Effects of high-order surface stress on buckling and resonance behavior of nanowires

Chiu, Min Sen; Chen, Tungyang

doi:10.1007/s00707-012-0673-5

Cited by 22 publications

(17 citation statements)

References 45 publications

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“…12 Later, the Y-L model was extended to the vibration problem of Timoshenko nanowires. 36,37 Chiu and Chen 38 further discussed the effect of the surface bending modulus on the resonant frequency of nanowires. Recently, Zhang et al 39 analyzed the motion equation of vibrating nanowires, based on which contributions of surface elasticity and surface stress to the resonant frequency can be abstracted, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…40 in which surface elastic constants, including the surface elastic modulus and surface bending modulus, serve as critical parameters influencing the size-dependent behavior of nanowires. 12,13,31,35,38 However, surface elastic constants needed by the surface elasticity theory can only be provided by MD simulation and hardly be measured by proper experiment techniques. 1,13,41,42 How to define the atomic layer as a surface layer, how to choose a proper atomic interaction potential and the size of a numerical model are still open questions in MD simulation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

Yao

Chen

2015

Journal of Applied Physics

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Articles you may be interested inA recently developed continuum theory considering surface effect in nanomaterials is adopted to investigate the resonant properties of nanowires with different boundary conditions in the present paper. The main feature of the adopted theory is that the surface effect in nanomaterials is characterized by the surface energy density of the corresponding bulk materials and the surface relaxation parameter in nanoscale. Based on a fixed-fixed beam model and a cantilever one, the governing equation of resonant frequency for corresponding nanowires is obtained. Numerical calculation of the fundamental resonant frequency is carried out, the result of which is well consistent with the existing numerical ones. Comparing to the result predicted by the conventionally structural dynamics, the resonant frequency of a fixed-fixed nanowire is improved, while that of a cantilever nanowire is weakened due to the surface effect. Both a decreasing characteristic size (height or diameter) and an increasing aspect ratio could further enhance the varying trend of resonant properties for both kinds of nanowires. The present result should be helpful for the design of nano-devices and nanostructures related to nanowires. V C 2015 AIP Publishing LLC.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

Yao

Chen

2015

Journal of Applied Physics

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“…New continuum theoretical models should be developed. Surface elasticity theory as an optional theory, which takes the surface effect into account [12,13], has been widely adopted to study the static and dynamic bending behaviors of nanowires successfully [14][15][16][17]. Molecular dynamics (MD) simulation method as a feasible numerical technique is also extensively used to investigate the size-dependent modulus of nanowires [18][19][20][21], besides the surface Cauchy-Born model [22] and the finite element calculation based on the surface elasticity theory [23].…”

Section: Introductionmentioning

confidence: 99%

Buckling behavior of nanowires predicted by a new surface energy density model

Yao

Chen

2016

Acta Mech

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The axial buckling behavior of nanowires is investigated with a new continuum theory, in which the surface effect of nanomaterials is characterized by the surface energy density. Only the surface energy density of bulk materials and the surface relaxation parameter are involved, instead of the surface elastic constants in the classical surface elasticity theory. Two kinds of nanowires with different boundary conditions are discussed. It is demonstrated that the new continuum theory can predict the buckling behavior of nanowires very well. Similar to the prediction of the classical elasticity theory, the critical compressive load of axial buckling of nanowires predicted by the new continuum theory increases with an increasing characteristic length, such as the diameter or height of nanowires. With the same aspect ratio, a nanowire with a rectangular cross section possesses a larger critical buckling load than that with a circular one. However, the surface effect could enhance the critical buckling load not only for a fixed-fixed nanowire but also for a cantilevered one in contrast to the classical elastic model. All the results predicted by the new continuum theory agree well with predictions by the surface elasticity models. The present research not only verifies the validation of the new continuum theory, but also gives a much more convenient characterization of buckling behaviors of nanowires. This should be helpful for the design of nanodevices based on nanomaterials, for example, nanobeams in NEMS or high-precision instruments.

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“…By checking the two ratios of C s /σ and L/D, the effects of surface elasticity and surface stress can be estimated. Similarly, Chiu & Chen [30] derived an analytical expression for the buckling load of a nanowire, which indicates that the surface stress contribution to the buckling load is also amplified by a factor of (L/D) 2 compared with that of surface elasticity. It is also necessary to bear in mind that in the modified YL models [28,31], the transverse surface stress and surface stress from side surfaces can significantly enhance the effective surface elasticity effect by increasing the nanowire bending stiffness.…”

Section: Model Developmentmentioning

confidence: 98%

“…The size-dependent properties of Δ and N are also noted. Compared with Δ, N has an amplification factor of (L/h) 2 for a rectangular beam and (L/D) 2 for a circular beam; L/h or L/D have been identified as important geometric parameters in the buckling and resonant frequencies of a nanowire [25,26,30]. Surface elasticity (Δ) in essence changes the effective Young modulus of a micro/nanostructure [42].…”

Section: Model Developmentmentioning

confidence: 99%

Determining the effects of surface elasticity and surface stress by measuring the shifts of resonant frequencies

2013

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Both surface elasticity and surface stress can result in changes of resonant frequencies of a micro/nanostructure. There are infinite combinations of surface elasticity and surface stress that can cause the same variation for one resonant frequency. However, as shown in this study, there is only one combination resulting in the same variations for two resonant frequencies, which thus provides an efficient and practical method of determining the effects of both surface elasticity and surface stress other than an atomistic simulation. The errors caused by the different models of surface stress and mode shape change due to axial loading are also discussed.

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Effects of high-order surface stress on buckling and resonance behavior of nanowires

Cited by 22 publications

References 45 publications

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

Buckling behavior of nanowires predicted by a new surface energy density model

Determining the effects of surface elasticity and surface stress by measuring the shifts of resonant frequencies

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