Size effect in the bending of a Timoshenko nanobeam

Jia, Ning; Yao, Yin; Yang, Yusen; Chen, Shaohua

doi:10.1007/s00707-017-1835-2

Cited by 29 publications

(7 citation statements)

References 47 publications

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“…Both parameters are easily found from Material Handbooks or simple MD simulations. Typical problems have been well analyzed based on such a novel theory and the predicted results agree well with the existing experimental data and numerical calculations [38][39][40][41] .…”

Section: Introductionsupporting

confidence: 67%

Surface effect on the resonant frequency of Timoshenko nanobeams

Jia

Yao

Yang

et al. 2017

International Journal of Mechanical Sciences

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The dynamic behavior of a Timoshenko nanobeam would be significantly different from a macro-one due to the large ratio of surface area to volume of nanomaterials. Furthermore, the shear deformation effect would be obvious for a Timoshenko nanobeam in contrast to an Eulerian one. In this paper, a recently developed elastic theory is adopted in order to predict the resonant frequency of a Timoshenko nanobeam, in which not only the surface effect but also the shear deformation effect and the rotary inertia one are considered. In contrast to the existing surface effect theories, surface effect of nanomaterials is characterized by the surface energy density in the adopted theory. The resonant frequency of both a fixed-fixed nanobeam and a cantilevered one is analyzed. It is found that the dynamic behavior of nanobeams deviates significantly from the one predicted by both the classical Timoshenko beam theory and the Euler-Bernoulli one due to the surface effect. Furthermore, the shear deformation effect and the rotary inertia effect cannot be neglected in nanobeams with a relative small aspect ratio, which cannot be precisely characterized by the Euler-Bernoulli beam theory. In addition, the influencing mechanism of surface effect on the dynamic behavior of nanobeams would depend on the boundary conditions. The resonant frequency of a fixed-fixed Timoshenko nanobeam would be improved, while that of a cantilevered one would be weakened by the surface effect in contrast to the corresponding classical solutions. The results in this paper should be useful for precise design of nano-devices and helpful for reasonable assessment of test results of nano-instruments.

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Section: Introductionsupporting

confidence: 67%

Surface effect on the resonant frequency of Timoshenko nanobeams

Jia

Yao

Yang

et al. 2017

International Journal of Mechanical Sciences

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“…The Von Kármán assumption tells us that the nonlinear terms related to the u can be excluded from the Lagrangian strain formula because these terms are sufficiently small compared to the other terms [ 18 , 19 , 20 , 21 , 22 , 23 , 24 ]. The general Lagrangian strain can be mentioned as

…”

Section: Mathematical Modelmentioning

confidence: 99%

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Malikan

Eremeyev

2020

Nanomaterials

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Among various magneto-elastic phenomena, flexomagnetic (FM) coupling can be defined as a dependence between strain gradient and magnetic polarization and, contrariwise, elastic strain and magnetic field gradient. This feature is a higher-order one than piezomagnetic, which is the magnetic response to strain. At the nanoscale, where large strain gradients are expected, the FM effect is significant and could be even dominant. In this article, we develop a model of a simultaneously coupled piezomagnetic–flexomagnetic nanosized Euler–Bernoulli beam and solve the corresponding problems. In order to evaluate the FM on the nanoscale, the well-known nonlocal model of strain gradient (NSGT) is implemented, by which the nanosize beam can be transferred into a continuum framework. To access the equations of nonlinear bending, we use the variational formulation. Converting the nonlinear system of differential equations into algebraic ones makes the solution simpler. This is performed by the Galerkin weighted residual method (GWRM) for three conditions of ends, that is to say clamp, free, and pinned (simply supported). Then, the system of nonlinear algebraic equations is solved on the basis of the Newton–Raphson iteration technique (NRT) which brings about numerical values of nonlinear deflections. We discovered that the FM effect causes the reduction in deflections in the piezo-flexomagnetic nanobeam.

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“…Both parameters are easily found from material handbooks or simple molecular dynamics simulations. Some statics and dynamics of beams have been well analyzed by surface energy density theory [31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Contact behaviors involving a nanobeam with surface effect by a rigid indenter

Wang,

Wu,

2023

Mathematics and Mechanics of Solids

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In this study, we present a novel surface model that utilizes surface energy density to predict the surface effect in nanobeam contact problems. To address the issue of a finite-length elastic nanobeam being indented by a rigid cylindrical indenter, we propose an equivalent substitution method. This method allows us to formulate analytical relations between the load and contact half-width for two different boundary cases. The explicit expressions of the contact-zone width, the pressure distribution in the contact zone, the deflection outside the contact zone, and the load–displacement relation are obtained for the nanobeam with surface effect and are compared with classical results in detail. The results show that the influence of the surface effect is very significant for nanobeam contact behavior, especially when the half-width of the contact zone increases and the contact zone becomes two independent symmetric strips. It is also found that the length-height ratio of nanobeam and the end support conditions have a fairly obvious effect on the normalized pressure distribution, which deviates significantly from the one predicted by the classical results due to the surface effect. However, for a given beam length and indenter radius, the ratio of the width of the contact zone to the beam thickness is almost constant, independent of the indenter load and beam boundary conditions. Meanwhile, the model predicts that the contact pressure distribution after the normalization of the average indentation pressure is almost independent of the indentation load and beam boundary conditions, but obviously depends on the surface effect parameters. The present method and result should be helpful not only to the measurement of mechanical properties of the indentation nanobeam but also to the design of the nanobeam-based devices.

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Size effect in the bending of a Timoshenko nanobeam

Cited by 29 publications

References 47 publications

Surface effect on the resonant frequency of Timoshenko nanobeams

Surface effect on the resonant frequency of Timoshenko nanobeams

On Nonlinear Bending Study of a Piezo-Flexomagnetic Nanobeam Based on an Analytical-Numerical Solution

Contact behaviors involving a nanobeam with surface effect by a rigid indenter

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