Two-to-one internal resonance of MEMS arch resonators

Type
Article

Authors
Hajjaj, Amal
Alfosail, Feras
Younis, Mohammad I.

KAUST Department
Mechanical Engineering Program
Physical Science and Engineering (PSE) Division

Online Publication Date
2018-10-06

Print Publication Date
2018-12

Date
2018-10-06

Abstract
We investigate experimentally and theoretically the two-to-one internal resonance between the first two symmetric vibrational modes of a micromachined arch resonator, which is electrothermally tuned and electrostatically driven. An electrothermal voltage is applied across the beam anchors, which controls its stiffness, and hence, tunes the ratio between the first two symmetric frequencies close to two. The dynamic behavior of the arch beam is examined when excited using large harmonic AC voltages, which leads to direct simultaneous excitation of the first two symmetric vibrational modes, in addition to the activation of the internal resonance. Varieties of complex behaviors are demonstrated including quasi-periodic and aperiodic motion leading to potential chaotic motion. A reduced order model based on the Galerkin procedure and the Euler–Bernoulli beam theory is utilized to analyze the dynamic response of the structure. Poincare sections, power spectra, and time histories are used to analyze the dynamic responses. A good agreement is shown among the experimental and theoretical results.

Citation
Hajjaj AZ, Alfosail FK, Younis MI (2018) Two-to-one internal resonance of MEMS arch resonators. International Journal of Non-Linear Mechanics 107: 64–72. Available: http://dx.doi.org/10.1016/j.ijnonlinmec.2018.09.014.

Acknowledgements
This research was support by KAUST, Saudi Arabia.

Publisher
Elsevier BV

Journal
International Journal of Non-Linear Mechanics

DOI
10.1016/j.ijnonlinmec.2018.09.014

Additional Links
https://www.sciencedirect.com/science/article/pii/S0020746218302397

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