Snap-through buckling behavior of piezoelectric bimorph beams: I. Analytical and numerical modeling

Piezoelectric structures are used in a variety of applications where instant response, high energy conversion efficiency and accurate control are required. However, it is widely known that piezoelectric structures suffer from a series of drawbacks, among which the most important is the small displacement capacity. A number of techniques have been used in order to transform the micron-scale displacements of PZT layers into meaningful millimeter-scale ones. Non-linear mechanics belong to this category, providing the possibility to transform a traditional bimorph linear output structure into a non-linear high displacement actuator with increased combination of force/displacement output. In the present work the analytical modeling and the subsequent analysis of non-linear actuators with enhanced characteristics in terms of displacement is presented. The piezoelectric structure that is studied is a traditional bimorph structure with two piezoelectric layers and an aluminum substrate. The main concept is to leverage non-linear mechanics, and more specifically snap-through buckling, so that large displacements can be achieved with the transition of the structure from one equilibrium position to another. During the development process the importance of boundary conditions has been revealed and thus special attention has been provided to this issue. A modified analytical model was elaborated in order to come up with a closed form solution including relaxed boundary conditions. The experimental verification of the analytical and numerical model is presented in part II.