Theses and Dissertations at Montana State University (MSU)
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Item Finite element modeling of piezoelectric bimorphs with conductive polymer electrodes(Montana State University - Bozeman, College of Letters & Science, 2010) Lediaev, Laura Marie; Chairperson, Graduate Committee: V. Hugo SchmidtThe 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.Item Modeling piezoelectric pvdf sheets with conductive polymer electrodes(Montana State University - Bozeman, College of Letters & Science, 2006) Lediaev, Laura Marie; Chairperson, Graduate Committee: V. Hugo SchmidtThe main concern of my research has been to find a good way to solve for the behavior of piezoelectric devices that are electroded not with metal electrodes (as has traditionally been the case) but with a conductive polymer material which has a much lower conductivity compared to metal. In this situation, if a time-varying voltage is applied at one end of the electrode, the voltage cannot be assumed to be uniform throughout the electrode because of the effects of resistivity. Determining the voltage in the electrodes as a function of time and position concurrently with the mechanical and electrical response of the piezoelectric material presents an added complexity. In this thesis the problem of the piezoelectric monomorph is considered. The piezoelectric sheet is PVDF, and the electrodes are PEDOT-PSS. As a first approximation the two problems of finding the voltage in the electrodes and the mechanical deformation in the piezoelectric material are decoupled. In order to determine the voltage distribution in the electrodes, the piezoelectric effects were neglected, which reduced the piezoelectric problem to a capacitor problem. Once the voltage function was determined the mechanical deformation of the PVDF sheet was calculated given the known voltage distribution as a function of position and time.