Finite element modeling of piezoelectric bimorphs with conductive polymer electrodes

Abstract

The purpose of my research has been to find a good way to solve for the mechanical and electrical behavior of piezoelectric polymer bimorphs which are electroded with a low to medium conductivity material. Traditionally, metal with very high conductivity has been used as the electrode material. Any applied voltage to an electrode will be distributed nearly instantaneously and uniformly throughout the electrode. Because of this quality, the voltage was assumed to be known and uniform for any applied voltage signal, including high frequency signals. The disadvantage of metal is that it is stiffer than polymers, and thus impedes the bending of the bimorph to a greater extent than for comparable polymer electrodes. With the modern invention of conductive polymers with acceptably high conductivities, it is now possible to manufacture piezoelectric devices with finite conductivity electrodes. For all but the very lowest frequencies of applied voltage signals, the voltage distribution cannot be assumed to be uniform throughout the electrode, nor can it be assumed to be exactly in phase. With finite conductivity electrodes there will be a loss in voltage amplitude due to resistivity, and there will also be a phase lag. The piezoelectric problem involves solving a coupled set of differential equations which involve mechanical displacement and electric potential. The electrical behavior of the electrodes is also included in the formulation, so that the voltage distribution in the electrodes is solved for simultaneously with the mechanical displacement and electric potential in the piezoelectric sheets. In this dissertation the coupled set of differential equations was solved using the Finite Element Method with quadratic Lagrange finite elements. The piezoelectric polymer which was modeled was polyvinylidene fluoride (PVDF). The conductive polymer of interest was PEDOT-PSS, although the model is valid for any type of isotropic finite conductivity material. The results of the work show that for moderate conductivity, the mechanical response of the bimorph is very good. There will not be a large phase lag within the first frequency mode. The bimorph resonates at low frequencies, and so any large effect from finite conductivity would only occur at higher modes.