• Advances in nano research
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• 제12권3호
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• pp.281-290
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• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Structural Engineering and Mechanics
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• 제73권3호
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• pp.287-302
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• 2020

This investigation deals with a size-dependent coupled thermoelasticity analysis based on Green-Naghdi (GN) theory in nano scale using a new modified nonlocal model of heat conduction, which is based on the GN theory and nonlocal Eringen theory of elasticity. In the analysis based on the proposed model, the nonlocality is taken into account in both heat conduction and elasticity. The governing equations including the equations of motion and the energy balance equation are derived using the proposed model in a nano beam resonator. An analytical solution is proposed for the problem using the Laplace transform technique and Talbot technique for inversion to time domain. It is assumed that the nano beam is subjected to sinusoidal thermal shock loading, which is applied on the one of beam ends. The transient behaviors of fields' quantities such as lateral deflection and temperature are studied in detail. Also, the effects of small scale parameter on the dynamic behaviors of lateral deflection and temperature are obtained and assessed for the problem. The proposed GN-based model, analytical solution and data are verified and also compared with reported data obtained from GN coupled thermoelasticity analysis without considering the nonlocality in heat conduction in a nano beam.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.103-119
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• 2018

In the present research, an attempt is made to obtain a semi analytical solution for both nonlinear natural frequency and forced vibration of embedded functionally graded double layered nanoplates with all edges simply supported based on nonlocal strain gradient elasticity theory. The interaction of van der Waals forces between adjacent layers is included. For modeling surrounding elastic medium, the nonlinear Winkler-Pasternak foundation model is employed. The governing partial differential equations have been derived based on the Mindlin plate theory utilizing the von Karman strain-displacement relations. Subsequently, using the Galerkin method, the governing equations sets are reduced to nonlinear ordinary differential equations. The semi analytical solution of the nonlinear natural frequencies using the homotopy analysis method and the exact solution of the nonlinear forced vibration through the Harmonic Balance method are then established. The results show that the length scale parameters give nonlinearity of the hardening type in frequency response curve and the increase in material length scale parameter causes to increase in maximum response amplitude, whereas the increase in nonlocal parameter causes to decrease in maximum response amplitude. Increasing the material length scale parameter increases the width of unstable region in the frequency response curve.

• 한국소음진동공학회논문집
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• 제22권1호
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• pp.38-45
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• 2012

In this paper, flow-induced flutter instability of a cantilever carbon nanotube conveying fluid and modelled as a thin-walled beam is investigated. Analytically nonlocal effect, transverse shear and rotary inertia are incorporated in this study. The governing equations and the boundary conditions are derived through Hamilton's principle. Numerical analysis is performed by using extended Galerkin method which enables us to obtain more exact solutions compared with conventional Galerkin method. Variation of critical flow velocity of carbon nanopipes based on three different models such as analytically nonlocal model, partially nonlocal model, and local model are investigated and pertinent conclusion is outlined.

• Advances in nano research
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• 제7권1호
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• pp.1-11
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• 2019

In this article, wave propagation characteristics in magneto-electro-elastic (MEE) nanotube considering shell model is studied in the framework nonlocal theory. To account for the small-scale effects, the Eringen's nonlocal elasticity theory of is applied. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton's principle. The results of this investigation have been accredited by comparing them of previous studies. An analytical solution of governing equations is used to obtain phase velocities and wave frequencies. The influences of different parameters, such as different mode, nonlocal parameter, length parameter, geometry, magnetic field and electric field on wave propagation responses of MEE nanotube are expressed in detail.

• Steel and Composite Structures
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• 제42권3호
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• pp.353-361
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• 2022

In this study, an estimation regarding nonlocal shell model based on wave propagation approach has been considered for vibrational behavior of the double walled carbon nanotubes with distinct nonlocal parameters. Vibrations of double walled carbon nanotubes for chiral indices (8, 3) have been analyzed. The significance of small scale is being perceived by developing nonlocal Love shell model. The influence of changing mechanical parameter Poisson's ratio has been investigated in detail. The dominance of boundary conditions via nonlocal parameter is shown graphically. It is found that on increasing the Poisson's ratio, the frequencies increases. It is noted that the frequencies of clamped-clamped frequencies are higher than that of simply-supported and clamped-free edge conditions. The outcomes of frequencies are tested with earlier computations.

• Structural Engineering and Mechanics
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• 제65권6호
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• pp.645-656
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• 2018

Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

• Advances in nano research
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• 제6권3호
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• pp.279-298
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• 2018

Present investigation deals with the free vibration characteristics of nanoscale-beams resting on elastic Pasternak's foundation based on nonlocal strain-gradient theory and a higher order hyperbolic beam model which captures shear deformation effect without using any shear correction factor. The nanobeam is lying on two-parameters elastic foundation consist of lower spring layers as well as a shear layer. Nonlocal strain gradient theory takes into account two scale parameters for modeling the small size effects of nanostructures more accurately. Hamilton's principal is utilized to derive the governing equations of embedded strain gradient nanobeam and, after that, analytical solutions are provided for simply supported conditions to solve the governing equations. The obtained results are compared with those predicted by the previous articles available in literature. Finally, the impacts of nonlocal parameter, length scale parameter, slenderness ratio, elastic medium, on vibration frequencies of nanosize beams are all evaluated.

• Steel and Composite Structures
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• 제27권3호
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• pp.371-388
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• 2018

In this paper, a new model based on nonlocal high order theory is proposed to study the size effect on the bending of nano-sandwich beams with a compliance core. In this model, in contrast to most of the available sandwich theories, no prior assumptions are made with respect to the displacement field in the core. Herein the displacement and the stress fields of the core are obtained through an elasticity solution. Equations of motion and boundary conditions for nano-sandwich beam are derived by using Hamilton's principle and an analytical solution is presented for simply supported nano-sandwich beam. The results are validated with previous studies in the literature. These results can be utilized in the study of nano-sensors and nano-actuators. The effect of nonlocal parameter, Young's modulus of the core and aspect ratio on the deflection of the nano-sandwich beam is investigated. It is concluded that by including the small-scale effects, the deflection of the skins is increased and by increasing the nonlocal parameter, the influence of small-scale effects on the deflections is increased.

• Structural Engineering and Mechanics
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• 제71권6호
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• pp.669-682
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• 2019

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von $K{\acute{a}}rm{\acute{a}}n$ geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams.