• Steel and Composite Structures
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• v.35 no.1
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• pp.147-157
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• 2020

In the present research, thermo-elastic buckling of small scale functionally graded material (FGM) nano-size plates with clamped edge conditions rested on an elastic substrate exposed to uniformly, linearly and non-linearly temperature distributions has been investigated employing a secant function based refined theory. Material properties of the FGM nano-size plate have exponential gradation across the plate thickness. Using Hamilton's rule and non-local elasticity of Eringen, the non-local governing equations have been stablished in the context of refined four-unknown plate theory and then solved via an analytical method which captures clamped boundary conditions. Buckling results are provided to show the effects of different thermal loadings, non-locality, gradient index, shear deformation, aspect and length-to-thickness ratios on critical buckling temperature of clamped exponential graded nano-size plates.

• Structural Engineering and Mechanics
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• v.67 no.2
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• pp.175-183
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• 2018

This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

• Structural Engineering and Mechanics
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• v.73 no.1
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• pp.37-52
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• 2020

This paper investigates the free and forced longitudinal vibration of a double nanorod system using doublet mechanics theory. The doublet mechanics theory is a multiscale theory spanning between lattice dynamics and continuum mechanics. Equations of motion and boundary conditions for the double nanorod system are obtained using Hamilton's principle. Clamped-clamped and clamped-free boundary conditions are considered. Frequencies and dynamic displacements are determined to demonstrate the effects of length scale parameter of considered material and geometry of the nanorods. It is shown that frequencies obtained by the doublet mechanics theory are bounded from above (van Hove singularity) and unlike classical elasticity theory doublet mechanics theory predicts finite number of modes depending on the length of the nanotube. The present doublet mechanics results have been compared to molecular dynamics, experimental and nonlocal theory results and good agreement is observed between the present and other mentioned results. The difference between wave frequencies of graphite is less than 10% between doublet mechanics and experimental results near to the end of the first Brillouin zone.

• Steel and Composite Structures
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• v.31 no.6
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• pp.641-653
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• 2019

In this paper, wave propagation is studied and analyzed in double-layered nanotubes systems via the nonlocal strain gradient theory. To the author's knowledge, the present paper is the first to investigate the wave propagation characteristics of double-layered porous nanotubes systems. It is generally considered that the material properties of nanotubes are related to the porosity and hygro-thermal effects. The governing equations of the double-layered nanotubes systems are derived by using the Hamilton principle. The dispersion relations and displacement fields of wave propagation in the double nanotubes systems which experience three different types of motion are obtained and discussed. The results show that the phase velocities of the double nanotubes systems depend on porosity, humidity change, temperature change, material composition, non-local parameter, strain gradient parameter, interlayer spring, and wave number.

• Advances in aircraft and spacecraft science
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• v.6 no.4
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• pp.273-282
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• 2019

This article is concerned with the investigation of geometrically non-linear vibration response of refined thick porous nanobeams. To this end, non-local theory of elasticity has been adopted to provide the nanobeam formulation. Voids or pores can affect the material characteristics of the nanobeam. So, their effects have been considered in this research and also there are various void distributions. The closed form solution of the non-linear problem has been used that is adopted from previous articles. Then, it is focused on the impacts of non-local field, void distribution, void amount and geometrical properties on non-linear vibrational characteristic of a nano-size beam.

• Advances in aircraft and spacecraft science
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• v.6 no.1
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• pp.1-18
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• 2019

This present article represents the study of the forced vibration of nanobeam of a single-walled carbon nanotube (SWCNTs) surrounded by a polymer matrix. The modeling was done according to the Euler-Bernoulli beam model and with the application of the non-local continuum or elasticity theory. Particulars cases of the local elasticity theory have also been studied for comparison. This model takes into account the different effects of the interaction of the Winkler's type elastic medium with the nanobeam of carbon nanotubes. Then, a study of the influence of the amplitude distribution and the frequency was made by variation of some parameters such as (scale effect ($e_0{^a}$), the dimensional ratio or aspect ratio (L/d), also, bound to the mode number (N) and the effect of the stiffness of elastic medium ($K_w$). The results obtained indicate the dependence of the variation of the amplitude and the frequency with the different parameters of the model, besides they prove the local effect of the stresses.

• Advances in nano research
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• v.14 no.6
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• pp.495-506
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• 2023

We study the bending wave, shear wave and longitudinal wave characteristics in the double nanobeams in this paper for the first time, in the process of research, based on the Reddy's higher-order shear deformation theory and considering shear layer stiffness, linear stiffness, inter-laminar stiffness, the pore volume fraction, temperature variation, functionally graded index influence on wave propagation, based on the nonlocal strain gradient theory and Hamilton variational principle, the wave equation of the double-nanometer beams are derived. Since there are three different motion states for the double nanobeams, which includes the cases of "in phase", "out of phase" and "one nanobeam fixed", the propagation characteristics of shear-, bending-, and longitudinal- waves in these three cases are discussed respectively, and some valuable conclusions are obtained.

• Advances in nano research
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• v.15 no.5
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• pp.411-422
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• 2023

In the present study, the axial vibration of the nanorods is investigated in the framework of the doublet mechanics theory. The equations of motion and boundary conditions of nanorods are derived by applying the Hamilton principle. A finite element method is developed to obtain the vibration frequencies of nanorods for different boundary conditions. A two-noded higher order rod finite element is used to solve the vibration problem. The natural frequencies of nanorods obtained with the present finite element analysis are validated by comparing the results of classical doublet mechanics and nonlocal strain gradient theories. The effects of rod length, mode number and boundary conditions on the axial vibration frequencies of nanorods are examined in detail. Mode shapes of the nanorods are presented for the different boundary conditions. It is shown that the doublet mechanics model can be used for the dynamic analysis of nanotubes, and the presented finite element formulation can be used for mechanical problems of rods with unavailable analytical solutions. These new results can also be used as references for the future studies.

• Structural Engineering and Mechanics
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• v.88 no.4
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• pp.355-368
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• 2023

Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.

• Steel and Composite Structures
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• v.50 no.1
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• pp.45-61
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• 2024

This research explores the domain of organic solar cells, a photovoltaic technology employing organic electronics, which encompasses small organic molecules and conductive polymers for efficient light absorption and charge transport, leading to electricity generation from sunlight. A computer simulation is employed to scrutinize resonance and dynamic stability in OSCs, with a focus on size effects introduced by nonlocal strain gradient theory, incorporating additional terms in the governing equations related to displacement and time. Initially, the Navier method serves as an analytical solver to delve into the dynamics of design points. The accuracy of this initial step is verified through a meticulous comparison with high-quality literature. The findings underscore the substantial impact of viscoelastic foundations, size-dependent parameters, and geometric factors on the stability and dynamic deflection of OSCs, with a noteworthy emphasis on the amplified influence of size-dependent parameters in higher values of the different layers' thicknesses.