本文是針對一根附有上下壓電片的Timoshenko樑，從兩個方面作探討與分析。首先以有限元素法於探討此根懸臂樑承受外力作用, 所呈現的動態行為。再設計一個有效的充電電路將壓電片產生的電能有效的儲存起來。
整體結構為鋁樑，第二跨距樑貼附上、下壓電片，透過靜態平衡方程式求得單位元素的有限元素之解, 再計算此單位元素的應變能與動能,而求得此單位元素的勁度矩陣與質量矩陣，接著應用元素的堆積於探討整體樑的動態響應與感應電壓變化的影響。
當此樑承受動態外力作用時，會因為上下壓電片的變形作用而產生電能之行為，並且產生的電能為一交流電，因此本文後半部將設計一組充電電路，將產生的電能經過整流濾波後並儲存。接著探討施加不同外力形式下，不同的濾波電容及儲存電容對充電時間影響。

The purpose of this thesis is to analyze the Timoshenko beam with two side surface mounted piezoelectric material in two aspects. The first is the use of the finite element method to study the cantilever beams under external force and its presented dynamic behavior. The second is the design of an electrically charged circuit to act as an efficient storage of piezoelectric energy.

1.D. H. Robbins and J. N. Reddy, "Analysis of Piezoelectricity Actuated Beams Using a Layer-wise Displacement Theory," Computers and Structures, Vol. 41, No. 2, pp. 265-279, 1991.
2.J. G. Smits, and W. S. Choi, "The Constituent Equations of Piezoelectric Heterogeneous Bimorphs," Ultrasonic, Ferroelectrics and Frequency Control, IEEE Transactions, Vol. 38, No. 3, pp. 256-270, 1991.
3.S. Brooks and P. Heyliger, "Static Behavior of Piezoelectric Laminates with Distributed and Patched Actuators," Journal of Intelligent Material Systems and Structures, Vol. 5, No. 5, pp. 635-646, 1994.
4.X. D. Zhang and C. T. Sun, "Formulation of an Adaptive Sandwich Beam," Smart Materials and Structures, Vol.5, No. 6, pp. 814-823, 1996.
5.C. Q. Chen, X. M. Wang and Y. P. Shen, "Finite Element Approach of Vibration Control Using Self-sensing Piezoelectric Actuators," Computers and Structures, Vol. 60, no. 3, pp. 505-512, 1996.
6.H. S. Tzou, and G. C. Wang, "Distributed Structural Dynamics Control of Flexible Manipulators-I. Structural Dynamics and Viscoelastic Actuator," Computers and Structures, Vol. 35, pp. 669-677, 1990.
7.S. K. Ha, C. Keilers, and F. K. Chang, "Finite Element Analysis of Composite Structures Containing Distributed Piezoelectric Sensors and Actuators," AIAA Journal, Vol. 30, pp. 772-780, 1992.
8.E. F. Crawley, and J. de. Luis, "Use of Piezoelectric Actuators as Elements of Intelligent Structures," AIAA Journal, Vol. 25, No. 10, pp. 1375-1385, 1987.
9.J. G. Smits, W. S. Choi, and A. Ballato, "Resonance and Antiresonance of Symmetric and Asymmetric Piezoelectric Flexors," Ultrasonic, Ferroelectrics and Frequency Control, IEEE Transactions, Vol. 44, No. 2, pp. 250-258, 1997.
10.H. Abramovich, and A . Livshits, "Dynamic Behavior of Cross-ply Laminated Beams with Piezoelectric Layers," Computer Structures, Vol. 25, pp. 371-379, 1993.
11.H. S. Tzou, and C. I. Tseng, "Distributed Vibration Control and Identification of Coupled Elastic/Piezoelectric System: Finite Element Formulation and Application," Mechanical Systems and Signal Processing, Vol. 5, No. 3, pp. 215-231, 1991.
12.I. Y. Shen, "A Variational Formulation, a Work-energy Relation and Damping Mechanisms of Active Constrained Layer Treatments," Journal of Vibration and Acoustics, Vol. 199, No. 2, pp. 192-199, 1997.
13.X. Q. Peng, K. Y. Lam and G. R. Liu, "Active Vibration Control of Composite Beams with Piezoelectric: A Finite Element Model with Third Order Theory," Journal of Sound and Vibration 209, 635-650 , 1998.
14.Angela Triplett and D. Dane Quinn, "The Effect of Non-linear Piezoelectric Coupling on Vibration-based Energy Harvesting," Journal of Intelligent Material Systems and Structures, Vol. 20 No. 16, pp. 1959-1967, 2009.
15.Q. Wang, and S. T. Quek, "A Model for the Analysis of Beams with Embedded Piezoelectric Layer," Journal of Intelligent Material System and Structures, Vol. 13, pp. 61-70, 2002.