Rayleigh-Ritz approximations, and Hamiltonian variational principle.
　　The nonlinear frequency responses under various accelerations and loads are approximated based on Harmonic Balance Method. Through the parameters provided by experiment, the frequency response is found to be of hardening type of nonlinearity. The results are validated by carrying out a series of experiment on micro piezoelectric unimorphs. In addition, the points initiating jump phenomenon almost remain the same under different electric loads, showing the weak electromechanical coupling.
　　On the other hand, the softening frequency response was observed by other samples with different substrate materials and sizes. A further examination on these substrate materials shows the hardening type of nonlinearity if the piezoelectric layers are completely removed. The internal stresses generated during the MEMS fabrication are postulated for explanation and will be verified in the near future.

並列關鍵字

piezoelectric energy harvesting ； piezoelectric MEMS generator ； nonlinear oscillation ； cantilever beam ； harmonic balance method

參考文獻

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[18] 張言誠, “非線性壓電振動子應用於能量擷取之研究,” 台灣大學應用力學所研究所博士論文, 2011.

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