1:6 Internal Resonance in CMOS-MEMS Multiple-Stepped CC-Beam Resonators

This work demonstrates, for the first time, internal resonance with a ratio as high as 1:6 in micromechanical CC-beam resonators. Particularly, multiple-stepped beams, similar to that used in [1] but with additional segments, of which the specifically tailored dimensions achieve the multiplication between its 1
^st
and 3
^rd
in-plane modes. Based on a CMOS-MEMS process platform, the stepped structure boosts the effect of geometric nonlinearity, resulting in strong intermodal coupling which leads to the 1:6 internal resonance. Instead of applying FEA to directly obtain the dimensions, this work first transforms the Euler-Bernoulli beam equation into algebraic expressions based on the Adomian decomposition method (ADM) [2], and then locates the initial combination using contour plots for the following fine tune in FEA. In addition to internal resonance, frequency combs are observed, possibly resulting from unidirectional mechanical excitation [3].