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Dynamics of a System of Two Coupled MEMS Oscillators

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IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems (ENOLIDES 2018)

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 37))

Abstract

We investigate the dynamics of two limit cycle MEMS oscillators connected via spring coupling. Each individual oscillator is based on a MEMS structure which moves within a laser-driven interference pattern. As the structure vibrates, it changes the interference gap, causing the quantity of absorbed light to change, producing a feedback loop between the motion and the absorbed light and resulting in a limit cycle oscillation. A simplified model of this MEMS oscillator, omitting parametric feedback and structural damping, has been previously presented (Rand et al in Proceedings of 9th European Nonlinear Dynamics Conference (ENOC 2017), 2017, [3]). For the coupled system, a perturbation method is used to obtain a slow flow which is investigated using AUTO and numerical integration. Various bifurcations which occur as a result of changing the coupling strength are identified.

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References

  1. Aubin, K., Zalalutdinov, M., Alan, T., Reichenbach, R.B., Rand, R., Zehnder, A., Parpia, J., Craighead, H.: Limit cycle oscillations in CW laser-driven NEMS. J. Microelectromechanical Syst. 13, 1018–1026 (2004)

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  2. Zehnder, A.T., Rand, R.H., Krylov, S.: Phase locking of electrostatically coupled thermo-optically driven MEMS limit cycle oscillators. Int. J. Non-Linear Mech. 102, 92–100 (2018)

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  3. Rand, R.H., Zehnder, A.T., Shayak B.: Analysis of a simplified MEMS oscillator. In: Proceedings of 9th European Nonlinear Dynamics Conference (ENOC 2017), 25–30 June 2017, Budapest, Hungary. https://congressline.hu/enoc2017/abstracts/77.pdf (2017)

  4. Rand, R.H.: Lecture Notes in Nonlinear Vibrations. The Internet-First University Press. http://ecommons.library.cornell.edu/handle/1813/28989 (2012)

  5. Doedel, E.: see AUTO homepage. http://indy.cs.concordia.ca/auto/ (1996)

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Acknowledgements

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

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Authors and Affiliations

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

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

Authors
  1. Richard H. Rand
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  2. Alan T. Zehnder
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  3. B. Shayak
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  4. Aditya Bhaskar
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Corresponding author

Correspondence to Richard H. Rand .

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Editors and Affiliations

  1. Centre for Vibro-Acoustic Systems and Signal Processing, Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia

    Ivana Kovacic

  2. Department of Civil and Building Engineering, and Architecture, Polytechnic University of Marche, Ancona, Italy

    Stefano Lenci

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Rand, R.H., Zehnder, A.T., Shayak, B., Bhaskar, A. (2020). Dynamics of a System of Two Coupled MEMS Oscillators. In: Kovacic, I., Lenci, S. (eds) IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems. ENOLIDES 2018. IUTAM Bookseries, vol 37. Springer, Cham. https://doi.org/10.1007/978-3-030-23692-2_20

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  • DOI: https://doi.org/10.1007/978-3-030-23692-2_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-23691-5

  • Online ISBN: 978-3-030-23692-2

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