Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams

Tang, Haishan; Li, Li; Hu, Yujin

doi:10.1016/j.apm.2018.09.027

Cited by 65 publications

(14 citation statements)

References 97 publications

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“…Here, it is noted that we have not taken the higher-order stresses σ (1) xz and σ (1) yz in the strain gradient of the above equations because we have assumed that the size-dependent effects in the thickness direction of the plate are small and thereby we have neglected them. In this regard, recently, Li et al [9] and Tang et al [48][49] studied the size-dependent effects in the thickness direction of beams and plates.…”

Section: Governing Equationsmentioning

confidence: 99%

An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

Sharifi

Khordad

Gharaati

et al. 2019

Appl. Math. Mech.-Engl. Ed.

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In this paper, we analytically study vibration of functionally graded piezoelectric (FGP) nanoplates based on the nonlocal strain gradient theory. The top and bottom surfaces of the nanoplate are made of PZT-5H and PZT-4, respectively. We employ Hamilton's principle and derive the governing differential equations. Then, we use Navier's solution to obtain the natural frequencies of the FGP nanoplate. In the first step, we compare our results with the obtained results for the piezoelectric nanoplates in the previous studies. In the second step, we neglect the piezoelectric effect and compare our results with those obtained for the functionally graded (FG) nanoplates. Finally, the effects of the FG power index, the nonlocal parameter, the aspect ratio, and the lengthto-thickness ratio, and the nanoplate shape on natural frequencies are investigated.

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Section: Governing Equationsmentioning

confidence: 99%

An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

Sharifi

Khordad

Gharaati

et al. 2019

Appl. Math. Mech.-Engl. Ed.

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“…Scale effects are usually assumed to be negligible along the thickness direction of nanobeams and nanoplates. Lately, NSGTbased beam models taking into consideration the thickness effect have been reported for the scale-dependent mechanical analysis of nanobeams [58][59][60]. The elastic energy variation  () e U and the viscous work variation (  v W ) can be written as…”

Section: Modified Continuum-based Modellingmentioning

confidence: 99%

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Farajpour

Ghayesh

Farokhi

2019

Microfluid Nanofluid

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A coupled continuum model incorporating size influences and geometric nonlinearity is presented for the coupled motions of viscoelastic nonlinear nanotubes conveying nanofluid.A modified model of nanobeams incorporating nonlocal strain gradient effects is utilised for describing size influences on the bifurcation behaviour of the fluid-conveying nanotube. Furthermore, size influences on the nanofluid are taken into account via Beskok-Karniadakis theory. To model the geometric nonlinearity, nonlinear strain-displacement relations are employed. Utilising Hamilton's principle and the Kelvin-Voigt model, the coupled equations of nonlinear motions capturing the internal energy loss are derived. A Galerkin procedure with a high number of shape functions and a direct time-integration scheme are then employed to extract the bifurcation characteristics of the nanofluid-conveying nanotube with viscoelastic properties. A specific attention is paid to the chaotic response of the viscoelastic nanosystem. It is found that the coupled viscoelastic bifurcation behaviour is very sensitive to the flow velocity.

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“…For convenience, the effects of size dependence in the thickness axis are not captured in the present analysis. Size-dependent theoretical models incorporating this effect have been recently proposed in the literature [51][52][53]. The effects of size dependence in the thickness axis on the mechanics of small-scale structures can be modelled in future analyses.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Chaos in fluid-conveying NSGT nanotubes with geometric imperfections

Ghayesh

Farokhi

Farajpour

2019

Applied Mathematical Modelling

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  Chaos in fluid-conveying nanotubes with initial deflections is analysed.  A scale-dependent model of nanobeams with large deformations is developed.  To comprehensively simulate size effects, the NSGT is utilised.

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Coupling effect of thickness and shear deformation on size-dependent bending of micro/nano-scale porous beams

Cited by 65 publications

References 97 publications

An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

An analytical study of vibration in functionally graded piezoelectric nanoplates: nonlocal strain gradient theory

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Chaos in fluid-conveying NSGT nanotubes with geometric imperfections

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