Free Vibration of Bistable Clamped–Clamped Beams: Modeling and Experiment

Abstract

Bistable clamped–clamped beams have been used in a wide range of applications such as switches, resonators, energy harvesting, and vibration reduction. Most studies on this classic buckling problem focus on obtaining either the static configuration and the required critical axial load or the natural frequencies and mode shapes of postbuckling vibrations analytically. In this article, we present our study including analytical modeling and experimental method on bistable clamped–clamped beams, aiming to understand the detailed snap-through process and the ensuing vibration. In the analytical model, by decomposing the transverse deflection into static buckling configuration and linear vibration, we obtain the natural frequencies and mode shapes for the buckled beam and investigate the effects of static deflection on the symmetric and antisymmetric modes. An experimental design using noncontact methods is implemented to directly measure the response of the whole beam in the snap-through process and the sound generated by the vibrating beam. The measurements are characterized in both time and frequency domain and found to be in good agreement with the analytical model. The study presented in this article enhances the fundamental understanding of the classical problem of bistable clamped–clamped beams.