本文為探討雙層壓電材料Timoshenko樑，考慮負載-電壓的耦合效應，以有限元素法於分析此壓電材料樑受外力和電壓作用時，計算出位移與轉角的大小。
此結構中母樑為鋁材樑，第二跨距貼附上、下壓電片，透過靜態平衡方程式代入應力場、應變場與連續位移條件，再利用應變能與能量平衡方程式計算得到元素勁度矩陣與質量矩陣，探討靜態位移、暫態位移、感應電壓變化的影響。
靜態外力施於樑末端時，結果顯示出壓電材料越長或放置位置距離固定端處越近或材料越厚，位移和轉角則越小。施予相同外力，分析減震效果，結果顯示出壓電材料越長、位置離固定端越近、厚度越薄，則減震效果越佳。

In this thesis, the cantilevered Timoshenko beam surface mounted with a pair of piezoelectric layer is presented. The finite element method is adopted to analyze the behavior of the entire beam, considering coupling effect of force and voltage.
The shape functions of one element are obtained from solving the equations of static equilibrium. The stiffness matrix and mass matrix of the element are obtained by substituting the shape functions into the stain energy and the kinetic energy. Using a resistor to connect two surfaces of the piezoelectric layer to acts as a passive damper. Results show that the length, location and thickness of the piezoelectric layer play the significant factor on deformation of the entire beam.

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