Finite Element Modellingand Simulations of Piezoelectric Actuators Responses with Uncertainty Quantification

Abstract

Piezoelectric structures are widely used in engineering designs including sensors, actuators, and energy-harvesting devices. In this paper, we present the development of a three-dimensional finite element model for simulations of piezoelectric actuators and quantification of their responses under uncertain parameter inputs. The implementation of the finite element model is based on standard nodal approach extended for piezoelectric materials using three-dimensional tetrahedral and hexahedral elements. To account for electrical-mechanical coupling in piezoelectric materials, an additional degree of freedom for electrical potential is added to each node in those elements together with their usual mechanical displacement unknowns. The development was validated with analytical and experimental data for a range of problems from a single-layer piezoelectric beam to multiple layer beams in unimorph and bimorph arrangement. A more detailed analysis is conducted for a unimorph composite plate actuator with different design parameters. Uncertainty quantification was also performed to evaluate the sensitivity of the responses of the piezoelectric composite plate with an uncertain input of material properties. This sheds light on understanding the variations in reported responses of the device; at the same time, providing extra confidence to the numerical model.