• Steel and Composite Structures
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• v.50 no.4
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• pp.429-441
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• 2024

This paper studies the free vibration behavior of trapezoidal shaped coupled double-layered graphene sheets (DLGS) system using first-order shear deformation theory (FSDT) and incorporating nonlocal elasticity theory. Two nanoplates are assumed to be bonded by an interlayer van der walls force and surrounded by an external kelvin-voight viscoelastic medium. The governing equations together with related boundary condition are discretized using a mapping-differential quadrature method (DQM) in the spatial domain. Then the natural frequency of the system is obtained by solving the eigen value matrix equation. The validity of the current study is evaluated by comparing its numerical results with those available in the literature and then a parametric study is thoroughly performed, concentrating on the series effects of angles and aspect ratio of GS, viscoelastic medium, and nonlocal parameter. The model is used to study the vibration of DLGS for two typical deformation modes, the in-phase and out-of-phase vibrations, which are investigated. Numerical results indicate that due to Increasing the damping parameter of the viscoelastic medium has reduced the frequency of both modes and this medium has been able to overdamped the oscillations and by increasing stiffness parameters both in-phase and out-of-phase vibration frequencies increased.

• Steel and Composite Structures
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• v.28 no.1
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• pp.99-110
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• 2018

In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

• Advances in nano research
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• v.9 no.3
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• pp.193-210
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• 2020

In this research, beside presenting real images of produced Functionally Graded Carbon Nanotube-Reinforced Composites (FG-CNTRCs) and a brief review of the synthesis method of FG-CNTRCs, static and buckling analysis of FG-CNTRC with piezoelectric layers are investigated. It is assumed that the material properties of FG-CNTRC are varied through the thickness direction using four different distributions of Carbon Nanotubes (CNTs). To capture the size effects, nonlocal elasticity theory proposed by A.C. Eringen is also adopted in our model. One of the topics in our paper is using a higher order theory with eight different displacement fields and comparing their results with each other. To solve the governing equations, an analytical method is used to find the deflections and critical buckling loads of FG-CNTRCs. To show the accuracy of present methodology, our results are compared with the results of simply supported rectangular nano plates available in the literature. In this research, the effects of aspect ratio, piezoelectric layer and nonlocal parameter are also studied. It is hoped that this work leads to more accurate models on FG-CNTRC.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.55-66
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• 2019

This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

• Advances in nano research
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• v.10 no.2
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• pp.175-189
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• 2021

In this article, frequency characteristics, and sensitivity analysis of a size-dependent laminated composite cylindrical nanoshell under bi-directional thermal loading using Nonlocal Strain-stress Gradient Theory (NSGT) are presented. The governing equations of the laminated composite cylindrical nanoshell in thermal environment are developed using Hamilton's principle. The thermodynamic equations of the laminated cylindrical nanoshell are obtained using First-order Shear Deformation Theory (FSDT) and Fourier-expansion based Generalized Differential Quadrature element Method (FGDQM) is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The novelty of the current study is to consider the effects of bi-directional temperature loading and sensitivity parameter on the critical temperature and frequency characteristics of the laminated composite nanostructure. Apart from semi-numerical solution, a finite element model was presented using the finite element package to simulate the response of the laminated cylindrical shell. The results created from finite element simulation illustrates a close agreement with the semi-numerical method results. Finally, the influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature, sensitivity, and frequency of the laminated composite nanostructure are investigated, in details.

• Steel and Composite Structures
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• v.48 no.4
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• pp.419-428
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• 2023

In this paper, dynamic and static bending of ball modelled by nanocomposite microbeam by nanoparticles seeing agglomeration is presented. The structural damping is considered by Kelvin-Voigt model. The agglomeration effects are assumed using Mori-Tanaka model. The football ball is modeled by third order shear deformation theory (TSDT). The motion equations are derived by principle of Hamilton's and energy method assuming size effects on the basis of Eringen theory. Using differential quadrature method (DQM) and Newmark method, the static and dynamic deflections of the structure are obtained. The effects of agglomeration and CNTs volume percent, damping of structure, nonlocal parameter, length and thickness of micro-beam are presented on the static and dynamic deflections of the nanocomposite structure. Results show that with increasing CNTs volume percent, the maximum dimensionless dynamic deflection is reduced about 17%. In addition, assuming CNTs agglomeration increases the dimensionless dynamic deflection about 14%. It is also found that with increasing the CNTs volume percent from 0 to 0.15, the static deflection is decreased about 3 times due to the enhance in the stiffness of the structure. In addition, with enhancing the nonlocal parameters, the dynamic deflection is increased about 3.1 times.

