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Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator

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Abstract

We study the dynamics of a resonantly driven nonlinear resonator (primary) that is nonlinearly coupled to a non-resonantly driven linear resonator (secondary) with a relatively short decay time. Due to its short relaxation time, the secondary resonator adiabatically tracks the primary resonator and modifies its response. Our model, which is motivated by experimental studies on the interaction between nano- and micro-resonators, is relatively simple and can be analyzed analytically and numerically to show that the driven response of the primary resonator can be enhanced significantly due to the interaction with the secondary resonator. Such an arrangement may pave the way for systematic control of driven responses and signal amplification in engineering applications involving nano- and micro-electro-mechanical-systems.

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Funding

The results described herein are based on previous efforts that were carried out over the last couple of years with Prof. Steven W. Shaw and Prof. Mark I. Dykman. The work of the authors is supported by the United States—Israel Binational Science Foundation (BSF) under Grant No. 2018041, and by the Pearlstone Center of Aeronautical Engineering Studies at Ben-Gurion University of the Negev. S.R. acknowledges the financial support of the Kreitman school of advanced graduate studies at Ben-Gurion University of the Negev under the STEM Scholarship.

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  1. Ben-Gurion University of the Negev, 84105, Beer-Sheva, Israel

    Sahar Rosenberg & Oriel Shoshani

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  1. Sahar Rosenberg
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  2. Oriel Shoshani
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Correspondence to Sahar Rosenberg.

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Rosenberg, S., Shoshani, O. Amplifying the response of a driven resonator via nonlinear interaction with a secondary resonator. Nonlinear Dyn 105, 1427–1436 (2021). https://doi.org/10.1007/s11071-021-06659-x

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