本文以壓電材料當作力電轉換之媒介，研究開發一壓電振動能量擷取系統（piezoelectric vibration power harvesting systems），針對該系統之力電耦合轉換機制及結構振動之關聯性進行分析，並以實驗輔以驗證。本文首先採用尤拉-伯努力樑之假設，建構一局部覆蓋壓電材料三層樑為理論模型，在忽略力電耦合效應之下，分別推導出各段樑之運動方程式，並配合各相容條件及邊界條件，得到系統之純機械性質模態；接著考慮力電耦合效應以及機械阻尼對樑之影響，計算出壓電懸臂樑之能量式，且由前述所得之模態，將能量式予以離散化，代入拉格朗日方程式，得到系統之運動方程式；其後部電路則採用標準電路的形式，並於開路端加上外掛電容為電路系統模型，推導及模擬該電容之充電情況。文末分別於不同夾持長度下，實驗量測系統頻率以及電容充電情形，驗證了方程式推導之準確性，以及比較多根壓電懸臂樑在不同連接方法下對充電效益之影響，最後將可調式壓電振動能量擷取系統予以實體化，並測試其實用性。
此模型於實務應用上之優點，是可利用固定端未覆蓋部分調整樑之頻率，使得系統共振頻率與環境頻率相近，產生共振而獲得較佳的回收效益；此設計概念可提供未來設計可調頻壓電振動能量擷取系統的工程人員一參考方向。

Piezoelectric materials are widely used as power harvesting device due to its ability to transform mechanical energy into electrical energy and vice versa. In this thesis, a power harvesting model is developed and electrical charge of the model is derived. The model is an adjustable Euler-Bernoulli beam with PZT bounded on its both surfaces. PZT electrodes are shunted with RLC circuit with a standard interface. In the analytic work, first we neglect the electro-mechanical coupling to estimate the mechanical mode shape of the beam. Next, excite the model with harmonic displacement on its boundary condition. The electro-mechanical coupling is considered to calculate the PZT energy form. Assume mode and separation variable method are used to derive the Lagrange equation of motion then with the electrical circuit model the electrical charge is derived. Experimental work is conducted to test and verify the model. Finally, it gives good results. The advantage of this model is the system frequency can be tuned into environment frequency to get better power harvesting which people can continue for future research.

[1] N.N. Rogacheva, C.C. Chou, and S.H. Chang, 1998, “Electromechanical Analysis of a Symmetric Piezoelectric/Elastic Laminate Structure：Theory and Experiment,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.45, No.2, pp.285-294.
[2] S.H. Chang, and C.C. Chou, 1999, “Electromechanical Analysis of an Asymmetric Piezoelectric/Elastic Laminate Structur：Theory and Experiment,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol.46, No.2, pp.441-451.
[3] C.Y.K. Chee, L. Tong, and G.P. Steven, 1999, “A Mixed Model for Composite Beams with Piezoelectric Actuators and Sensors,” Smart Materials and Structures, vol.8, pp.417-432.
[4] M. Kommer, 2001, “On the Correction of the Bernoulli-Euler Beam Theory for Smart Piezoelectric Beams,” Smart Materials and Structures, vol.10, pp.668-680.
[5] H.A. Sodano, G. Park, and D.J.inman, 2004, “Estimation of Electric Charge Output for Piezoelectric Energy Harvesting,” Strain, 40, 49-58.
[6] Y.B. Jeon, R. Sood, J.-h. Jeong, and S.-G. Kim, 2005, “MEMS Power Generator with Transverse Mode Thin Film PZT,” Sensors and Actuators A, 122, 16-22.
[7] G.K. Ottman, H.F. Hofmann, and A.C. Lesieutre, 2002, “Optimized Piezoelectric Energy Harvesting Circuit using Step-down Converter in Discontinuous Conduction Mode,” PESC Record – IEEE Annual Power Electronics Specialists Conference, vol.4, pp.1988-1994.
[8] G.K. Ottman, H.F. Hofmann, A.C. bhatt, and A.C. Lesieutre, 2002, “Adaptive Piezoelectric Energy Harvesting Circuit for Wireless remote Power Supply,” IEEE Transactions on Power Electronics, vol.17, pp.669-676.
[9] H. A. Sodano, D.J. Inman, and G. Park, 2005, “Comparison of Piezoelectric
Energy Harvesting Devices for Recharging Batteries,” Journal of Intelligent Material Systems and Structures, vol.16, pp.799-807.
[10] H. A. Sodano, G. Park, D.J. Leo, and D.J. Inman, 2003, “Use of piezoelecteic
energy harvesting device for charging batteries,” Proceedings of Smart Structures and Materials, vol.5050
[11] D. Guyomar, A. Badel, E. Lefeuvre, and C. Richard, 2005, “Toward Energy
Harvesting Using Sctive Materials and Conversion Improvement by Nonlinear
Processing,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency
Control, vol.52, pp.584-594.
[12] Y.C. shu and I.C. Lien, 2006, “Analysis of Power Output for Piezoelectric Energy Harvesting System,” Smart Materials and Structures, vol.15
, pp.1499-1512.
[13] J. Kymissis, C. Kendall, J. Paradiso, N. Gershenfeld, 1998, “Parasitic Power
Harvesting in Shoes,” the Second IEEE International Conference on Wearable Computing.
[14] W.J. Wu, Y.Y. Chen, B.S. Lee, J. J. He and Y.T. Peng, 2006, “ Tunable Resonant Frequency Power Harvesting Devices,” Proceedings of Smart Structures and Materials, vol.6169, 61690A.
[15] V.R. Challa, M.G. Prasad and F.T. Fisher, 2008, “High Efficiency Energy Harvesting Device with Magnetic Frequency Tuning,” Proceedings of Sensord and Structures Technologies for Civil, Mechanical, and Aerospace Systems, vol.6932, 69323Q.
[16] V.R. Challa, M.G. Prasad, Y. shi and F.T. Fisher, 2008, “A Vibration Energy Harvesting Device with Bidirectional Resonance Frequency Tenability,” Smart Materials and Structures, vol.17, pp.015035.
[17] S.C. Huang and Y.C.Chen, 1999, “Parametric Effects on the Vibration of Plates with CLD treatment.” Journal of the Chinese Society of Mechanical Engineers, 20(2), pp.159-167.
[18] 賴炳佑，2004，具拘束阻尼層部份覆蓋樑之振動與阻振分析，國立台灣科
技大學機械工程研究所碩士學位論文。
[19] 莊政縉，2008，壓電振動能量擷取器在標準介面與SSHI介面之分析，國立台灣大學工學院應用力學研究所碩士學位論文。
[20] L. Meirovitch, 1967, “Analytical Methods in Vibrations,” New York, Macmillan
[21] 周卓明，2003，壓電力學，全華科技圖書股份有限公司。