• Structural Engineering and Mechanics
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• v.61 no.1
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• pp.65-76
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• 2017

Prediction of the characteristics of both in-plane and out-of-plane elastic waves within conducting nanoplates in the presence of bidirectionally in-plane magnetic fields is of interest. Using Lorentz's formulas and nonlocal continuum theory of Eringen, the nonlocal elastic version of the equations of motion is obtained. The frequencies as well as the corresponding phase and group velocities pertinent to the in-plane and out-of-plane waves are analytically evaluated. The roles of the strength of in-plane magnetic field, wavenumber, wave direction, nanoplate's thickness, and small-scale parameter on characteristics of waves are discussed. The obtained results show that the in-plane frequencies commonly grow with the in-plane magnetic field. However, the transmissibility of the out-of-plane waves rigorously depends on the magnetic field strength, direction of the propagated transverse waves, small-scale parameter, and thickness of the nanoplate. The criterion for safe transferring of the out-of-plane waves through the conducting nanoplate immersed in a bidirectional magnetic field is also explained and discussed.

• Advances in nano research
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• v.7 no.6
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• pp.431-442
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• 2019

Vibration analysis of carbon nanotubes (CNTs) is very essential field owing to their many promising applications in tiny instruments. In current study, the Eringen's nonlocal elasticity theory with clamped-clamped and clamped-free end conditions is utilized for the vibration analysis of armchair and zigzag SWCNTs. The Fourier method is utilized to solve the ordinary differential equation. The motion equation for this system is developed using a novel wave propagation method. Complex exponential functions have been used and the axial model depends on BCs that has been described at the edges of CNTs. The behavior of different nonlocal parameters is considered to find the vibrational frequency of SWCNTs. It is exhibited that the effect of frequencies against aspect ratio by varying the bending rigidity. It has been investigated that by increasing the nonlocal parameter decreases the frequencies and on increasing the aspect ratio increases the frequencies for both the tubes. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.555-563
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• 2020

The objective of present paper is assessment of dynamic buckling behavior of an embedded sandwich microplates in thermal environment in which the layers are reinforced through functionally graded carbon nanotubes (FG-CNTs). Therefore, mixture rule is taken into consideration for obtaining effective material characteristics. In order to model this structure much more realistic, Kelvin-Voigt model is presumed and the sandwich structure is rested on visco-Pasternak medium. Exponential shear deformation theory (ESDT) in addition to Eringen's nonlocal theory are utilized to obtain motion equations. Further, differential cubature method (DCM) as well as Bolotin's procedure are used to solve governing equations and achieve dynamic instability region (DIR) related to sandwich structure. Different parameters focusing on volume percent of CNTs, dispersion kinds of CNTs, thermal environment, small scale effect and structural damping and their influences upon the dynamic behavior of sandwich structure are investigated. So as to indicate the accuracy of applied theories as well as methods, the results are collated with another paper. According to results, presence of CNTs and their dispersion kind can alter system's dynamic response as well.

• Structural Engineering and Mechanics
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• v.73 no.5
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• pp.565-584
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• 2020

The nonlinear thermo-electro-elastic buckling behavior of viscoelastic nanoplates under magnetic field is investigated based on nonlocal elasticity theory. Employing nonlinear strain-displacement relations, the geometrical nonlinearity is modeled while governing equations are derived through Hamilton's principle and they are solved applying semi-analytical generalized differential quadrature (GDQ) method. Eringen's nonlocal elasticity theory considers the effect of small size, which enables the present model to become effective in the analysis and design of nano-sensors and nano actuators. Based on Kelvin-Voigt model, the influence of the viscoelastic coefficient is also discussed. It is demonstrated that the GDQ method has high precision and computational efficiency in the buckling analysis of viscoelastic nanoplates. The good agreement between the results of this article and those available in literature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as electric voltage, small scale effects, elastomeric medium, magnetic field, temperature effects, the viscidity and aspect ratio of the nanoplate on its nonlinear buckling characteristics. It is explicitly shown that the thermo-electro-elastic nonlinear buckling behavior of viscoelastic nanoplates is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of viscoelastic nanoplates as fundamental elements in nanoelectromechanical systems.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.179-200
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• 2016

