| 摘要: | 本研究針對多元壓電調諧質量阻尼器(Piezoelectric Multiple Tuned Mass Dampers, Piezo-MTMDs)，進行數學建模、特徵分析、參數最佳化與風洞實驗驗證，探討其對氣彈模型之減振與能量擷取效能。首先利用壓電本構方程式結合尤拉梁理論，推導雙層壓電層梯形寬懸臂梁之力電耦合方程式，建立短路、開路與外接電阻等電路條件之控制模型。考量實務上Piezo-TMD需結合剛性桿件與外接質量塊，以便調整頻率與氣彈模型相互調諧，進一步以虛功法與多項式形狀函數推導單自由度模型，並轉換為狀態空間形式進行系統特徵分析與頻率響應分析。為探討變寬度對壓電阻尼比之影響，比較了矩形寬與梯形寬兩種壓電懸臂梁，分析其最大壓電阻尼比表現。結果顯示，梯形寬梁雖可提高壓電阻尼比，但另行製作梯形壓電材料模具，其成本高、彈性差，故綜合效益評估後，後續模擬與實驗皆採用矩形寬壓電懸臂梁作為Piezo-MTMDs構件。接續以氣彈模型做為主結構，搭配多顆Piezo-TMD形成Piezo-MTMDs系統，並採用平均功率最大化做為最佳化設計目標，以直接搜尋法設計各顆Piezo-TMD之最佳匹配外接質量與電阻，以提升整體能量擷取效率與減振效果。另外，建立阻尼比推估能量分配比例方法以預估能量消散比例。透過數值模擬隨機風力作用下之動力分析可知，Piezo-MTMDs不僅有效降低氣彈模型之位移反應，並可較穩定產生電能輸出，且驗證以阻尼比推估能量分配比例方法之可行性，說明壓電阻尼比為評估能量轉換效率之關鍵指標。實驗部分製作6顆Piezo-TMD試體，進行自由振動實驗以識別其材料參數，再進行參數最佳化設計，得各顆Piezo-TMD匹配之外接質量與電阻，並將Piezo-MTMDs安裝於氣彈模型上進行風洞實驗。實驗結果顯示，Piezo-MTMDs具有顯著減振效果，對主結構之最大位移減振率達41.11%，且於風速4.0(m/sec)下其平均功率達0.52(mW)。而於風速2.0~4.0 (m/sec)下所測得之轉換電能比例為23.4~33.3%之間，介於阻尼比推估轉換電能比例26%上下，顯示本研究所建立之壓電阻尼比估算法具有良好之參考價值。;This study focuses on the development, modeling, optimization, and experimental validation of Piezoelectric Multiple Tuned Mass Dampers (Piezo-MTMDs), aiming to investigate their effectiveness in vibration reduction and energy harvesting for a aeroelastic model. The electromechanical coupling equations of a trapezoidal-width cantilever beam with double-layer piezoelectric layers are derived based on piezoelectric constitutive equations and Euler-Bernoulli beam, and control models are established under resistor circuit conditions. Considering practical tuning requirements, each Piezo-TMD is designed by a rigid rod and an external mass at the free end. A SDOF-model is formulated using the virtual work principle and polynomial shape functions, and rewriting into a state-space for frequency response analysis. To explore the effect of geometry on electromechanical coupling performance, rectangular and trapezoidal piezoelectric cantilever beams are compared under same condition. Results show that while the trapezoidal beam provides slightly higher piezo-damping ratio, it requires custom molds and results in higher costs and lower flexibility. Therefore, the rectangular beam is chosen as the practical Piezo-MTMD component in subsequent simulations and experiments. The Piezo-MTMD system is then installed in the aeroelastic model, and an optimization strategy is implemented using a direct search method to determine the optimal external mass and resistance for each Piezo-TMD, based on maximizing harvested mean power. Additionally, an energy ratio estimation method based on damping ratios is proposed. Numerical simulations under random wind excitation show that the Piezo-MTMDs effectively reduce the structural response while simultaneously producing stable electrical output. The close match between the energy ratio estimation method and the simulated energy dissipation confirms the reliability of estimation method, and shows that the piezoelectric damping ratio is a useful indicator for estimating energy conversion and dissipation ratios. In the experiment, six Piezo-TMD prototypes are fabricated and tested through free vibration experiments to identify material properties, followed by optimization of external mass and resistance parameters. The wind tunnel experiments show that the Piezo-MTMD system significantly reduces displacement by 41.11% and generated 0.52 (mW) mean power at wind-speed 4 (m/sec). The measured converted energy ratio (23.4~33.3%) is close to the predicted 26%, confirming the reliability of the proposed damping-based estimation. |
