Experimental Evidence of Two Competing Effects in the Nonlinear Response of Cantilever Beams

This work considers the nonlinear stiffening or softening response of cantilever beams that are made from (100) single-crystalline-silicon (SCS). A stiffening or softening response indicates a respective increase or decrease of the resonance frequency, as vibration amplitude is increased. We demonstrate, for the first time ever, how this effect depends on: 1) Crystal orientation of the beam axis - [100] or [110], and 2) The ratio between the width and length of the beam. We describe two competing effects, one that causes a softening response and the other that causes a stiffening response. The relevance of this work is that it points the way to designing linear cantilever resonators that are exactly in-between stiffening and softening, which means that their resonance frequency is independent of vibration amplitude.