Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

Asaf Asher,Rivka Gilat,Slava Krylov

doi:10.3390/app12052704

Abstract

Configuration-dependent spectral behavior of initially curved circular microplates loaded by a distributed nonlinear electrostatic force is investigated. The structures under consideration are distinguished by two interesting features. The first is that the plates are initially bell-shaped, rather than flat or spherical, and therefore have regions of both positive and negative curvature. Second, the plates are sufficiently curved to exhibit snap-through buckling and bistability. The structure is described in the framework of the nonlinear Föppl von Kármán shallow plate theory. The influence of the initial curvature and loading on the free vibrations around unloaded and deformed equilibria is investigated. The results of the Galerkin model backed by the finite elements analysis show that the modes of even slightly curved bell-shaped unloaded plates differ significantly from those of the initially flat plates. As a result, when the natural modes of a curved plate are used as the base functions, a significantly better convergence of the RO model is achieved. In the vicinity of the critical snap-through and snap-back configurations, the sensitivity of the natural frequencies to the plate deflection is much higher than in the unloaded state. This high tunability opens new opportunities for the design of better resonant sensors with enhanced performance.

Highlights

Bistable micro and nanostructures such as initially curved beams, plates, or spherical caps manifest several unique features making them attractive for implementation in microand nanoelectromechanical systems (MEMS/NEMS)
Prior to using the ROM for the vibration analysis of the plate, the ROM was verified by comparing its results with those provided by the finite elements (FE) simulation carried out using Ansys package
The RO model is used to describe the static responses of the plates to the quasi-static loading and to obtain the frequencies and modes of the free vibrations of the mechanically and electrostatically actuated plates around the equilibrium configurations

Summary

Introduction

Bistable micro and nanostructures such as initially curved beams, plates, or spherical caps manifest several unique features making them attractive for implementation in microand nanoelectromechanical systems (MEMS/NEMS). When subject to a quasi-statically increasing loading, these devices manifest abrupt , commonly referred as a snap-through (ST), transition between two different stable configurations once the loads exceed a certain critical ST value. The decrease of the force below another, snap-back (SB) or release (R), critical value is followed by the snapping of the device back to its first, associated with the smaller deflection, stable configuration.The intrinsic hysteresis of the loading–unloading cycle (since SB and ST forces and deflections are different) is exploited in electrical and optical switches, micro- and nanomechanical nonvolatile memories, or MEMS/NEMS logic elements [1–3]. The extremely high sensitivity of the bistable devices in the vicinity of the critical ST and SB configurations lies in the foundations of threshold accelerometers, inertial switches, gas, pressure, and flow sensors [1,2,8–10], as well as event-based wake-up sensors for Internet of Things (IoT) applications [11,12]. Wideband natural frequencies tunability of bistable devices in the configurations close to the ST or SB points is exploit to increase the sensitivity of resonant sensors [13,14]

Methods

Results

Conclusion