Surface stress effect on the postbuckling and free vibrations of axisymmetric circular Mindlin nanoplates subject to various edge supports

Ansari, R.; Mohammadi, V.; Shojaei, M. Faghih; Gholami, R.; Sahmani, S.

doi:10.1016/j.compstruct.2014.02.028

Cited by 23 publications

(6 citation statements)

References 30 publications

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“…where 𝜅 𝑠 (= 𝜋 2 ∕12) is the shear correction factor. Substituting Equations ( 17) and (18) into Equations ( 19)-( 21), respectively, the radial axial force, 𝑁 𝑟 , circumferential axial force, 𝑁 𝜃 , radial bending moment, 𝑀 𝑟 , circumferential bending moment, 𝑀 𝜃 , and shear force, 𝑄 𝑟 , are expressed in terms of the displacements as the following forms:…”

Section: Constitutive Relationmentioning

confidence: 99%

“…To capture surface effects, Gurtin and Murdoch's [16] initial proposal of surface elasticity was groundbreaking and has been widely applied to interpreting the size-dependent behavior of nanostructures [17]. Applied the Gurtin Murdoch surface theory to Mindlin plate theory, postbuckling as well as vibrations of circular nanoplates were studied by Ansari et al [18], who used GDQ method to achieve the natural frequencies and corresponding vibration modes of circular nanoplates. Combining the surface elasticity theory of Gurtin Murdoch, Bochkarev [19] established a nonlinear von Karman type model for the bending of nanoplates and confirmed the influence of surface tension on various mechanical responses of nanoplates through solving.…”

Section: Introductionmentioning

confidence: 99%

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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

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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.

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Section: Constitutive Relationmentioning

confidence: 99%

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

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“…Ansari et al [36] implemented Gurtin-Murdoch elasticity theory in conjunction with von Karman nonlinear geometrically into the classical Timoshenko beam theory to analyze nonlinear forced vibration response of nanobeams with surface effects. They also investigated the free vibration response of postbuckled circular Mindlin nanoplate based on surface elasticity theory [37]. In a recent work, Sahmani et al [38] predicted natural frequencies of third-order shear deformable nanobeams in the vicinity of the postbuckling domain incorporating surface effects.…”

Section: Introductionmentioning

confidence: 98%

Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects

Sahmani

Bahrami

Aghdam

et al. 2015

Applied Mathematical Modelling

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Please cite this article as: S. Sahmani, M. Bahrami, M.M. Aghdam, R. Ansari, Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects, Appl. Math. Modelling (2014), doi: http://dx. AbstractThe effects of surface energy are generally ignored in traditional continuum elasticity. However, due to the high surface to volume ratio in nanostructures, this is not the case for them. In this work, the nonlinear postbuckling characteristics of circular nanoplates are predicted in the presence of surface energy effects including surface elasticity and residual surface tension. For this objective, Gurtin-Murdoch elasticity theory is implemented into the classical higher-order shear deformation plate theory. In order to satisfy the balance conditions on the surfaces of nanoplate, it is assumed the normal stress of the bulk is distributed cubically through the thickness of nanoplate. Hamilton's principle in conjunction with von Karman geometric nonlinearity is utilized to derive non-classical nonlinear governing differential equations of motion and related boundary conditions. Afterwards, an efficient numerical methodology based generalized differential quadrature (GDQ) method is carried out using the shifted ChebyshevGauss-Lobatto grid points to discretize the governing partial differential equations. Then, the Galerkin's method is employed to reduce the set of nonlinear equations into a time-varying set of ordinary differential equations of Duffing type. At the end, the pseudo arc-length continuation technique is utilized in order to obtain the solution of the parameterized equation.

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“…Utilizing a nonclassical geometrically nonlinear beam model on the basis of the Euler-Bernoulli theory, Wang and Wang [38] performed a study on the non-linear pull-in instability of nano-switches and discovered that surface energy effects on the pull-in voltage depends on the geometric parameters such as length, height and initial gap of the nanoswitch. Ansari et al [39] examined the surface effects on the free vibration characteristics of circular nanoplates in the vicinity of postbuckling domain based on a newly developed nonlinear circular Mindlin nanoplate model and numerical solution procedure.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports

Ansari

Gholami

2016

Acta Astronautica

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Surface stress effect on the postbuckling and free vibrations of axisymmetric circular Mindlin nanoplates subject to various edge supports

Cited by 23 publications

References 30 publications

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

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

Postbuckling behavior of circular higher-order shear deformable nanoplates including surface energy effects

Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports

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