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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2410.03109 |
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| _version_ | 1866909335699849216 |
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| author | Donmez, Ata Herath, Hansaja Cho, Hanna |
| author_facet | Donmez, Ata Herath, Hansaja Cho, Hanna |
| contents | 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-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03109 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theoretical Insights into 1:2 and 1:3 Internal Resonance for Frequency Stabilization in Nonlinear Micromechanical Resonators Donmez, Ata Herath, Hansaja Cho, Hanna Applied Physics 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-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. |
| title | Theoretical Insights into 1:2 and 1:3 Internal Resonance for Frequency Stabilization in Nonlinear Micromechanical Resonators |
| topic | Applied Physics |
| url | https://arxiv.org/abs/2410.03109 |