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Nonlocal plate model for dynamic pull-in instability analysis of circular higher-order shear deformable nanoplates including surface stress effect

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Abstract

In the present paper, dynamic pull-in instability and free vibration characteristics of circular higher-order shear deformable nanoplates subjected to hydrostatic and electrostatic forces are studied including surface stress effect. For this purpose, Eringen’s nonlocal elasticity continuum in conjunction with the Gurtin-Murdoch elasticity theory is incorporated into the classical higher-order shear deformation plate theory to develop size-dependent plate model able to consider both of small scale and surface stress effects. The non-classical governing differential equations are then discretized along with simply supported and clamped edge supports by employing generalized differential quadrature (GDQ) method. To evaluate the size-dependent pull-in voltage of nanoplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. It is demonstrated that the pull-in instability occurs at lower voltages for nanoplates with higher values of nonlocal parameters. Moreover, it is found that surface stress effect can increase or decrease the pull-in voltage of nanoplates which depends on the sign of surface elastic constants.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amirkabir University of Technology, P.O. Box 15875-4413, Tehran, Iran

    Saeid Sahmani & Mohsen Bahrami

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  1. Saeid Sahmani
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  2. Mohsen Bahrami
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Correspondence to Saeid Sahmani.

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Recommended by Chief-in-Editor Maenghyo Cho

Saeid Sahmani received his B.S. degree in Mechanical Engineering from University of Guilan, Iran, in 2006. He then received his M.S. degree from Iran University of Science and Technology in 2009. He is now continuing his study as Ph.D. student of Mechanical Engineering in Amirkabir University of Technology. He has published several scientific articles in excellent international journals. His research interests are nanomechanics and computational solid mechanics.

Mohsen Bahrami received his B.S. degree in Mechanical Engineering from Amirkabir University of Technology and received his M.S. and Ph.D. degrees in Mechanical Engineering from Oregon State University, United States, in 1982. Dr. Bahrami is currently a professor of solid mechanics at Department of Mechanical Engineering of Amirkabir University of Technology. He has published various journal papers and books. His research interests include mathematical modeling and analysis of robots, smart structures and computational micro- and nanomechanics.

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Sahmani, S., Bahrami, M. Nonlocal plate model for dynamic pull-in instability analysis of circular higher-order shear deformable nanoplates including surface stress effect. J Mech Sci Technol 29, 1151–1161 (2015). https://doi.org/10.1007/s12206-015-0227-6

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