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Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators

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Abstract

Motivated by the dynamics of microscale oscillators with thermo-optical feedback, a simplified third-order model capturing the key features of these oscillators is developed, where each oscillator consists of a displacement variable coupled to a temperature variable. Further, the dynamics of a pair of such oscillators coupled via a linear spring is analyzed. The analytical procedures used are the variational equation method and the two-variable expansion method. It is shown that the analytical results are in agreement with the results of numerical integration. The bifurcation structure of the system is revealed through a bifurcation diagram.

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Acknowledgements

This material is based upon work supported by the National Science Foundation under Grant Number CMMI-1634664. The authors wish to thank Professor John Guckenheimer for advising them on the bifurcations involved in this paper.

Funding

Funding has been received from NSF as acknowledged above. The entire research presented here is the authors’ own. No part of this article has been reproduced from other Articles or is under consideration elsewhere.

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Authors and Affiliations

  1. Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, 14853, USA

    Richard H. Rand, Alan T. Zehnder, B. Shayak & Aditya Bhaskar

  2. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Richard H. Rand

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  1. Richard H. Rand
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  2. Alan T. Zehnder
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  3. B. Shayak
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Correspondence to Richard H. Rand.

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Rand, R.H., Zehnder, A.T., Shayak, B. et al. Simplified model and analysis of a pair of coupled thermo-optical MEMS oscillators. Nonlinear Dyn 99, 73–83 (2020). https://doi.org/10.1007/s11071-019-05182-4

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