軸向施力之非線性簡支樑獵能系統之研究

Axial Controlled Nonlinear Simple Beam Vibration Energy Harvester System

温語昂(Yu-Ang Wan)

指導教授 ： 王怡仁

淡江大學/工學院/航空太空工程學系碩士班/碩士(2019年)

https://doi.org/10.6846/TKU.2019.00068

摘要

本研究針對歐拉-伯努力樑受軸向簡諧力和非線性拉伸效應的影響討論，並置入壓電材料，討論其壓電耦合之效應。本文探討在橫樑軸向施力，而非在側向施力，從而改變樑之固有頻率。
本研究的目的是為了避免該系統內部共振並且有效控制系統振動。本系統由Mathieu方程控制，端點之致動器外力將影響整個系統的穩定性。因此本文將探討其振動情形與致動器之振幅及頻率對於系統穩定性之影響並利用附加之壓電材料(Piezoelectric material)擷取振動轉換電能。
首先利用牛頓定律推導其運動方程，接著採用多尺度法(Method of Multiple Scales(MOMS)) 分析系統於穩態固定點(Fixed Point Plot)時各模態之頻率響應，並藉由振幅觀察其振動現象。
本文利用實驗測量來驗證理論結果，驗證項目包括不同振動模態(mode)之頻率、振幅，並且置入壓電材料，將用以量測本研究實測之電壓電流等數據，並且最後與理論值相互比對，檢驗實驗與理論是否吻合。
本研究之模式可藉由調整致動器 (Actuator) 之振幅大小及頻率或相位，以達到控制橫樑振動之振幅及穩定性，可用於一般振動主體之振動控制，亦可適用於振動能量 (Vibration Energy) 與電能 (Electric Power Generator) 之間之轉換，應用範圍廣泛。

關鍵字

非線性振動(Nonlinear Vibration) ； 致動器(Actuator) ； 內共振(Internal Response) ； 振動控制(Vibration Control) ； 壓電材料(Piezo Electric Material)

並列摘要

This study investigates a slender hinged-roller nonlinear Euler-Bernoulli Beam subjected to a simple harmonic force applied in the axial direction. This nonlinear beam considered the stretching effect and also attached with a piezoelectric-patch (PZT-patch) to transfer nonlinear vibration energy into the electric power. Instead of applying the force on the beam’s transversal direction, the present work applies an axial force (an axial actuator) on the longitudinal direction to change the natural frequency of the beam (as shown in Fig.1) and hence control the beam vibration to achieve a maximum vibration energy harvesting.
The actuator's external force amplitude could also affect the stability of the entire system. Therefore, stability analysis will be studied to ensure the energy reliability of this vibration energy harvester (VEH) system. We employed the Method of Multiple Scales (MOMS) to analyse this nonlinear system. The Fixed-Point plots (steady state frequency response) were obtained and compared with the numerical results to verify if the internal resonance existed in this system.
The VEH system's stability information was obtained by the input-output amplitude plot. The proposed model can be used to adjust the amplitude or frequency of the actuator to control the beam's vibration amplitude and hence to have the maximum vibration energy transferring effect.
A simple experiment was performed (see Fig.2) to verify the analytical and numerical results. The output voltage of this VEH system from the present model agrees with experimental results very well. Our proposed model shows a wide application on energy engineering problems.

並列關鍵字

Nonlinear Vibration ； Vibration Energy Harvester (VEH) ； Vibration Control ； Piezoelectric-Patch(PZT-Patch)

參考文獻

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