| 1. |
- Czaplewski, David A., et al.
(författare)
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Bifurcation Generated Mechanical Frequency Comb
- 2018
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Ingår i: Physical Review Letters. - 1079-7114 .- 0031-9007. ; 121:24
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Tidskriftsartikel (refereegranskat)abstract
- We demonstrate a novel response of a nonlinear micromechanical resonator when operated in a region of strong, nonlinear mode coupling. The system is excited with a single drive signal and its response is characterized by periodic amplitude modulations that occur at timescales based on system parameters. The periodic amplitude modulations of the resonator are a consequence of nonlinear mode coupling and are responsible for the emergence of a "frequency-comb" regime in the spectral response. By considering a generic model for a 13 internal resonance, we demonstrate that the novel behavior results from a saddle node on an invariant circle (SNIC) bifurcation. The ability to control the operating parameters of the micromechanical structures reported here makes the simple micromechanical resonator an ideal test bed to study the dynamic response of SNIC behavior demonstrated in mechanical, optical, and biological systems.
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| 2. |
- Eriksson, Axel, 1989, et al.
(författare)
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Controllable branching of robust response patterns in nonlinear mechanical resonators
- 2023
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Ingår i: Nature Communications. - : Springer Science and Business Media LLC. - 2041-1723 .- 2041-1723. ; 14:1, s. 161-
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Tidskriftsartikel (refereegranskat)abstract
- In lieu of continuous time active feedback control in complex systems, nonlinear dynamics offers a means to generate desired long-term responses using short-time control signals. This type of control has been proposed for use in resonators that exhibit a plethora of complex dynamic behaviors resulting from energy exchange between modes. However, the dynamic response and, ultimately, the ability to control the response of these systems remains poorly understood. Here, we show that a micromechanical resonator can generate diverse, robust dynamical responses that occur on a timescale five orders of magnitude larger than the external harmonic driving and these responses can be selected by inserting small pulses at specific branching points. We develop a theoretical model and experimentally show the ability to control these response patterns. Hence, these mechanical resonators may represent a simple physical platform for the development of springboard concepts for nonlinear, flexible, yet robust dynamics found in other areas of physics, chemistry, and biology.
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