本文利用半雙曲線近似下推導而得的線彈性壓電控制方程式與本構方程式，解析一含有限長裂紋之無窮域壓電材料，於裂紋面上施加反平面庭; 力及平面電位移的簡諧載荷問題。本文利用積分轉換法求得含裂紋之壓電材料受簡諧載荷時的解析解，並與穩靜態近似下所得到之解作比較。最後針對所求之應力強度因子振幅大小以及相位，做詳細的數值計算與討論。 In this study, the quasi-hyperbolic approximation is used to investigate the dynamic behavior of a crack under the action of anti-plane stresses and in-plane electric displacements in a piezoelectric material. First, the steady-state response of a finite crack subjected to harmonically anti-plane loading and in-plane electric displacement on crack faces is analyzed. The stress intensity factors and electric displacement intensity factors are obtained for the problem. Finally, numerical results of the first problem are evaluated and discussed in detail.
