The effect of thickness on the mechanics of nanobeams

Li, Li; Tang, Haishan; Hu, Yujin

doi:10.1016/j.ijengsci.2017.11.021

Cited by 132 publications

(33 citation statements)

References 49 publications

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“…Moreover, Challamel and Wang [37] proposed the application of a nonlocal strain gradient model to overcome the reported paradox in nonlocal cantilever beams subjected to a point load, whereby in [38] the authors accounted for the effect of three small-scale parameters within the model, while checking for its accuracy with respect to some MD-based results for carbon nanotubes. Further numerical predictions about the size-dependent behavior of functionally graded materials and structures can be found in [39][40][41][42][43][44][45][46], in the presence or not of porosities, in accordance to the nonlocal strain gradient model of elasticity. Based on limitations from the literature, in the current work the free vibrations of triclinic nanobeams with varying thickness along the length are studied for the first time, while applying the Timoshenko beam theory in conjunction with the nonlocal strain gradient model.…”

Section: Introductionmentioning

confidence: 74%

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

Karami¹,

Janghorban²,

Dimitri³

et al. 2019

Applied Sciences

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In this work, the nonlocal strain gradient theory is applied to study the free vibration response of a Timoshenko beam made of triclinic material. The governing equations of the problem and the associated boundary conditions are obtained by means of the Hamiltonian principle, whereby the generalized differential quadrature (GDQ) method is implemented as numerical tool to solve the eigenvalue problem in a discrete form. Different combinations of boundary conditions are also considered, which include simply-supports, clamped supports and free edges. Starting with some pioneering works from the literature about isotropic nanobeams, a convergence analysis is first performed, and the accuracy of the proposed size-dependent anisotropic beam model is checked. A large parametric investigation studies the effect of the nonlocal, geometry, and strain gradient parameters, together with the boundary conditions, on the vibration response of the anisotropic nanobeams, as useful for practical engineering applications.

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Section: Introductionmentioning

confidence: 74%

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

Karami¹,

Janghorban²,

Dimitri³

et al. 2019

Applied Sciences

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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%

“…The significant size-dependent effect has been authenticated in nanoscale structures. For example, Li et al [9] used nonlocal strain gradient models in examining the sizedependent effects on the static and dynamical behaviors of micro/nano structures. Also, Zhu and Li [10] formulated the longitudinal dynamic problem of a size-dependent elasticity rod by utilizing an integral form of the nonlocal strain gradient theory.…”

Section: Introductionmentioning

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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“…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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The effect of thickness on the mechanics of nanobeams

Cited by 132 publications

References 49 publications

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

Free Vibration Analysis of Triclinic Nanobeams Based on the Differential Quadrature Method

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

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