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Investigation of the internal stress effects on static and dynamic characteristics of an electrostatically actuated beam for MEMS and NEMS application

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Abstract

Internal stress is often encountered in fixed–fixed beam based devices with micron or sub-micron length scales during device fabrication or operation. In this paper, we have investigated the effects of internal stress on static and dynamic characteristics of an electrostatically actuated cylindrical beam. The beam has been modelled using Euler–Bernoulli theory including the nonlinearities due to beam stretching and electrostatic forcing. The analysis has been carried out by solving the governing differential equations using a Galerkin based multi-modal reduced order modelling technique. A standard collocation based numerical scheme has also been used to confirm the results of the reduced order method. Our study shows that internal stress significantly influences the static and dynamic characteristics of the beam. We also find that, when compressive internal stress is high, it is important to include higher modes in the reduced order model. A design technique to achieve high resonant frequency stability under temperature variation, for electrostatically actuated beam oscillators, has also been proposed as a result of this investigation.

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Acknowledgments

The authors gratefully acknowledge financial support from the Industrial Research and Consultancy Centre, IIT Bombay and the Department of Science and Technology, Government of India. The author would like to thank to Prof. Mandar M. Desmukh and Mr. Hari S. Solanki of Tata Institute of Fundamental Research and Mr. Manish M. Joglekar of IIT Bombay for useful discussions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    A. Bhushan & D. N. Pawaskar

  2. Department of Civil Engineering, Indian Institute of Technology Bombay, Mumbai, 400076, India

    M. M. Inamdar

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  1. A. Bhushan
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  2. M. M. Inamdar
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  3. D. N. Pawaskar
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Correspondence to D. N. Pawaskar.

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Bhushan, A., Inamdar, M.M. & Pawaskar, D.N. Investigation of the internal stress effects on static and dynamic characteristics of an electrostatically actuated beam for MEMS and NEMS application. Microsyst Technol 17, 1779–1789 (2011). https://doi.org/10.1007/s00542-011-1367-y

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