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Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment

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Abstract

This research deals with nonlinear-free vibration responses of the sandwich nano-beams with functionally graded (FG) face-sheets reinforced with carbon nanotubes (CNTs) based on various higher-order shear deformation beam theories (HSDBT) and nonlocal strain gradient theory. Three various patterns of CNTs are employed in our analyses. The beam is subjected to thermal and electrical loads while it is resting on nonlinear Pasternak foundation. The nonlinear Von-Karman relations as well as nonlocal strain gradient theory is employed for this analysis. The governing equations of motion are derived using Hamilton principle based on various shear deformation theories. The nonlinear governing equations of motion are solved using differential quadrature method (DQM). After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as various shear deformation theories, length scale parameter, nonlocal parameter, volume fraction of the CNTs, Pasternak foundation parameters, applied voltage, and temperature change on the vibration characteristics of sandwich nano-beam. The numerical results indicate that the FG-VA pattern represents nonlinear natural frequencies greater than other patterns.

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Abbreviations

FG:

Functionally graded

CNTs:

Carbon nanotubes

PDE:

Partial differential equation

ODE:

Ordinary differential equation

MTS:

Multiple times scale

UD:

Uniform distribution

SWCNT:

Single-walled carbon nanotube

CFs:

Carbon fibers

CNTRCs:

Carbon nanotube-reinforced composites

MEMS:

Micro-electro-mechanical systems

NEMS:

Nano-electro-mechanical systems

MLPG:

Meshless local Petrov–Galerkin

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Acknowledgements

The research described in this paper was financially supported by the University of Kashan. (Grant No 574613/41). The first author would also like to thank the Iranian Nanotechnology Development Committee for their financial support.

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Authors and Affiliations

  1. Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, 87317-53153, Kashan, Iran

    M. Arefi, M. Pourjamshidian & A. Ghorbanpour Arani

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  1. M. Arefi
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Correspondence to M. Arefi.

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Arefi, M., Pourjamshidian, M. & Ghorbanpour Arani, A. Application of nonlocal strain gradient theory and various shear deformation theories to nonlinear vibration analysis of sandwich nano-beam with FG-CNTRCs face-sheets in electro-thermal environment. Appl. Phys. A 123, 323 (2017). https://doi.org/10.1007/s00339-017-0922-5

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