Université Libre de Bruxelles-BATir, 50 av FD Roosevelt, CP 194/02 B-1050 Brussels.
J Acoust Soc Am. 2011 Feb;129(2):681-90. doi: 10.1121/1.3523338.
When a voltage is applied across the electrodes of a flat piezoelectric transducer attached to a thin plate structure, the transducer acts as equivalent loads applied to the host plate structure. In this paper, analytical expressions of these equivalent loads are derived for the general case of an orthotropic piezoelectric actuator using Hamilton's principle and two different mathematical approaches leading to the same results: Green's theorem and derivation using the theory of distributions. The equivalent loads are a function of the material properties as well as the normal to the contour of the transducer. Examples of applications to simple geometric shapes (triangle, rectangle, and circle) are given.
当电压施加在附着于薄平板结构的平面压电换能器的电极上时，换能器充当等效负载施加于主平板结构。本文利用哈密尔顿原理和两种不同的数学方法（格林定理和分布理论的推导），针对各向异性压电致动器的一般情况，推导出这些等效负载的解析表达式。等效负载是材料特性以及换能器轮廓法线的函数。还给出了应用于简单几何形状（三角形、矩形和圆形）的示例。
