We investigate theoretically and experimentally the two-to-one internal resonance in micromachined arch beams, which are electrothermally tuned and electrostatically driven. By applying an electrothermal voltage across the arch, the ratio between its first two symmetric modes is tuned to two. We model the nonlinear response of the arch beam during the two-to-one internal resonance using the multiple scales perturbation method. The perturbation solution is expanded up to three orders considering the influence of the quadratic nonlinearities, cubic nonlinearities, and the two simultaneous excitations at higher AC voltages. The perturbation solutions are compared to those obtained from a multimode Galerkin procedure and to experimental data based on deliberately fabricated Silicon arch beam. Good agreement is found among the results. Results indicate that the system exhibits different types of bifurcations, such as saddle node and Hopf bifurcations, which can lead to quasi-periodic and potentially chaotic motions.
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January 2019
Research-Article
Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators
Feras K. Alfosail,
Feras K. Alfosail
Physical Sciences and Engineering Division,
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
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Amal Z. Hajjaj,
Amal Z. Hajjaj
Physical Sciences and Engineering Division,
King Abdullah University of Science
and Technology,
Thuwal 23955-9600, Saudi Arabia
King Abdullah University of Science
and Technology,
Thuwal 23955-9600, Saudi Arabia
Search for other works by this author on:
Mohammad I. Younis
Mohammad I. Younis
Physical Sciences and Engineering Division,
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
e-mail: Mohammad.Younis@KAUST.EDU.SA
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
e-mail: Mohammad.Younis@KAUST.EDU.SA
Search for other works by this author on:
Feras K. Alfosail
Physical Sciences and Engineering Division,
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
Amal Z. Hajjaj
Physical Sciences and Engineering Division,
King Abdullah University of Science
and Technology,
Thuwal 23955-9600, Saudi Arabia
King Abdullah University of Science
and Technology,
Thuwal 23955-9600, Saudi Arabia
Mohammad I. Younis
Physical Sciences and Engineering Division,
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
e-mail: Mohammad.Younis@KAUST.EDU.SA
King Abdullah University of Science and
Technology,
Thuwal 23955-9600, Saudi Arabia
e-mail: Mohammad.Younis@KAUST.EDU.SA
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 22, 2018; final manuscript received October 7, 2018; published online November 19, 2018. Assoc. Editor: Eihab Abdel-Rahman.
J. Comput. Nonlinear Dynam. Jan 2019, 14(1): 011001 (15 pages)
Published Online: November 19, 2018
Article history
Received:
May 22, 2018
Revised:
October 7, 2018
Citation
Alfosail, F. K., Hajjaj, A. Z., and Younis, M. I. (November 19, 2018). "Theoretical and Experimental Investigation of Two-to-One Internal Resonance in MEMS Arch Resonators." ASME. J. Comput. Nonlinear Dynam. January 2019; 14(1): 011001. https://doi.org/10.1115/1.4041771
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