Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory

Lei, Jian; He, Yuming; Zhang, Bo; Gan, Zhipeng; Zeng, Pengcheng

doi:10.1016/j.ijengsci.2013.06.012

Cited by 129 publications

(33 citation statements)

References 44 publications

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“…The plane stress problem of an orthotropic functionally graded beam with arbitrary graded material properties along the thickness direction is investigated recently by the displacement function approach by Nie et al [10]. Also, the study of dynamic characteristics of functionally graded beams have been discussed in [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Pradhan

Chakraverty

2015

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Pradhan

Chakraverty

2015

Applied Mathematics and Computation

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“…The strain energy U in a deformed isotropic linear elastic material occupying region X is given by Lei et al (2013a), Ghorbanpour Arani et al (2012):…”

Section: Strain Gradient Elasticity Theorymentioning

confidence: 99%

“…Akgöz and Civalek (2013a, b) presented a size-dependent shear deformation beam model based on the strain gradient elasticity theory. Bending and vibration of functionally graded sinusoidal micro beams based on the strain gradient elasticity theory were carried out by Lei et al (2013a). Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory was investigated by Akgöz and Civalek (2012).…”

Section: Introductionmentioning

confidence: 99%

Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method

Arani

Kolahchi

Mosayyebi

et al. 2014

Int J Mech Mater Des

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This research deals with the dynamic instability analysis of double-walled carbon nanotubes (DWCNTs) conveying pulsating fluid under 2D magnetic fields based on the sinusoidal shear deformation beam theory (SSDBT). In order to present a realistic model, the material properties of DWCNTs are assumed viscoelastic using Kelvin-Voigt model. Considering the strain gradient theory for small scale effects, a new formulation of the SSDBT is developed through the Gurtin-Murdoch elasticity theory in which the effects of surface stress are incorporated. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The van der Waals interactions between the adjacent walls of the nanotubes are taken into account. The size dependent motion equations and corresponding boundary conditions are derived based on the Hamilton's principle. The differential quadrature method in conjunction with Bolotin method is applied for obtaining the dynamic instability region. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of DWCNTs. The results depict that the surface stress effects on the dynamic instability of visco-DWCNTs are very significant. Numerical results of the present study are compared with available exact solutions in the literature. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems in advanced biomechanics applications with magnetic field as a parametric controller.

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“…Thai and Vo focused on bending and free vibration behavior of FG beams using HSDTs in the microscopic scale [30]. Also, bending and vibration behavior of FG micro-beams based on the sinusoidal shear deformation theory was proposed by Lei et al [43]. In addition, analytical solutions to bending and buckling of FG nanobeams via the nonlocal Timoshenko beam theory were presented by S im sek and Yurtcu [9].…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories

2017

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Abstract. In the present study, various Higher-order Shear Deformation beam Theories (HSDTs) are applied in order to achieve the exact analytical solution to bending, buckling, and free vibration of Functionally Graded (FG) nanobeam lying on the Winkler and Pasternak elastic foundations. HSDTs are those in which the e ect of transverse shear strain is included. The displacement eld of these theories involves a quadratic variation of transverse shear strains and stresses; hence, this hypothesis leads to the diminishing of transverse shear stresses at the top and bottom surfaces of a beam. Thus, necessarily, there is no need to use a shear correction factor in the HSDTs. Nanobeam has been made of FG materials in which the properties of these materials are changed through the thickness direction of nanobeam according to the power-law distribution. Hamilton's principle is used to derive the equation of motions and the related boundary conditions of simply supported nanobeam. The present study shows that the stability and vibration behaviors of FG nanobeam are extremely dependent on the Winkler and Pasternak elastic foundation, gradient index, aspect ratio, and nonlocal parameter. The obtained results of the present study might be useful in the advanced eld of micro/nano electromechanical systems.

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Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory

Cited by 129 publications

References 44 publications

Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams

Pulsating fluid induced dynamic instability of visco-double-walled carbon nano-tubes based on sinusoidal strain gradient theory using DQM and Bolotin method

An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using different nonlocal higher order shear deformation beam theories

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