An analytical model for the determination of resonance frequencies of perforated beams

In this paper, we develop closed expressions for the equivalent bending and shear stiffness of beams with regular square perforations, and apply them to the problem of determining the resonance frequencies of slender, regularly perforated clamped-clamped beams, which are of interest in the development of MEMS resonant devices. We prove that, depending on the perforation size, the Euler-Bernoulli equation or the more complex shear equation needs to be used to obtain accurate values for these frequencies. Extensive finite element method simulations are used to validate the proposed model over the full practical range of possible hole sizes. An experimental verification of the model is also presented.