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Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He’s iteration perturbation method

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Abstract

A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamic pull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-in instability of electrically actuated CNTs by employing an analytic approach namely He’s iteration perturbation method (IPM). The effects of basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on the pull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.

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Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61357-43337, Iran

    Hamid M. Sedighi

  2. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada

    Farhang Daneshmand

  3. Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec, H9X 3V9, Canada

    Farhang Daneshmand

  4. School of Mechanical Engineering, Shiraz University, Shiraz, Iran

    Farhang Daneshmand

Authors
  1. Hamid M. Sedighi
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Correspondence to Hamid M. Sedighi.

Additional information

Recommended by Associate Editor Ohseop Song

Hamid Mohammad-Sedighi was born in 1983 in Iran. He is currently a member of engineering faculty at Shahid Chamran University of Ahvaz in Iran. He obtained his Ph.D. (2013) from Shahid Chamran University, M.S. degree (2007) from the Shahid Chamran University and his undergraduate B.S. degree (2005) from the Shiraz University. His general academic areas of interest include the Applied Mathematics, Nonlinear Dynamical Systems, MEMS/NEMS and Machine Design.

Farhang Daneshmand is currently Adjunct Professor in the Department of Bioresource Engineering and Department of Mechanical Engineering at McGill University. He is also Associate Professor in the Department of Mechanical Engineering at Shiraz University in Iran. He received his Ph.D. in the Mechanical Engineering from Shiraz University on the Fluid- Structure Interaction Problems. His experience is related to computational solid mechanics and mathematical (analytical or semi-analytical) modelling of bio- and nano-structures from the view point of dynamic behaviour and vibration analysis. His current research interest concerns the fundamental understanding of mechanics of microtubules, nanotubes and nanoscale biological shell structures, including the effects of small-scale effects using nonlocal elasticity theory.

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Sedighi, H.M., Daneshmand, F. Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He’s iteration perturbation method. J Mech Sci Technol 28, 3459–3469 (2014). https://doi.org/10.1007/s12206-014-0807-x

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  • DOI: https://doi.org/10.1007/s12206-014-0807-x

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