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

Abstract

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.

Contactless, photoinitiated snap-through in azobenzene-functionalized polymers

“…In addition to informing the underlying mechanics of instructive examples from the natural world, such as the closing of the Venus fly-trap (10) or Hummingbird's beak (11), understanding and exploiting the mechanics of snap-through (also referred to as snapbuckling) can be useful for engineering active structures (12)(13)(14)(15)(16). Our demonstration of ultrafast actuation via photomechanical instabilities may offer a unique design paradigm, where an otherwise passive unit is prompted into motion by a directed photonic source.…”

Voltage-Induced Snap-Through of an Asymmetrically Laminated, Piezoelectric, Thin-Film Diaphragm Micro-Actuator—Part 1: Experimental Studies and Mathematical Modeling

“…Furthermore, these coefficients would vanish if the elastic properties of the piezoelectric layer had been ignored, which was assumed in many studies for piezoelectric smart structures, e.g., in Refs. [44], [46], and [47]. Second, it is also worth noting that the presence of the inner and outer electrodes has a similar effect with S nleÀ and S nleþ , as manifested by the coefficients S nle .…”

“…[30], and should be taken into account. Furthermore, for piezoelectric smart structures, the thickness of piezoelectric layers is often much thinner than elastic layers and assumed to be negligible, and so are their elastic properties [44,46,47]. However, as will be shown later in this paper, when the elastic properties of the piezoelectric layers are not negligible, the applied voltage affects the stiffness of a curved structure via the converse piezoelectric effect.…”

Elasticity and stability of shape-shifting structures

“…A recent review on this topic by Hu et al will hopefully provide a nice compliment to the following discussion [83]. There have been demonstrations of actuating snapthrough instabilities for just about every conceivable mechanical and non-mechanical stimulus, including temperature [84], light [85], acoustic excitation [86,87], elastomer or gel swelling [88,89,90,12], magnetic fields [91,92], fluid flow [93], surface tension or elastocapillarity [94], and electrical current with materials that include from ceramic (piezoelectric) [95,96], metallic (electrostatic) [97,98], and rubber (dielectric elastomers) [99,100,23,101]. Laminated composites of epoxy and carbon fiber or fiber glass may exhibit bistability or multistability while thermally curing [102,103,104,105].…”