Investigation of the size effect on the resonant behavior of mesoscale cantilever beams

Abstract

A vibrational resonant cantilever beam device is a type of tactile vision substitution device for the visually impaired that has the potential to achieve a high resolution in a small space. In order to realize a device of this type, it is necessary to accurately model the resonant behavior of the mesoscale (0.1–1.0 mm) metal cantilever beams of which the device is composed. Specifically, the natural frequencies and damping ratios of these beams must be analytically modeled in order to design beam dimensions for the device. In this paper, the resonant frequencies and damping ratios of a set of A2 tool-steel mesoscale cantilever beams are obtained using three different methods: calculation based on a mass–spring–damper model of the beams; a forced response experiment; and a free response experiment. The results are compared, and the size effect on stiffness and elastic modulus is investigated. Based on the modified couple stress theory, the length scale parameter is calculated. The damping ratio difference depending on the dimension of material in the mesoscale is also investigated.