The Effect of Poisson Ratio and Beam Width on the Fundamental Frequency of a Cantilever Beam

This study considers the influence of the Poisson ratio and beam width on the fundamental frequency of cantilever beams, i.e. their natural frequency at infinitesimal amplitudes of vibrations. We show that the fundamental frequency of a cantilever increases with increasing Poisson ratio, and also increases with increasing beam width. Within the context of linear theory, we show that this effect is caused by a decrease in inertia rather than an increase in stiffness. This insight may be relevant to studies of the nonlinear response of cantilevers, where an increase in the fundamental frequency may be partially attributed to a decrease of inertia.