Shape Optimization of Cantilevered Piezoelectric Devices

Abstract

Energy harvesting using piezoelectric devices has received considerable attention in the past few years. The most commonly used devices have been cantilevered bimorphs with a large proof mass attached to it. The goal of this paper is to discuss the effects of varying geometry to enhance the average strain through a material via shape optimization into triangular type geometries from a quantitative point of view, while studying the internal strain energy and the stress distribution over the surface when a cantilevered device is loaded. When a triangular cantilever is compared to a rectangular counterpart with the same volume, the stress over its surface is linear, as it has a more constant radius of curvature, and its loading capacity effectively doubles. These concepts are explored numerically using ANSYS. The concept of internal strain energy per unit area over the length span of the beam is used to evaluate the amount of average energy stored in the material over the surface, and shows that regardless of geometry, the value is strictly a function of volume of the device. The linear stress distribution over the length of triangular beams, and their relations with the volume when compared to a rectangular cantilever is the standout property that would allow much more reliable operation of cantilevered brittle piezoelectric ceramic devices.