不同激振角度下雙模態耦合渦流誘發振動能量採集器之設計及分析

Design and Analysis of a Dual-modal Coupled Vortex-induced Piezoelectric Energy Harvester at Various Angles of Excitation

顏子洋(Zih-Yang Yen)

指導教授 ： 蘇偉儁

國立臺灣大學/工學院/機械工程學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101358

摘要

傳統的壓電能量採集器為懸臂梁結構，由於其頻寬過窄且振動方向性單一，在應用上受到諸多限制。因此本研究提出一具有雙方向振動自由度的框形梁壓電能量採集裝置以改善以上限制。藉由改變其激振角度，使其在同一個激振環境下產生兩模態耦合的現象，從而拓增頻寬的大小。另外，利用風力作為激振外力源，藉由框形樑上的圓柱形受風結構來產生渦流，並受益於其特殊的鎖定現象，探討其對於框形樑在雙模態耦合與單一模態時的表現差異。本研究使用Euler-Bernoulli梁理論與壓電本構方程式作為基礎，推導出框形梁的力電耦合振動方程式，並藉由基底激振實驗擬合出系統之阻尼比與壓電片之壓電常數。透過瑞利振盪器數學模型模擬出渦流對採集器產生的動態響應，推導出完整的力電耦合聯立方程式。藉由改變輔梁長度與激振角度，來觀察其對採集器的輸出電壓與採集能力的影響。結果顯示，在渦流誘發激振環境下，當角度從0° 開始變大時，兩模態逐漸發生耦合的現象，使其有效共振風速區間的範圍對比只有單一模態時明顯提升，尤以輔梁長度40 mm時更為明顯。在激振角度同為45° 的情況下，輔樑長度40 mm較輔梁長度30 mm時的有效共振風速區間增加大約25 %。在輔樑長度40 mm下，激振角度45° 對比角度0° 時，採集範圍提升了53.8%；對比角度90° 時，則提升了33.3%。

關鍵字

壓電能量採集器 ； 雙方向 ； 渦流誘發激振 ； 可變激振角度 ； 雙模態耦合

並列摘要

A conventional piezoelectric energy harvester is based on a cantilever structure. Its applications are limited due to the narrow bandwidth and single-directional sensitivity. This study proposes a bi-directional frame-shaped beam with a rotatable base structure to overcome those issues. By changing the excitation angle, two fundamental modes can occur simultaneously under excitations to broaden the bandwidth. This study also uses the wind energy as the excitation force to cause a periodic vortex and generate the “lock-in” phenomenon, thereby discussing the differences of the output voltage performance between dual-mode coupled and single mode case. This study derive the mechanical-electrical coupling motion equation of the system based on Euler-Bernoulli beam theory and piezoelectric constitutive equation. The damping of the system and the piezoelectric constant are obtained by the base excitation experiment. The dynamic of the vortex-induced vibration can be modeled as the Rayleigh oscillator. After combining those equation of motion, we can obtain the complete model of the system. By changing the length of the auxiliary beam and the excitation angle of the harvester, we can observe their effect on the output voltage and the capability of the harvester. The results of this study show that the two fundamental modes are gradually coupled when the angle increases from 0° in the vortex-induced vibration. The lock-in wind speed range is improved significantly while compared to the single mode case when the excitation angle is 0° or 90°. The effective wind speed range in the 40 mm auxiliary beam case increase by 25% compared to the case in 30 mm when the excitation angle are both 45°. When the excitation angle is 45°, the wind speed range increase by 53.8% and 33.3% comparing to the angle in 0°, and 90°, respectively, when the auxiliary beam length are both 40 mm.

並列關鍵字

Piezoelectric energy harvester ； bi-directional ； vortex-induced vibration ； variable angles of excitation ； dual-modal coupled

參考文獻

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