非線性壓電振動子應用於能量擷取之研究

Abstract

從壓電振動能量擷取的研究中，過去使用之線性振動子，其工作範圍通常僅限於共振頻率附近，然而日常環境中之振動源並非為固定頻率之簡諧形式振盪，有鑑於此，本論文以壓電振動子為主軸，探討非線性振動子應用於壓電能量擷取系統之機制及其寬頻效應，並且與過去使用之線性振動子作詳細的分析比較。 本團隊採用於系統中置放磁鐵的方式，使壓電樑受到一磁能保守力影響而改變其運動行為，並透過兩磁鐵間相互作用產生之磁位能，推導出非線性振動子之統御方程式。此外，進一步透過實驗及模擬探討非線性系統之機械動態行為及其電學之輸出響應。 由實驗與模擬結果得知，將非線性振動子應用於壓電能量擷取系統能有效提升系統之輸出功率，除此之外，受磁場影響下系統之電性輸出亦有顯著的寬頻效果。探究其動態行為可發現不同磁場大小會改變系統之位能及其運動行為之間的關係：當系統受到較小磁場影響時總位能曲線將較平滑，隨著磁場增加，會開始出現雙位能井的現象。結果顯示於適當的磁場作用下，非線性振動子將具有較大的振幅，故系統具有較高的電壓及功率輸出，相較於線性振動子，受到外加磁場而改變系統等效勁度之非線性振動子能有效彰顯壓電材料體本身之力電轉換效應。

It has been shown that optimum power output of a linear piezoelectric energy harvester occurs when the driving frequency is close to the resonance of the device. However, the vibration sources typically have a wide range of frequency bands. This motivates us developing nonlinear piezoelectric oscillators for vibration energy harvesting. The nonlinear oscillator is constructed by introducing magnetic couplings on the cantilever beam. As a result, the stiffness of the structure varies depending on the strength of magnetic couplings. The governing equations are derived assuming a suitable form of magnetic potential energy, and their solutions are numerically solved and validated by experiment. The result shows that the magnitudes of harvested power depend on the relative strength of magnetic couplings. At small coupling, the potential energy has a single well, while it exhibits double wells under large magnetic coupling. As a result, the optimal harvested power occurs at the transition from a single well structure to the double well structure. In addition, it is observed that harvested power is enhanced significantly and exhibits wideband effect in a nonlinear system under either harmonic or random excitation.