延伸式挫曲樑壓電能量採集器之設計與分析：非線性與後挫曲下的雙穩態特性

Abstract

本論文提出一種延伸式挫曲樑壓電能量採集器，藉由軸向預位移使主樑產生挫曲行為。隨著預位移的增加，系統可分為兩個階段：在受力低於臨界應力、尚未發生挫曲時，稱為「預挫曲」階段，具有硬化型非線性特徵；當受力超過臨界應力進入「挫曲後」階段，則呈現軟化型非線性特徵。挫曲後，系統會形成雙穩態結構，在特定條件下可能出現躍遷現象，進而提升能量採集效率。

為了進一步進行設計與分析，本文首先推導延伸式挫曲樑的統御方程式。藉由不同預位移下計算出來的模態形狀，可建立對應的動態方程式；同時，透過量測軸向力並估算系統的軸向剛性，可獲得數值模型需要的擬合參數。實驗與模擬結果均驗證了所推導方程式在預挫曲與挫曲後階段的適用性。在雙穩態系統中，數學模型顯示當躍遷現象發生時，可有效提升能量採集效能。此外，透過調整樑的剛性，實驗結果驗證了加速度與末端質量對躍遷現象的影響。最後，考量旋轉運動為常見的能量採集來源，本文以能量法推導出延伸式簡支樑在旋轉激振下的動態方程式，為後續應用奠定理論基礎。

This dissertation proposes an extended buckled-beam piezoelectric energy harvester, in which axial pre-displacement induces buckling of the main beam. As the pre-displacement increases, the system can be divided into two stages: the pre-buckling stage, where the applied force is below the critical stress and the beam exhibits hardening-type nonlinearity; and the post-buckling stage, where the applied force exceeds the critical stress and the beam exhibits softening-type nonlinearity. In the post-buckling regime, the system forms a bistable structure, in which snap-through phenomena may occur under specific conditions, thereby enhancing the energy harvesting performance.

To enable further design and analysis, the governing equations of the extended buckled beam are first derived. Based on the mode shapes calculated under different pre-displacement conditions, the corresponding dynamic equations are established. In addition, by measuring the axial force and estimating the axial stiffness, the fitting parameters required for the numerical model are obtained. Experimental and simulation results verify the applicability of the derived equations in both pre-buckling and post-buckling stages. In the bistable system, the mathematical model demonstrates that the occurrence of snap-through effectively enhances the performance of the energy harvester. Furthermore, by varying the stiffness of the main beam, the experiments validate the influence of acceleration and tip mass on the snap-through behavior. Finally, considering that rotational motion is a common energy source, this dissertation derives the dynamic equation of an extended simply supported beam under rotational excitation using the energy method, providing a theoretical foundation for subsequent applications.