Matthijs de Jong
Applied Mathematics, University of Waterloo
Stabilizability of piezoelectric material
Certain crystalline materials have the ability to develop an electric charge proportional to the mechanical stress in the material. This property is called the direct piezoelectric effect and was discovered in 1880 by the Curie brothers. These materials can also be deformed by the application of an electric charge. These characteristics allow for a wide application of piezoelectric materials as actuators or sensors in smart structures. Piezoelectric materials are used in many applications as a strip or patch of piezoelectric material known as piezoelectric beams and plates, respectively. The behavior of piezoelectric beam and plates depend on the interaction between the electric, magnetic, and mechanical effects and is non-trivial. The partial differential equations that describe the behavior can be made under various assumptions for the mechanical part of the beam and the electric-field. The resulting models have their own stabilizability properties and system performance. It is advisable to use the simplest model allowed for the application. In high-precision applications more accurate dynamic descriptions that incorporate nonlinear behavior, hysteresis, and creep are necessary. For control purposes, the models are approximated. The aim of the research project is to obtain a clear picture of the underlying mechanisms of the frameworks, assumptions, and approximation methods in relation to stabilizability, control, and system performance of piezoelectric material.