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Surface energy and thermal stress effect on nonlinear vibration of electrostatically actuated circular micro-/nanoplates based on modified couple stress theory

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Abstract

Electrostatically actuated circular micro-/nanoplates are commonly used in micro-/nanoswitches and pumps. This paper models the thermal and size effects on the nonlinear vibration behavior of electrostatically actuated circular micro-/nanoplates. Surface elasticity and modified couple stress theories are simultaneously applied to the modeling. A reduced-order model incorporating temperature change is derived and solved numerically. Results show that the material length scale, surface energy, negative temperature change, and geometry nonlinear strain increase frequency and pull-in voltage of the plate. However, Casimir force and positive temperature change reduce the frequency of the plate. Moreover, the effects of surface energy, material length scale and temperature change on frequency become more obvious for thinner plates. The influence of the geometrically nonlinear strain on the frequency is significant for large initial gap to thickness ratio of the plate.

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Acknowledgments

This research was supported by the Natural Science Foundation of Guangdong Province of China (project nos. 2016A030310367, 2016A030311006), Research Innovation Fund of Shenzhen City of China (project no. JCYJ20150805142729431, JCYJ20160427184645305), the National Natural Science Foundation of China (project nos. 1167020127, 11372086, 1160020094), and China Postdoctoral Science Foundation Funded Special Project (project no.2016T90275).

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Authors and Affiliations

  1. Graduate School at Shenzhen, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    K. F. Wang & B. Wang

  2. School of Civil Engineering, Qingdao University of Technology, Qingdao, 266033, People’s Republic of China

    C. Zhang

  3. Institute for Infrastructure Engineering, Western Sydney University, Penrith, NSW, 2751, Australia

    B. Wang & C. Zhang

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  1. K. F. Wang
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  2. B. Wang
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  3. C. Zhang
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Correspondence to K. F. Wang.

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Wang, K.F., Wang, B. & Zhang, C. Surface energy and thermal stress effect on nonlinear vibration of electrostatically actuated circular micro-/nanoplates based on modified couple stress theory. Acta Mech 228, 129–140 (2017). https://doi.org/10.1007/s00707-016-1701-7

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  • DOI: https://doi.org/10.1007/s00707-016-1701-7

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