Free vibration analysis of nanocones using a nonlocal continuum model

Firouz-Abadi, R. D.; Fotouhi, Morteza; Haddadpour, H.

doi:10.1016/j.physleta.2011.08.035

Cited by 43 publications

(14 citation statements)

References 34 publications

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“…(15) and (16). Initial conditions (53) and (54) are obtained combining Eqs. (21) and (22), whereas initial conditions (55) are obtained by derivation of Eqs.…”

Section: Solution For the Time-dependent Functions S N And Q Nmentioning

confidence: 99%

“…From the pioneer work of Peddieson et al [29], this theory has been also used to solve problems involving nanostructures. Thus, the Eringen nonlocal theory of elasticity has been used to address the behavior of beams [30][31][32][33][34][35][36], beams under rotation [37][38][39][40], rods [41][42][43][44][45][46], plates [47][48][49], cylindrical shells [50][51][52], conical shells [53,11,12], rings [54,55] and particles [56], as well as carbon nanotubes (CNTS) [57][58][59][60][61][62][63][64].…”

Section: Introductionmentioning

confidence: 99%

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Axisymmetric free vibration of closed thin spherical nano-shell

Zaera

Fernández-Sáez

Loya

2013

Composite Structures

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This work investigates the free axisymmetric vibrations of a closed spherical nano-shell using the Eringen nonlocal elasticity theory. The motion equations are properly formulated considering the hypotheses of thin shells and the solution is obtained using the classical separation of variables method. The effect of the nonlocal parameter on the natural frequencies and modal shapes are discussed in comparison to their local counterparts. This study could be useful in biomedical and bioengineering applications as well as in other fields related with the nanotechnology.

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“…(15) and (16). Initial conditions (53) and (54) are obtained combining Eqs. (21) and (22), whereas initial conditions (55) are obtained by derivation of Eqs.…”

Section: Solution For the Time-dependent Functions S N And Q Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Axisymmetric free vibration of closed thin spherical nano-shell

Zaera

Fernández-Sáez

Loya

2013

Composite Structures

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“…Today, because MD simulation is a time-consuming procedure especially for macro scale structures, it has been supplanted by the use of continuum mechanics in the modeling of structures in the nanoscale. As classical continuum models are unable to make a correct prediction of size-dependent behaviors happening in micro/nanoscale structures, researchers have attempted to use non-classical continuum theories such as non-local elasticity theory, couple stress theory and strain gradient theory, which take size effect into account in the investigation of micro/nanostructures [15][16][17]. The couple stress theory, which contains two higher order material length scale parameters as well as two Lame constants, was introduced by Mindlin, Toupin, Mindlin and Tiersten, and Koiter in 1960's [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Thermo-Mechanical Vibration of Size Dependent Shear Deformable Functionally Graded Conical Nanoshell Resting On Elastic Foundation

Mehralian¹,

Beni²

2016

International Journal of Engineering &Amp; Applied Sciences

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In this paper, the size-dependent shear deformable conical shell formulation is derived based on the modified couple stress theory and first order shear deformation model to investigate the free vibration of functionally graded conical shell embedded in an elastic Pasternak medium and subjected to thermal environment. The material properties are considered temperature-dependent and graded in thickness direction according to power law distribution. The governing equations and boundary conditions are derived using Hamilton's principle. The size effect is taken into account using the modified couple stress theory, and, the free vibration of simply supported FG truncated conical nanoshell is investigated as a special case. The effects of different parameters such as dimensionless length scale parameter, temperature change and distribution of the nanoshell components on the natural frequency are investigated based on the modified couple stress theory and classical continuum theory.

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“…Subsequently, the Eringen non-local theory of elasticity has been used to address the behavior of nanobeams [32,44,46,71,74,89,90,93], nanobeams under rotation [3,57,64,70], nanorods [34,42,45,56,59,61,62,81], nanoplates [30,33,58], cylindrical nanoshells [31,91,92], conical nanoshells [21,43,86], nanorings [55,88], spherical nanoshells [24,87,96], as well as particles [25] and carbon nanotubes (CNTS) [2,10,19,22,28,60,63,75,97].…”

Section: Introductionmentioning

confidence: 99%

A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics

2015

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In this paper we present a theoretical analysis of free axial vibrations of rods described in terms of the fractional continuum mechanics. This formulation is able to capture the size effect arising in different problems of solid mechanics. The natural frequencies and modal shapes for clamped rods are obtained and the effects of the derivative order, as well as the corresponding length-scale parameters in the fractional model are discussed. The results are compared with those derived from the Eringen non-local elasticity theory, which is an approach widely used to model structures showing size effects.

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Free vibration analysis of nanocones using a nonlocal continuum model

Cited by 43 publications

References 34 publications

Axisymmetric free vibration of closed thin spherical nano-shell

Axisymmetric free vibration of closed thin spherical nano-shell

Thermo-Mechanical Vibration of Size Dependent Shear Deformable Functionally Graded Conical Nanoshell Resting On Elastic Foundation

A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics

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