In this paper the differential transformation method (DTM) is utilized for vibration and buckling analysis of nanotubes in thermal environment while considering the coupled surface and nonlocal effects. The Eringen's nonlocal elasticity theory takes into account the effect of small size while the Gurtin-Murdoch model is used to incorporate the surface effects (SE). The derived governing differential equations are solved by DTM which demonstrated to have high precision and computational efficiency in the vibration analysis of nanobeams. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of thermal loading, small scale and surface effects, mode number, thickness ratio and boundary conditions on the normalized natural frequencies and critical buckling loads of the nanobeams in detail. The results show that the surface effects lead to an increase in natural frequency and critical buckling load of nanotubes. It is explicitly shown that the vibration and buckling of a nanotube is significantly influenced by these effects and the influence of thermal loadings and nonlocal effects are minimal.

• Advances in nano research
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• v.4 no.1
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• pp.51-64
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• 2016

This paper investigates the effects of thermal load and shear force on the buckling of nanobeams. Higher-order shear deformation beam theories are implemented and their predictions of the critical buckling load and post-buckled configurations are compared to those of Euler-Bernoulli and Timoshenko beam theories. The nonlocal Eringen elasticity model is adopted to account a size-dependence at the nano-scale. Analytical closed form solutions for critical buckling loads and post-buckling configurations are derived for proposed beam theories. This would be helpful for those who work in the mechanical analysis of nanobeams especially experimentalists working in the field. Results show that thermal load has a more significant impact on the buckling behavior of simply-supported beams (S-S) than it has on clamped-clamped (C-C) beams. However, the nonlocal effect has more impact on C-C beams that it does on S-S beams. Moreover, it was found that the predictions obtained from Timoshenko beam theory are identical to those obtained using all higher-order shear deformation theories, suggesting that Timoshenko beam theory is sufficient to analyze buckling in nanobeams.

• Structural Engineering and Mechanics
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• v.69 no.4
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• pp.457-466
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• 2019

This paper presents an efficient higher-order nonlocal beam theory for the Critical buckling, of functionally graded (FG) nanobeams with porosities that may possibly occur inside the functionally graded materials (FG) during their fabrication, the nonlocal elastic behavior is described by the differential constitutive model of Eringen. The material properties of (FG) nanobeams with porosities are assumed to vary through the thickness according to a power law. The governing equations of the functionally graded nanobeams with porosities are derived by employing Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam with porosities. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, Illustrative examples are given also to show the effects of porosity volume fraction, and thickness to length ratios on the critical buckling of the FG beams.

• Advances in nano research
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• v.10 no.1
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• pp.25-42
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• 2021

In this article, the vibration behavior of embedded Functionally Graded Nanoplate (FGNP) employing nonlocal Kirchhoff's plate theory has been investigated under hygrothermal environment. The FGNP is considered to be supported by Winkler-Pasternak foundation. The Eringen's differential theory is used for size effect on the vibration of the FGNP. Rayleigh-Ritz method with orthogonal polynomials are employed for the governing equations and edge constraints. The advantage of this method is that it overcomes all the drawbacks of edge constraints and can easily handle any combinations of mixed edge constraints. The coefficients viz. moisture expansion, thermal expansion and elastic coefficients are considered to be transversely graded across the FGNP. The similarity of the calculated natural frequencies is examined with the previous research, and a good concurrency is seen. The objective of this article is to analyze the parameters' effect on the nondimensionalized frequency of embedded FGNP under hygrothermal environment subjected to all possible edge constraints. For this, uniform and linear rise of temperature and moisture concentration are considered. The study highlights that the nonlocal effect is pronounced for higher modes. Moreover, the effect of the Pasternak modulus is seen to be prominent compared to the Winkler modulus on non dimensionalized frequencies of FGNP.

• Coupled systems mechanics
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• v.10 no.1
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• pp.39-60
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• 2021

The present paper is concerned with the study of nonlinear ultrasonic waves in a magneto thermo (MT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. The analytical formulation is developed based on Eringen's nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analyzed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Parametric work is carried out to scrutinize the influence of the non local scaling, magneto-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter, and tube geometrical parameters have significant effects on dimensionless frequency of nano tubes. The results presented in this study can provide mechanism for the study and design of the nano devices like component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro- magneto-mechanical systems (NEMMS) that make use of the wave propagation properties of armchair single-walled carbon nanotubes embedded on polymer matrix.

• 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.