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Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

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Abstract

In the present work, based on strain gradient theory, the free vibration analysis of tapered viscoelastic micro-rod resting on visco-Pasternak foundation is investigated. The material properties of micro-rod are assumed the visco-elastic and modeled as the Kelvin-Voigt. Using Hamilton's principle and energy method, the governing equation of motion of viscoelastic micro-rods is derived, then this obtained equation using the differential quadrature method (DQM) for different boundary conditions is solved. In this study, the effects of various parameters such as the structural damping coefficient, Winkler and Pasternak foundation modulli, damping coefficient of the elastic medium and material length scale parameters on the non-dimensional natural frequencies of viscoelastic micro-rod are investigated. The results show that with an increase in the Winkler and Pasternak coefficients, the natural frequency increases as well as the obtained nondimensional natural frequencies by MCST and SGT decrease by increasing the material length to radius ratio. It can be seen that the nondimensional frequency for SGT is higher than that of the other theories. It is shown that the non-dimensional frequencies increase by increasing the damping coefficient for all theories. Moreover, at the specified value of damping coefficient of the elastic medium, the variation of non-dimensional natural frequency is approximately smooth.

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Authors and Affiliations

  1. Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

    M. Mohammadimehr, A. A. Monajemi & M. Moradi

Authors
  1. M. Mohammadimehr
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  2. A. A. Monajemi
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  3. M. Moradi
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Corresponding author

Correspondence to M. Mohammadimehr.

Additional information

Recommended by Associate Editor Moon Ki Kim

Mehdi Mohammadimehr received his B.S. degree from the University of Kashan in Kashan, Iran, in 2002. He then received his M.Sc and Ph.D. degrees from Shahid Bahonar University of Kerman in Kerman, Iran, in 2004 and 22 May 2010. Dr. Mehdi Mohammadimehr is currently an Assistant Professor in Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan in Kashan, Iran. His research interests include elasticity, plasticity, continuum mechanics, nanomechanics, composite and nanocomposite materials, functionally graded materials (FGMs), smart materials, beams, plates and shells theories, buckling, postbuckling and vibration analyses of carbon nanotubes(CNTs) and boron nitride nanotubes (BNNTs), and numerical method such as finite element method (FEM), differential quadrature method (DQM), Galerkin and Rayleigh-Ritz methods.

Ahmad Ali Monajemi received his B.S. degree from the University of Kashan in Kashan, Iran, in 2011. He is currently a M.S. student at University of Kashan, Iran. His research interests are vibration analyses of carbon nano-tubes (CNTs), functionally graded materials (FGMs) smart materials, and finite element method.

Mehdi Moradi received his B.S. degree from the University of Razi in Kermanshah, Iran, in 2010. He then received his M.S. degree from University of Kashan in Kashan, Iran, in 2012. He is currently a Ph.D. student at University of Kashan. His research interests include plasticity, creep, damage mechanism, composite materials, functionally graded materials (FGMs), and vibration analysis.

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Mohammadimehr, M., Monajemi, A.A. & Moradi, M. Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM. J Mech Sci Technol 29, 2297–2305 (2015). https://doi.org/10.1007/s12206-015-0522-2

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  • DOI: https://doi.org/10.1007/s12206-015-0522-2

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