本文目的為探討具有貼附式壓電材料之複合材料曲樑的結構特性；此結構上層與下層為壓電材料薄片，中間層為堆疊六層之複合材料，總合構成一曲樑。
為了瞭解曲樑之力學行為，利用應力場、應變場、連續位移條件與溫度分佈公式的關係推導出應變能和動能公式，再以Hamilton’s Principle求得運動方程式(governing equations)和邊界條件(boundary conditions)。
利用靜態結構方程式推導出位移場通解，並代入不同的邊界條件可以後獲得其位移場特解。
再代入不同負載之集中外力、溫差與電位差以求得曲樑的應力與應變的分佈情形，進而加以比較分析。

A curved composite beam surface-mounted with piezoelectric material is considered in this paper. The curved beam element is based on Timoshenko beam theory. The mathematical model is based on a continuous displacement conditions piezoelectric field and temperature distribution formula. Then the strain energy and kinetic energy derived by the stress and the strain. Governing equations and boundary conditions are derived by Hamilton's Principle.
General solution of displacement field equations derived from the static structure. General solution can obtain special solutions constant by different boundary conditions. In the role of external force, temperature and potential difference, Stress and strain distribution can be obtained.

1. A. E. H. Love, “A Treatist on the Mathematical Theory of Elasticity,” 4thEdn. Dove, New York,1994.
2. J. P. Den Hartog, “Mechanical Vibrations,” 4thEdn. MaGraw-Hill, New York, 1956.
3. S. S. Rao, “Effects of transverse and rotary inertia on the coupled twist-bending vibrations of circular ring,” Journal of Sound and Vibration, Vol.16, pp.551-556, 1971.
4. Jan G. Smits and Wai-shing Cho, “The Constituent Equations of Piezoelectric Heterogeneous Bimorphs,” IEEE of Ferroelectrics and Frequency Control, Vol.38, No.3, 1991.
5. Qingyuan Meng, Mehran Mehregany and Keren Deng, “Modeling of the electromechanical performance of piezoelectric Iaminated microactuators,” Journal of Micromech. Microeng, Vol.3, 18-23, 1993.
6. Sang-Kwan Lee, Joon-Hyung Byun and Soon Hyung Hong, “Effect of fiber geometry on the elastic constants of the plain woven fabric reinforced aluminum matrix composites,” Materials Science and Engineering, A347, 346-358, 2003.
7. James R. Gaier, Yvonne Yoder Vandenberg and Steven erkebileb, “The electrical and thermal conductivity of woven pristine and intercalated graphite fiber–polymer composites,” Carbon 41, 2187-2193, 2003.
8. Wen Huang, Xu Nie and Yuanming Xia, “Effects of heat-treatment and strain rate on the mechanical properties of SiC/Al composite wires—experimental and constitutive modeling,” Composites, Part A 36, 1316-1322, 2005.
9. J.R. Vinson and R.L. Sierakowski, “The Behavior of Structures Composed of Composite Materials,” Martinus Nijhoff Publishers, DORDRECHT. NL/BOSTON.USA/LANCASTER.UK, 1986.
10. Robert C. Wetherhold and Jianzhong Wang, “Tailoring Termal Deformation by Using Layered Beams,” Composites Science and Technology 53, 1-6, 1995.
11. Stephen Brooks and Paul Heyliger, “Static Behavior of Piezoelectric Laminates withDistributed and Patched Actuators,”
Journal of Intelligent Material Systems and Structures, Vol.5,1994.
12. Li Jun and Hua Hongxing, “Dynamic stiffness analysis of laminated composite beams using trigonometric shear deformation theory,” Composite Structures 89, 433-442, 2009.
13. H.J. Xiang and Z.F. Shi, “Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load,” European Journal of Mechanics A/Solids 28, 338-346, 2009.
14. Anil Kumar and D. Chakraborty, “Effective properties of thermo-electro-mechanically coupled piezoelectric fiber reinforced composites,” Materials and Design 30, 1216-1222, 2009.
15. Nilanjan Mallik and M. C. Ray, “Effective Coef. Cients of Piezoelectric Fiber-Reinforced Composites,” AIAA JOURNAL, Vol. 41, No. 4, 2003.
16. Manas Chandra Ray, “Micromechanics of piezoelectric composites with improved effective piezoelectric constant,” Int J Mech Mater Des 3, 361–371, 2006.
17. Chung-De Chen, “On the singularities of the thermo-electro-elastic fields near the apex of a piezoelectric bonded wedge,” International Journal of Solids and Structures 43, 957-981, 2006.
18. Sang Wook Park, Hak Sung Kim and Dai Gil Lee, “Optimum design of the co-cured double lap joint composed of aluminum and carbon epoxy composite,” Composite Structures 75, 289-297, 2006.
19. Harald Berger, Sreedhar Kari, Ulrich Gabbert, Reinaldo Rodriguez-Ramos, Raul Guinovart, Jose A. Otero and Julian Bravo-Castillero, “An analytical and numerical approach for calculating effective material coefficients of piezoelectric fiber composites”, International Journal of Solids and Structures 42, 5692-5714, 2005.
20. Mehrdad N. Ghasemi-Nejhad, Saeid Pourjalali, Mark Uyema and Ali Yousefpour, “Finite Element Method for Active Vibration Suppression of Smart Composite Structures using Piezoelectric Materials,” Journal of Thermoplastic Composite Materials, Vol.19, 2006.
21. S.Raja, R. Sreedeep and G. Prathap “Bending Behavior of Hybrid-actuated Piezoelectric Sandwich Beams,” Journal of Intelligent Material Systems and Structures, Vol.15, 2004.
22. 張大猷，熱探針連續量測法應用於緩衝材料熱傳導係數之量測與分析，2004.
23. 鄭明昌，碳纖複合材料吸水性質及應變量測方法研究，2005.
24. 李官峰，實驗方法計算複合材料之材料係數，2003.
25. 蔡昆協，梭織物複合材料熱膨脹係數之研究，2003.
26. 余冠宏，雙層複合材料之熱傳導行為研究，2004.
27. 蔡昆協， 預測梭織物複合材料之熱膨脹係數，2002.
28. 劉文縉，碳纖維自行車 前叉之剛性與強度分析，2007.
29. 劉文縉，碳纖維自行車 前叉之疲勞壽命分析，2007.
30. 劉文縉，碳纖維自行車 架之剛性分析，2007.