Experimental and theoretical investigation of the 2:1 internal resonance in the higher-order modes of a MEMS microbeam at elevated excitations

Abstract

We analyze the dynamics induced by a 2:1 internal resonance between the third (second symmetric) and the fifth (third symmetric) mode of a MEMS microbeam. An extensive experimental investigation is conducted, where forward and backward sweeps are systematically acquired up to elevated excitations. As ramping the voltage, a change along the forward sweep of the resonant branch is noted. This is analyzed via the combined use of different analytical and numerical tools, which show a phase shift between the modes involved in the 2:1 internal resonance. Constantly referring to the experimental data, simulations examine the underlying features of the system's behavior. The dynamics observed in the experimental frequency sweeps are part of a more complex scenario, where different attractors appear and coexist. The experimental behavior bifurcation chart is reported and compared with simulations, which offers a comprehensive view of the 2:1 internal resonance activation. The concurrence of numerical results and experimental data confirms on the effective actuality of these complex features in safe conditions, along wide ranges of the parameters space.