本文目的為探討單層貼附式壓電片Timoshenko懸臂樑之振動分析，將壓電片貼附在結構的下方，採用有限元素法來探討壓電懸臂樑的動態響應且用模態法來驗證有限元素法的可行性，以此有限元素為基底配合 對結構進行動態模擬並探討壓電材料產生的電壓大小。
在模態法方面，為了解壓電樑力學行為，則利用應力場、應變場與位移的關係推導應變能項與動能項，再以 求得壓電樑之運動方程式，進而計算出模態頻率，並討論在不同幾何參數下對模態頻率的影響。
在有限元素法方面，用靜態平衡方程式推導其位移場之通解，藉由應變能項與動能項計算結構的質量矩陣及勁度矩陣，建立有限元素模型，再利用堆疊方式經 解出系統的模態頻率。
在力電耦合方面，利用有限元素法為基底再以Newmark直接積分法對此結構進行位移分析，接著利用 ，探討壓電材料位置、長度、厚度產生的電壓大小。

In the thesis, the cantilevered Timoshenko beam with partially surface mounted piezoelectric material is presented. A resistor connected two surfaces of the piezoelectric material forms a network. The governing equation of the entire system is derived from the Hamilton’s principle. The modal frequencies are obtained by the analytic approach. The shape functions of one element of the entire beam are obtained by solving the equations of static equilibrium with nodal displacements of the element. Then, the finite element technique is set to investigate the coupling between the motion of the entire beam and induced voltage on the piezoelectric material under an external excitation. The modal frequencies obtained the finite technique will be compared with those analytic results. The effects of resistance of resistor, and the location, length and thickness of the piezoelectric material on the vibration of the entire beam are studied. Results show that larger resistance and piezoelectric material can reduce the vibration more efficiently.

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