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

Abstract

Piezoelectric structures are used in a variety of applications where instant response, highenergy conversion efficiency and accurate control are required. However, it is widely knownthat piezoelectric structures suffer from a series of drawbacks, among which the mostimportant is the small displacement capacity. A number of techniques have been used inorder to transform the micron-scale displacements of PZT layers into meaningfulmillimeter-scale ones. Non-linear mechanics belong to this category, providing thepossibility to transform a traditional bimorph linear output structure into a non-linearhigh displacement actuator with increased combination of force/displacementoutput. In the present work the analytical modeling and the subsequent analysis ofnon-linear actuators with enhanced characteristics in terms of displacement ispresented. The piezoelectric structure that is studied is a traditional bimorph structurewith two piezoelectric layers and an aluminum substrate. The main concept is toleverage non-linear mechanics, and more specifically snap-through buckling, so thatlarge displacements can be achieved with the transition of the structure from oneequilibrium position to another. During the development process the importanceof boundary conditions has been revealed and thus special attention has beenprovided to this issue. A modified analytical model was elaborated in order tocome up with a closed form solution including relaxed boundary conditions. Theexperimental verification of the analytical and numerical model is presented in part II.