Suppression of Mechanical Stresses in Shaped Piezoelectric Bimorph-Structures

High local stress decreases the lifetime of products and is responsible for early breakdown due to material fatigue, and thus it is of great importance in the engineering industry. The objective of the present project is the suppression of mechanical stresses in flexible structures by means of piezoelectric transducers. So far, the research on structural control is mainly restricted to the control of displacements or strains. For purely elastic systems, the annihilation of the deformation field leads to the simultaneous suppression of mechanical stresses. For piezoelectric systems this is not the case. Due to the electromechanical coupling of the electrical field, the electric displacement, the mechanical strain and the mechanical stress, the latter is not necessarily zero, even if the displacement field vanishes, and vice versa. This fact leads to the question to be solved in the course of the project how to control mechanical stresses instead of vibrations themselves. At the beginning of the project the constitutive relations for piezoelectric materials are studied, in order to derive stress-based formulations. As a next step, electrical and kinematical beam and plate assumptions are combined in order to derive differential equations for the stress. First of all a piezoelastic bimorph is studied, for which control strategies for the suppression of axial and shear stresses are derived. These strategies are refined to control thick beams and plates. Special attention is paid to passively controlled systems. Conditions for the spatial distribution of the electroded piezoelectric layers, for the sheet resistance and for the electric circuit are found based on the electromechanically coupled beam and plate formulations. They are finally tested on a three- dimensional finite element model in ANSYS. The modeling of more complex, advanced strength-of- material theories for piezoelastic systems is a further major part of the project. Passive piezoelectric models for beams and plates are extended by the following effects: coupling to nonlinear circuits, higher order kinematical assumptions for the deformation of the cross-section, sandwich structures, interlaminar slip between layers and electrodes with finite conductivity. At last, energy harvesting concepts from the literature are combined with the derived stress suppression methods, i.e. stress- control methods are modified, such that the maximum axial stress is reduced and also the vibrational energy can be converted to electrical energy. An electrical circuit for a vibrating bimorph is designed, which on the one hand reduces stress and on the other hand harvests energy by switching between two kinds of electric circuits: one is responsible for stress control when the axial stress is above the fatigue stress level, and the other circuit is only active if the stress is low and energy harvesting is possible without decreasing the life-time of the structure.

The single-person project "Suppression of Mechanical Stresses in Shaped Piezoelectric Bimorph-Structures" investigates the question how to manipulate the state of stress in technical constructions. This question plays an important role since stress cracking may start and propagate due to overloading, which might cause material failure and malfunction. The project of Dr. Schöftner needs to be understood as a basic research project in which the practical applicability still plays a subordinate role. Rather, the question is answered with which technology it is possible to influence the mechanical stress in so-called slender beam structures in such a way that excessive load peaks remain below a permissible critical value. Not only static but also dynamic loads are examined. Only materials which couple at least more than two physical domains with one another are possible candidates: e.g. the piezoelectric material. The piezoelectric effect implies that mechanical shape changes (e.g. deformations) affect the electrical behavior (e.g. electric charge generation), and vice versa. With the help of this coupling effect, technically relevant constructions have been investigated, both theoretically and practically, to find solutions that have a positive effect on the life cycle of piezoelectric materials.