Free Vibration of Bistable Clamped-Clamped Beams: A Preliminary Study

Abstract

We present a preliminary study on bistable clamped-clamped beams both analytically and experimentally relating the linear post-buckling vibrations to the generated sound. In the analytical study, closed-form natural frequencies and mode shapes around the first buckled configuration are derived from an eigenvalue problem. It is found that as the static deflection of the buckled beam increases, the natural frequencies of the anti-symmetric vibrational modes stay constant, while those of the symmetric vibrational modes increase asymptotically. In the experimental study, a bistable clamped-clamped buckled beam made of steel is switched quasi-statically by hand between the two stable configurations. The generated sound is measured by a microphone and analyzed in both temporal and frequency domains, which agrees well with the analytical results. This work lays the foundation for using bistable beams in a variety of applications such as actuators, resonators, energy harvesters, and vibration reduction.