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Theoretical insights into 1:2 and 1:3 internal resonance for frequency stabilization in nonlinear micromechanical resonators

Year: 2025
Type: article
Abstract: Micromechanical resonators are essential components in time-keeping and sensing devices due to their high frequency, high quality factor, and sensitivity. However, their extremely low damping can lead to various nonlinear phenomena that can compromise frequency stability. A major limiting factor is the Duffing hardening effect, which causes frequency drift through amplitude variations, known as the amplitude-frequency effect. Recently, internal resonance (InRes) has emerged as an effective approach to mitigate this issue and enhance frequency stabilization. In this study, we investigate the frequency stabilization mechanisms of 1:2 and 1:3 InRes using a generalized two-mode reduced-order model that includes Duffing nonlinearity and nonlinear modal coupling. By analyzing the frequency response curves and $$\pi /2$$ π / 2 –backbone curves, we demonstrate how different parameters affect the effectiveness of frequency stabilization. Our results identify two distinct regimes depending on the coupling strength relative to the stiffening effect as a key factor in determining the stabilization mechanism. For the regime of weak coupling, both 1:2 and 1:3 InRes achieve frequency stabilization through amplitude and frequency saturation over a range of forcing amplitudes. In contrast, strong coupling reduces the amplitude-frequency effect by forming an asymptote line for 1:2 InRes or a zero-dispersion point for 1:3 InRes. These insights offer valuable guidelines for designing micromechanical resonators with high-frequency stability, highlighting InRes as a robust tool for enhancing performance in practical applications.
DOI: 10.1007/s11071-025-10987-7
Language: English
Open Access status: hybrid
Estimated APC paid: $4,790
OpenAlex ID: W4408314711
FWCI: 5.34
Cites: 48
Cited by: 14
Related to: 10