ANALYSIS AND SHAPE MODELING OF THIN PIEZOELECTRIC ACTUATORS

ANALYSIS AND SHAPE MODELING OF PIEZOELECTRIC ACTUATORS Makram Mouhli, B.S. A Thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering at Virginia Commonwealth University Virginia Commonwealth University, 2005 Advisor: Dr. Karla Mossi Assistant Professor, Department of Mechanical Engineering The field of smart materials is an increasingly growing area of research. In aerodynamics applications especially, transducers have to fulfill a series of requirements such as light weight, size, energy consumption, robustness and durability. Piezoelectric transducers, devices which transform an electrical signal into motion, fulfill many of these requirements. Specifically, piezoelectric composites are of interest due to their added toughness and ease of integration into a structure. Resulting composites have a characteristic initial curvature with accompanying residual stresses that are responsible for enhanced performance, relative to flat actuators, when the active material is energized. A number of transducer designs based on composites have been developed. Two of these piezoelectric composites called Thunder and Lipca are analyzed. Thunder is a xi composite of steel, polyimide adhesive, PZT, polyimide adhesive, and aluminum; and Lipca is a composite of fiberglass epoxy, carbon/epoxy, PZT, and fiberglass epoxy. Room temperature shapes of circular and rectangular Thunder and Lipca actuators are predicted by using the Rayleigh-Ritz model. This technique is based on the assumption that the stable geometric configuration developed in the actuator after manufacturing, is the configuration that minimizes the total potential energy. This energy is a function of the displacement field which can be approximated by two functions, a four term model, and a twenty-three term model. The coefficients in the models are determined by minimizing the total potential energy of the actuator. The actuator deformations are assumed to obey the Kirchhoff hypothesis and the actuator layers are assumed to be in the state of plane stress. The four coefficient model produces results not comparable to threedimensional surface topology maps. The twenty-three coefficient model however, is shown to have generally good agreement with the data for all studied actuators. To quantify the difference, at the cross section of each actuator, a profile is fitted by using a quadratic equation obtaining regression coefficients above 99%. For all actuators, the error between experimental and the calculated centerline data is less than 6%. For the 6R model however, the error is approximately 25%. One of the possible reasons for the error may be the tolerance of the thickness of the PZT layer. By changing the PZT thickness ±6% of the nominal value, over predicts the experimental dome height by 20%. Another possible reason for the discrepancy is the thickness of the actuator, thicker than all actuators used in this study, which might contradict the validity of the xii thin actuator assumption. Furthermore, by calculating the side-length-to-thickness ratio, 115 in this case, as stated by Aimmanee & Hyer (2004), may cause instability, and could result in unexpected behavior. The neutral axis position, calculated by using a force balance at equilibrium under the assumption of pure bending, for all actuators used in this study is determined and compared to the ceramic layer position. The results indicated that for all Thunder models the neutral axis is located below the ceramic layer indicating that the PZT wafer may be in total tension. For the Lipca C2 device however, the neutral axis is found to be above the ceramic layer, indicating that the piezoelectric layer may be in total compression. Strain fields are also predicted with contradicting results when compared to the theory that the ceramic is in tension in the Thunder actuators. The contradiction on the strain calculations can be explained by the manner the strain field is derived: by differentiating and squaring the high-order polynomials of the approximated displacement component losing accuracy when it comes to predicting normal and shear strains. The Rayleigh-Ritz technique can become a tool to perform parametric studies of the key elements for manufacturing to optimize specific features of the actuators.