• Smart Structures and Systems
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• v.23 no.2
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• pp.141-153
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• 2019

This research deals with wave propagation of the functionally graded (FG) nano-beams based on the nonlocal elasticity theory considering surface and flexoelectric effects. The FG nano-beam is resting in Winkler-Pasternak foundation. It is assumed that the material properties of the nano-beam changes continuously along the thickness direction according to simple power-law form. In order to include coupling of strain gradients and electrical polarizations in governing equations of motion, the nonlocal non-classical nano-beam model containg flexoelectric effect is used. Also, the effects of surface elasticity, dielectricity and piezoelectricity as well as bulk flexoelectricity are all taken into consideration. The governing equations of motion are derived using Hamilton principle based on first shear deformation beam theory (FSDBT) and also considering residual surface stresses. The analytical method is used to calculate phase velocity of wave propagation in FG nano-beam as well as cut-off frequency. After verification with validated reference, comprehensive numerical results are presented to investigate the influence of important parameters such as flexoelectric coefficients of the surface, bulk and residual surface stresses, Winkler and shear coefficients of foundation, power gradient index of FG material, and geometric dimensions on the wave propagation characteristics of FG nano-beam. The numerical results indicate that considering surface effects/flexoelectric property caused phase velocity increases/decreases in low wave number range, respectively. The influences of aforementioned parameters on the occurrence cut-off frequency point are very small.

• Advances in materials Research
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• v.12 no.2
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• pp.161-177
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• 2023

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

• Structural Engineering and Mechanics
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• v.73 no.2
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• pp.191-207
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• 2020

This study aims at investigating the size-dependent free vibration of porous nanoplates when exposed to hygrothermal environment and rested on Kerr foundation. Based on the modified power-law model, material properties of porous functionally graded (FG) nanoplates are supposed to change continuously along the thickness direction. The generalized nonlocal strain gradient elasticity theory incorporating three scale factors (i.e. lower- and higher-order nonlocal parameters, strain gradient length scale parameter), is employed to expand the assumption of second shear deformation theory (SSDT) for considering the small size effect on plates. The governing equations are obtained based on Hamilton's principle and then the equations are solved using an analytical method. The elastic Kerr foundation, as a highly effected foundation type, is adopted to capture the foundation effects. Three different patterns of porosity (namely, even, uneven and logarithmic-uneven porosities) are also considered to fill some gaps of porosity impact. A comparative study is given by using various structural models to show the effect of material composition, porosity distribution, temperature and moisture differences, size dependency and elastic Kerr foundation on the size-dependent free vibration of porous nanoplates. Results show a significant change in higher-order frequencies due to small scale parameters, which could be due to the size effect mechanisms. Furthermore, Porosities inside of the material properties often present a stiffness softening effect on the vibration frequency of FG nanoplates.

• Advances in nano research
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• v.10 no.2
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• pp.151-163
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• 2021

The main target of this study is to investigate nonlinear transient responses of moving polymer nano-size plates fortified by means of Graphene Platelets (GPLs) and resting on a Winkler-Pasternak foundation under a transverse pressure force and a temperature variation. Two graphene spreading forms dispersed through the plate thickness are studied, and the Halpin-Tsai micro-mechanics model is used to obtain the effective Young's modulus. Furthermore, the rule of mixture is employed to calculate the effective mass density and Poisson's ratio. In accordance with the first order shear deformation and von Karman theory for nonlinear systems, the kinematic equations are derived, and then nonlocal strain gradient scheme is used to reflect the effects of nonlocal and strain gradient parameters on small-size objects. Afterwards, a combined approach, kinetic dynamic relaxation method accompanied by Newmark technique, is hired for solving the time-varying equation sets, and Fortran program is developed to generate the numerical results. The accuracy of the current model is verified by comparative studies with available results in the literature. Finally, a parametric study is carried out to explore the effects of GPL's weight fractions and dispersion patterns, edge conditions, softening and hardening factors, the temperature change, the velocity of moving nanoplate and elastic foundation stiffness on the dynamic response of the structure. The result illustrates that the effects of nonlocality and strain gradient parameters are more remarkable in the higher magnitudes of the nanoplate speed.