• Advances in concrete construction
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• v.13 no.6
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• pp.471-479
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• 2022

In this paper, vibrational attributes of double-walled carbon nanotubes (CNTs) has been studied based upon nonlocal elastic shell theory. The implication of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. The comparison of local and nonlocal model has been overtly explored by means of scaling parameter. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of changing mechanical parameter Young's modulus has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.693-701
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• 2018

This paper develops a nonlocal strain gradient plate model for vibration analysis of graphene sheets under thermal environments. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Graphene sheet is modeled via a two-variable shear deformation plate theory needless of shear correction factors. Governing equations of a nonlocal strain gradient graphene sheet on elastic substrate are derived via Hamilton's principle. Differential quadrature method (DQM) is implemented to solve the governing equations for different boundary conditions. Effects of different factors such as temperature rise, nonlocal parameter, length scale parameter, elastic foundation and aspect ratio on vibration characteristics a graphene sheets are studied. It is seen that vibration frequencies and critical buckling temperatures become larger and smaller with increase of strain gradient and nonlocal parameter, respectively.

• Smart Structures and Systems
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• v.25 no.4
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• pp.501-514
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• 2020

This article presents a comprehensive model to investigate a free vibration and resonance frequencies of nanostructure perforated beam element as nano-resonator. Nano-scale size dependency of regular square perforated beam is considered by using nonlocal differential form of Eringen constitutive equation. Equivalent mass, inertia, bending and shear rigidities of perforated beam structure are developed. Kinematic displacement assumptions of both Timoshenko and Euler-Bernoulli are assumed to consider thick and thin beams, respectively. So, this model considers the effect of shear on natural frequencies of perforated nanobeams. Equations of motion for local and nonlocal elastic beam are derived. After that, analytical solutions of frequency equations are deduced as function of nonlocal and perforation parameters. The proposed model is validated and verified with previous works. Parametric studies are performed to illustrate the influence of a long-range atomic interaction, hole perforation size, number of rows of holes and boundary conditions on fundamental frequencies of perforated nanobeams. The proposed model is supportive in designing and production of nanobeam resonator used in nanoelectromechanical systems NEMS.

• Smart Structures and Systems
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• v.17 no.2
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• pp.257-274
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• 2016

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

• Advances in concrete construction
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• v.9 no.6
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• pp.577-588
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• 2020

In this paper, vibration attributes of chiral double-walled carbon nanotubes (CNTs) based on nonlocal elastic shell model have been investigated. The impact of small scale is being perceived by establishing Flügge shell model. The wave propagation is engaged to frame the ruling equations as eigen value system. The influence of nonlocal parameter subjected to different end supports has been overtly examined. A suitable choice of material properties and nonlocal parameter been focused to analyze the vibration characteristics. The new set of inner and outer tubes radii investigated in detail against aspect ratio and length. The dominance of boundary conditions via nonlocal parameter is shown graphically. Whereas for lower aspect ratio the frequencies coincide but as it continues to expand the difference between all respective boundary conditions slightly tend to increase. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

• Geomechanics and Engineering
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• v.36 no.1
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• pp.19-26
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• 2024

Erigen's nonlocal thermoelasticity model is used to study the effect of viscosity on a micropolar thermoelastic solid in the context of the multi-phase-lag model. The harmonic wave analysis technique is employed to convert partial differential equations to ordinary differential equations to get the solution to the problem. The physical fields have been presented graphically for the nonlocal micropolar thermoelastic solid. Comparisons are made with the results of three theories different in the presence and absence of viscosity as well as the gravity field. Comparisons are made with the results of three theories different for different values of the nonlocal parameter. Numerical computations are carried out with the help of Matlab software.

• Advances in nano research
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• v.6 no.2
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• pp.93-112
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• 2018

An analytical solution of the buckling governing equations of functionally graded piezoelectric (FGP) nanobeams obtained by using a developed third-order shear deformation theory is presented. Electro-mechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of a FG nanobeams made of piezoelectric materials are obtained and they are solved using Navier-type analytical solution. Results are provided to show the effect of different external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of the size-dependent FGP nanobeams. The accuracy of the present model is verified by comparing it with nonlocal Timoshenko FG beams. So, this study makes the first attempt for analyzing buckling behavior of higher order shear deformable FGP nanobeams.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.137-146
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• 2017

The size-dependent behavior of single walled carbon nanotubes (SWCNT) embedded in the elastic medium and subjected to the initial axial force is investigated using the mixed finite element method. The SWCNT is assumed to be Euler-Bernoulli beam incorporating nonlocal theory developed by Eringen. The mixed finite element model shows its great advantage of dealing with nonlocal behavior of SWCNT subjected to a concentrated load owing to the existence of two coefficients ${\alpha}_1$ and ${\alpha}_2$. This is the first numerical approach to deal with a puzzling fact of nonlocal theory with concentrated load. Numerical examples are performed to show the accuracy and efficiency of the present method. In addition, parametric study is carefully carried out to point out the influences of nonlocal effect, the elastic medium, and the initial axial force on the behavior of the carbon nanotubes.

• Advances in nano research
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• v.5 no.2
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.257-269
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• 2019

This paper develops a nonlocal strain gradient plate model for damping vibration analysis of smart magneto-electro-viscoelastic nanoplates resting on visco-Pasternak medium. For more accurate analysis of nanoplate, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. Viscoelastic effect which is neglected in all previous papers on magneto-electro-viscoelastic nanoplates is considered based on Kelvin-Voigt model. Governing equations of a nonlocal strain gradient smart nanoplate on viscoelastic substrate are derived via Hamilton's principle. Galerkin's method is implemented to solve the governing equations. Effects of different factors such as viscoelasticity, nonlocal parameter, length scale parameter, applied voltage and magnetic potential on damping vibration characteristics of a nanoplate are studied.