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A unified model for electrostatic sensors in fluid media

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Abstract

We present a unified model of electrostatic sensors comprising cantilever microbeam resonators in fluid media. The model couples Euler–Bernoulli beam equation to the nonlinear Reynolds equation. Static, damped eigenvalue, and dynamic reduced-order models were developed and validated by comparing a nonlinear frequency response of a gas sensor to its experimentally measured counterpart. Experiments were conducted to verify the capability of the developed model to predict the out-of-plane and in-plane natural frequencies of the sensor. The models were also used to investigate the potential operation of electrostatic chemical sensors based on different sensing mechanisms. While in-plane and out-of-plane vibration modes were found to be viable alternatives for resonant gas sensors, only in-plane modes were suitable to implement resonant chemical sensors due to the added mass and damping of liquid media. Similarly, higher-order modes were found more sensitive than lower order modes. Further, evidence was found for elastic interaction between out-of-plane modes and liquids in the channel underneath them but none for in-plane modes. Finally, the model predicts that in-plane modes provide the multi-valuedness necessary to implement bifurcation chemical sensors in liquid media.

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Acknowledgements

The author M. Ghommem gratefully acknowledges the financial support via the Biosciences and Bioengineering Research Institute Grant EN0277-BBRI18.

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Authors and Affiliations

  1. Department of Mechanical Engineering, American University of Sharjah, Sharjah, 26666, UAE

    Mehdi Ghommem

  2. Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, B.P. 743, 2078, La Marsa, Tunisia

    Fehmi Najar

  3. Systems Design Engineering, University of Waterloo, Waterloo, ON, Canada

    Mohamed Arabi & Eihab Abdel-Rahman

  4. Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada

    Mustafa Yavuz

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  1. Mehdi Ghommem
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  2. Fehmi Najar
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Correspondence to Mehdi Ghommem.

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Ghommem, M., Najar, F., Arabi, M. et al. A unified model for electrostatic sensors in fluid media. Nonlinear Dyn 101, 271–291 (2020). https://doi.org/10.1007/s11071-020-05780-7

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