Nonlinear size-dependent vibration behavior of graphene nanoplate considering surfaces effects using a multiple-scale technique

Allahyari, Ehsan; Asgari, Masoud; Jafari, Ali

doi:10.1080/15376494.2018.1494870

Cited by 11 publications

(6 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One of the advantages of the multiple scale method, with respect to other methods, is that, by using this method, the effects of system parameters on the system responses can be recognized accurately. One begins by introducing new independent variables according to [33,34] The first and the second derivatives are written as Now by considering the above equations, the expanded function can be seen as follow (29) T n = n t for n = 0, 1, 2, … (30)…”

Section: Multiple Scale Techniquementioning

confidence: 99%

See 1 more Smart Citation

Effects of in-phase and anti-phase large amplitude nonlinear models for double-layer nanostructures

Allahyari

Asgari

2019

SN Appl. Sci.

Self Cite

View full text Add to dashboard Cite

Double layer nano plates have magnificent applications in nanostructures such as, nano sensors, nano actuators and nano transistors. So, the main aim of the presented study is to propose an analytical model based on Reddy's third-order shear deformation theory of plates which has a difficult procedure due to the great number of partial differential equations and nonlocal strain gradient theory. Due to the fact that numerical approaches aren't good enough accurate and need more time to calculate, the multiple scales method which is a useful method in systems characterized by disparate time scales and in a variety of situations for extracting the slow time dependence of patterns or other systems is adopted. Based on von Kármán equations as well as the theory of nonlocal strain gradient, the coupled nonlinear equations are derive. Compared to the other related published literature, acceptable agreement can be seen under different boundary conditions. Effect of size depended parameter on in-phase and anti-phase modes considering the SSSS and CCCC boundary condition is indescribable which means by increasing the nonlocal parameter nonlinear frequency and also the natural frequency of nanostructure reduces.

show abstract

Section: Multiple Scale Techniquementioning

confidence: 99%

“…Secular terms, which are the terms that produce non-periodic solutions, must be eliminated from Eq. (34). Substituting for W 1 and W 2 into Eq.…”

Section: Multiple Scale Techniquementioning

confidence: 99%

Effects of in-phase and anti-phase large amplitude nonlinear models for double-layer nanostructures

Allahyari

Asgari

2019

SN Appl. Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Because the surface phase of nanostructures has different atomic arrangements and larger specific surface area compared to the bulk phase, atoms near the solid surface experience different local conditions compared to atoms far from the surface. Therefore, as one of the reasons for the size-related characteristics of nanostructures, surface effects play an essential role in affecting the whole performance of nanomaterials or structures [9]. Altenbach et al [10] addressed the surface effects on the bending of a nanosize plate.…”

Section: Introductionmentioning

confidence: 99%

The influence of surface effects on axisymmetric vibration of graded porous Mindlin circular nanoplate in a temperature field

Li,

Zhang,

Wang

et al. 2023

Z Angew Math Mech

View full text Add to dashboard Cite

The surface effect significantly affects the mechanical response of nanoscale materials. In this work, we introduce Gurtin‐Murdoch surface elasticity theory into Mindlin plate theory to study the axisymmetric vibration characteristic of graded porous circular nanoplate in a temperature field. The main structure is a porous graded material with uniform or non‐uniform porosity distribution in its thickness. The numerical shooting technique was applied to solve the governing differential equations derived from Hamilton's principle. Responses for the vibration characteristic of the graded porous nanoplate for both clamped and simply supported boundary conditions were obtained. The numerical results show that when the surface effect is removed, the classical results of Mindlin circular plate will be obtained. Natural frequencies and mode shapes varying with thermal and porosity coefficients were present graphically. And then the effects of surface material properties on the axisymmetric vibration characteristic of the nanoplates were discussed in detail. The parametric study examined the influence of porosity coefficient, porosity distribution mode, surface elastic parameters, and residual surface stress on the vibration characteristics of porous circular nanoplates.

show abstract

“…For example, they are used in radio-frequency switches, microscaled pumps, and electrostatic actuators [1][2][3][4][5][6]. Their bending, buckling and vibration of many MEMS/NEMS structures involving ultra-thin films (nano-scale thick) depend on their absolute geometrical parameters in the scale of submicron [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Size-dependent frequency of simply supported elastic ultra-thin films with surface effect under periodic vibration

Huang¹,

Wang²,

Ni³

et al. 2022

Mater. Res. Express

View full text Add to dashboard Cite

Although surface effects play an important role in the mechanical properties of ultra-thin films, the nonlinear vibrations of ultra-thin films influenced by surface effects have not been fully understood. This paper develops an analytical framework for studying the nonlinear vibrations of simply supported ultra-thin films with surface effects. The framework is based on the modified Kirchhoff plate theory. The surface stress effects are treated by the Gurtin–Murdoch surface elasticity model and the motion equations include the effects of curvature and classical inertia. The dimensionless frequency of forcibly vibrated ultra-thin films with a simple support and surface effects is explicitly deduced through a series of perturbation procedure. Finally, the surface effects are evaluated in two numerical examples. In these demonstrations, the surface effects significantly influenced the dimensionless frequency when the film thickness reduced to one micrometer or less.

show abstract

Nonlinear size-dependent vibration behavior of graphene nanoplate considering surfaces effects using a multiple-scale technique

Cited by 11 publications

References 53 publications

Effects of in-phase and anti-phase large amplitude nonlinear models for double-layer nanostructures

Effects of in-phase and anti-phase large amplitude nonlinear models for double-layer nanostructures

The influence of surface effects on axisymmetric vibration of graded porous Mindlin circular nanoplate in a temperature field

Size-dependent frequency of simply supported elastic ultra-thin films with surface effect under periodic vibration

Contact Info

Product

Resources

About