本文探討半平面之壓電陶瓷，表面有極薄之實圓或環形電極，探討其電彈場之軸對稱問題。假設材料沿著對稱軸 軸的方向極化。根據線彈性壓電力學，利用漢可轉換將實圓與環形表面電極問題，分別化簡為對偶積分方程與三聯立積分方程。查表可得對偶積分方程之解，求得實圓電極之電彈場的閉合解。經複雜的數學推導，三聯立積分方程將化簡為一組無窮聯立代數方程，求得環形電極之部份電彈場的數值解。結果顯示實圓與環形電極之電彈場，慣例性地在電極尖端皆呈現r-0.5的奇異性。

In this paper the axisymmetric problem of the electroelastic of piezoelectric ceramic in a half-plane with thin circular or ring surface electrode is formulated and analyzed. The material is polarized along z-axis, the axial direction. Based on the linear electroelastic theory, Hankel transform method is used to reduce the circular and ring surface electrode problems to dual integral equations and triple integral equations, respectively. The electroelastic field of the circular electrode problem is obtained in closed form by exactly solving the dual integral equations. However, due to the complicated mathematics, the triple integral equations will reduced to an infinite set of simultaneous equations. Part of the electroelastic field for the ring electrode problem can be obtained numerically. The results show that the electroelastic filed near the electrode tips has the conventional square root singularity for both electrode problems.

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