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A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams

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Abstract

This paper uses He’s Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkin’s projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For verification, a numerical approach was implemented to solve the nonlinear equation. of vibration. A comparison between analytical and numerical results shows that HPM can predict system nonlinear vibrational behavior significantly more accurately than previously used methods in the literature.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Hamid Moeenfard & Mahdi Mojahedi

  2. Center of Excellence in Design, Robotics, and Automation, Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

    Mohammad Taghi Ahmadian

Authors
  1. Hamid Moeenfard
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  2. Mahdi Mojahedi
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  3. Mohammad Taghi Ahmadian
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Corresponding author

Correspondence to Mohammad Taghi Ahmadian.

Additional information

This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin

Hamid Moeenfard receives the M.Sc degree in mechanical engineering from Sharif university of technology, Tehran, Iran, 2008. He is currently working toward PhD degree in mechanical engineering at Sharif university of technology. His main interests are nonlinear vibration, N/MEMS and MOEMS, perturbation theory, Kantorovich method and fuzzy logic and control. His researches are mainly about modeling and analysis of static and dynamic pull-in in electrostatically actuated microbeams/plates using analytical models. His current research is the mechanical modeling of nonlinear vibration and static and dynamic pull-in of electrostatically actuated tosional micromirrors considering squeeze film damping and nonlinear electrical and mechanical nonlinearities.

Mahdi Mojahedi is currently PhD candidate in School of Mechanical Engineering at the Sharif University of Technology, Tehran, Iran. He has done his master of science in static instability and nonlinear vibrations of electrostatically actuated microbeams from the Sharif University of Technology, Tehran, Iran in 2009. His M.Sc. Work has been published in the refereed journals and conference proceedings. His research interests are static, dynamic and nonlinear vibration of micro/nano electromechanical systems.

Mohammad Taghi Ahmadian received his B.S. & M.S. degree in physics 1972 from Shiraz University, Shiraz, Iran and completed the requirements for B.S. & M.S. degree in mechanical Engineering in 1980 from university of Kansas in Lawrence. He received his PhD in Physics and PhD in Mechanical Engineering in 1981 and 1986 respectively from the same University. His research interests are Micro and Nano mechanics as well as bioengineering. He is currently a professor in the school of mechanical engineering and director of bioengineering research center at Sharif University of technology, Tehran, Iran.

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Moeenfard, H., Mojahedi, M. & Ahmadian, M.T. A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams. J Mech Sci Technol 25, 557–565 (2011). https://doi.org/10.1007/s12206-011-0130-8

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  • DOI: https://doi.org/10.1007/s12206-011-0130-8

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