Piezoelectric materials have a wide range of industrial applications in different branches of engineering due to their electromechanical coupling. So, investigating their responses to either mechanical or electric loadings helps engineers for efficient design of smart systems. However, most of the studies have assessed the well-known 6 mm piezoelectric materials or piezoceramics and few papers have studied other piezoelectric crystals despite of their application in industry. In this paper, fundamental solutions of a trigonal piezoelectric half-plane belonging to 3m crystal class is obtained. The governing differential equations are derived and solved analytically using potential method. It is shown that the solution for the 3m material can be degenerated to 6 mm solution as a special case. The contour lines were depicted for two practical piezoelectric materials belonging to 3m and 6 mm crystal classes including lithium niobate and PZT-4 and they were compared to each other. The numerical results showed that the response of the trigonal material is asymmetric due to anisotropy and the effect of anisotropy on some responses is considerable causing totally different behavior from 6 mm piezoelectric material.

压电材料由于其机电耦合，在不同工程领域具有广泛的工业应用。因此，调查他们对机械或电力负载的响应有助于工程师有效地设计智能系统。但是，大多数研究评估了众所周知的6 mm压电材料或压电陶瓷，尽管在工业中得到了应用，但很少有论文研究其他压电晶体。本文获得了属于3m晶体类的三角压电半平面的基本解。控制微分方程被推导并使用势能方法解析求解。结果表明，在特殊情况下，3m材料的溶液可以退化为6mm溶液。描绘了两种实用的压电材料的轮廓线，它们属于3m和6 mm的晶体类别，包括铌酸锂和PZT-4，并将它们相互比较。数值结果表明，由于各向异性，三角材料的响应是不对称的，并且各向异性对某些响应的影响相当大，从而导致行为与6 mm压电材料完全不同。