Subcombination internal resonance of the additive type in the response dynamics of micromachined resonators crossing the impacting threshold

Abstract

In the present paper, a microbeam-based MEMS device is experimentally driven to experience a subcombination internal resonance (IR) of the additive type, where the second mode internally resonates with both the first and the third modes inducing a range of quasi-periodic dynamics. The main features of the experimental quasi-periodicity are analyzed, which inherently depend on the ratios established by the frequencies of the involved modes. Experimental Poincaré maps are established and tracked, exhibiting a specific underlying pattern. Numerical simulations are developed and the Fast Fourier Transform frequency trend lines are examined, showing the variations of the modes frequencies values while keeping the subcombination IR relationship. We investigate the evolution of the quasi-periodic waveform as increasing the excitation frequency. Special attention is devoted to the hardening dominance of the system, which influences the modes frequencies components. The last part of the paper is focused on the impacting regime. Since the microbeam is constituted by a dielectric layer (Silicon Nitride), impacts take place as raising the oscillation amplitudes. We analyze the experimental behavior at impacts, showing the possibility of dynamics with different characteristics, including both quasi-periodic, chaotic and periodic regions, all of them holding subcombination IR signature.