本文為探討具有壓電材料貼附之懸臂樑的動態響應，以有限元素法為基礎，分析出此懸臂樑受集中外力作用時, 考慮應變-電壓的耦合效應，計算出此結構的位移與感應電壓的大小。
數學模型的假設建立在Timoshenko理論的三明治樑所組成。此結構中第一三跨距為單層的鋁材，第二跨距為三層的三明治壓電複合層樑所組成，利用結構的應力 場、應變場與連續位移條件推導出應變能＆動能方程式，再以Hamilton’s Principle求得運動方程式與邊界條件。
應用靜態平衡方程式求解單一元素的位移場通解，進而求得此元素的位移形狀函數組，再利用應變能項與動能項計算出此元素的勁度矩陣與質量矩陣，接著應用推疊方式後經由Lagrange’s equation建立此系統的運動與電壓變化的統馭方程式。
施予結構自由端一集中外力，應用Newmark’s scheme數值積分法解出此樑內位移與電壓變化的時間歷程，探討壓電片之長度、位置與厚度等效應對於懸臂樑振動的位移與感應電壓變化的影響。

In this thesis, the Timoshenko beam partially surface mounted with a pair of piezoelectric layers is presented. The finite element technique is developed to analyze the vibration of the entire beam and to investigate the voltage on the top piezoelectric layer. The governing equations and boundary conditions of the entire are formulated via the Hamilton’s principle. The set of shape functions of one element is obtained from solving the equations of static equilibrium of the element. The stiffness matrix and mass matrix of the element are obtained by substituting the displacements of the element into the calculation of strain energy and kinetic energy. The governing equations of motion of the entire beam and voltage on the surface of the top piezoelectric layer are derived via the Lagrange’s equations. The Newmark’s method is adopted to compute the dynamic response of entire beam and the voltage response of the top piezoelectric layer. The effects of length, thickness and location of the pair piezoelectric layers on the displacement at the free end of the cantilever and the voltage on the top piezoelectric layer are investigated.

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