Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams

Mohammad Arefi, Mahmoud Pourjamshidian, Ali Ghorbanpour Arani, Timon Rabczuk

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.

Original languageEnglish
JournalJournal of Low Frequency Noise Vibration and Active Control
DOIs
Publication statusAccepted/In press - 2018 Jan 1

Fingerprint

residual stress
Residual stresses
vibration
power law
elasticity
Elasticity
Equations of motion
piezoelectricity
gradients
elastic properties
Functionally graded materials
Piezoelectricity
scale effect
equations of motion
Shear deformation
nonlinearity
stiffness
shear
Natural frequencies
Materials properties

Keywords

  • Flexoelectric
  • functionally graded beam
  • nonlinear vibration
  • residual surface stresses
  • sigmoid and power
  • surface effects

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Geophysics
  • Mechanical Engineering

Cite this

Influence of flexoelectric, small-scale, surface and residual stress on the nonlinear vibration of sigmoid, exponential and power-law FG Timoshenko nano-beams. / Arefi, Mohammad; Pourjamshidian, Mahmoud; Ghorbanpour Arani, Ali; Rabczuk, Timon.

In: Journal of Low Frequency Noise Vibration and Active Control, 01.01.2018.

Research output: Contribution to journalArticle

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abstract = "This research deals with the nonlinear vibration of the functionally graded nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The flexoelectric functionally graded nano-beam is resting on nonlinear Pasternak foundation. Cubic nonlinearity is assumed for foundation. It is assumed that the material properties of the nano-beam change continuously along the thickness direction according to different patterns of material distribution. In order to include coupling of strain gradients and electrical polarizations in equation of motion, the nonlocal, nonclassical nano-beam model containing flexoelectric effect is employed. In addition, the effects of surface elasticity, di-electricity, and piezoelectricity as well as bulk flexoelectricity are accounted in constitutive relations. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory and the nonlocal strain gradient elasticity theory considering residual surface stresses. The differential quadrature method is used to calculate nonlinear natural frequency of flexoelectric functionally graded nano-beam as well as nonlinear vibrational mode shape. After validation of the present numerical results with those results available in literature, full numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface and bulk, residual surface stresses, nonlocal parameter, length scale effects (strain gradient parameter), cubic nonlinear Winkler and shear coefficients, power gradient index of functionally graded material, and geometric dimensions on the nonlinear vibration behaviors of flexoelectric functionally graded nano-beam. The numerical results indicate that, considering the flexoelectricity leads to the decrease of the bending stiffness of the flexoelectric functionally graded nano-beams.",
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