On the resonance frequencies of microbridges

The authors present the exact analysis of the natural frequencies of transverse bending of flat clamped-clamped beams subject to an axial force. Extensions of this model are presented for several aspects of transversely vibrating microbridges for which this model falls short. The behavior of buckled or initially deflected beams is modeled, as well as the behavior of beams with a small length-to-width ratio. The deformation of the elastic support is analyzed, revealing a significant compliance of the support compared to typical compliances of microbridges. The results of these models are compared with experimental results obtained from a resonating microbridge mass flow sensor.<>