摘 要
本文採用模態法與有限元素法來求取壓電曲樑之模態頻率，並討論兩種方法模態頻率差異，並藉由有限元素法搭配 所推導出動力有限平衡方程式與電壓方程式使用 數值積分法求出電壓與曲樑運動之耦合關係；此壓電結構中的第一和第三跨距為單層的 樑，第二跨距為壓電複合層曲樑組成
在模態法方面，為瞭解壓電曲樑之力學行為，則利用應力場、應變場與位移場的關係推導出應變能項和動能項，再以漢米爾頓原理求得曲樑之運動方程式，利用位移場與應力場搭配曲樑之邊界條件計算出模態頻率，並討論在不同的幾何參數下對模態頻率之影響。
在有限元素法方面，擷取單層與雙層的一個元素，並且以靜態平衡模式找出此元素各節點位移與轉角之形狀函數，計算此塊有限元素的表示式，再藉由應變能項與動能項計算出此結構的勁度矩陣和質量矩陣，進而利用 及推疊技巧解出系統的模態頻率。
最後改變壓電曲樑的外觀尺寸，來探討曲樑位移圖形與壓電片所產生電壓結果的關係。
關鍵詞：曲樑、壓電材料、有限元素、電壓

Abstract
In this thesis, the Timoshenko curved beam with partially surface mounted piezoelectric material is presented. A resistor connected two surfaces of the piezoelectric material forms a network. The governing equations of the entire system are derived via the Hamilton’s principle. The analytic approach is adopted into the calculation of modal frequencies. Furthermore, the shape functions of one element of the entire beam are derived from the equations of static equilibrium and the nodal displacements of the element. Based on the shape functions of one element, the finite technique is presented in the study of the coupling between motion of the entire beam and induced voltage of the piezoelectric material. The effects of location, length and thickness of the piezoelectric material and resistance of the resistor on the vibration of the entire beam caused by an external load are investigated. Results show that larger resistance can suppress the vibration more efficiently. Furthermore, a larger piezoelectric material makes the beam to have less vibration.
Keywords: Curved beam, piezoelectric material, resistor, modal frequencies, finite element.

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