• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.701-711
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• 2018

Herein, the thermo-magneto-elastic wave dispersion answers of functionally graded (FG) double-nanobeam systems (DNBSs) are surveyed implementing a nonlocal strain gradient theory (NSGT). The kinematic relations are derived employing the classical beam theory. Also, scale influences are covered precisely in the framework of NSGT. Moreover, Mori-Tanaka homogenization model is introduced in order to obtain the effective material properties of FG nanobeams. Meanwhile, effects of external forces such as thermal and Lorentz forces are included in this research. Also, based upon the Hamilton's principle, the Euler-Lagrange equations are developed; afterwards, these equations are incorporated with those of NSGT to reach the nonlocal governing equations of FG-DNBSs. Furthermore, according to an analytical approach, the governing equations are solved to obtain the wave frequencies and phase velocities of FG-DNBSs. At the end, some illustrations are rendered to clarify the influences of a wide range of involved parameters.

• Advances in nano research
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• v.10 no.1
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• pp.1-14
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• 2021

In the present computational approach, thermal buckling and frequency characteristics of a doubly curved laminated nanopanel with the aid of Two-Dimensional Generalized Differential Quadrature Method (2D-GDQM) and Nonlocal Strain Gradient Theory (NSGT) are investigated. Additionally, the temperature changes along the thickness direction nonlinearly. The novelty of the current study is in considering the effects of laminated composite and thermal in addition of size effect on frequency, thermal buckling, and dynamic deflections of the laminated nanopanel. The acquired numerical and analytical results are compared by each other to validate the results. The results demonstrate that some geometrical and physical parameters, have noticeable effects on the frequency and pre-thermal buckling behavior of the doubly curved open cylindrical laminated nanopanel. The favorable suggestion of this survey is that for designing the laminated nano-sized structure should pay special attention to size-dependent parameters because nonlocal and length scale parameters have an important role in the static and dynamic behaviors of the laminated nanopanel.

• Steel and Composite Structures
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• v.49 no.4
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• pp.361-380
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• 2023

A size dependent bending behavior of piezoelectrical flexoelectric layered perforated functionally graded (FG) composite nanobeam rested on an elastic foundation is investigated analytically. The composite beam is composed of regularly cutout FG core and two piezoelectric face sheets. The material characteristics is graded through the core thickness by power law function. Regular squared cutout perforation pattern is considered and closed forms of the equivalent stiffness parameters are derived. The modified nonlocal strain gradient elasticity theory is employed to incorporate the microstructure as well as nonlocality effects into governing equations. The Winkler as well as the Pasternak elastic foundation models are employed to simulate the substrate medium. The Hamiltonian approach is adopted to derive the governing equilibrium equation including piezoelectric and flexoelectric effects. Analytical solution methodology is developed to derive closed forms for the size dependent electromechanical as well as mechanical bending profiles. The model is verified by comparing the obtained results with the available corresponding results in the literature. To demonstrate the applicability of the developed procedure, parametric studies are performed to explore influences of gradation index, elastic medium parameters, flexoelectric and piezoelectric parameters, geometrical and peroration parameters, and material parameters on the size dependent bending behavior of piezoelectrically layered PFG nanobeams. Results obtained revealed the significant effects both the flexoelectric and piezoelectric parameters on the bending behavior of the piezoelectric composite nanobeams. These parameters could be controlled to improve the size dependent electromechanical as well as mechanical behaviors. The obtained results and the developed procedure are helpful for design and manufacturing of MEMS and NEMS.

• Steel and Composite Structures
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• v.49 no.5
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• pp.487-502
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• 2023

In the realm of nanotechnology, the nonlocal strain gradient theory takes center stage as it scrutinizes the behavior of spinning cantilever nanobeams and nanotubes, pivotal components supporting various mechanical movements in sport structures. The dynamics of these structures have sparked debates within the scientific community, with some contending that nonlocal cantilever models fail to predict dynamic softening, while others propose that they can indeed exhibit stiffness softening characteristics. To address these disparities, this paper investigates the dynamic response of a nonlocal cantilever cylindrical beam under the influence of external discontinuous dynamic loads. The study employs four distinct models: the Euler-Bernoulli beam model, Timoshenko beam model, higher-order beam model, and a novel higher-order tube model. These models account for the effects of functionally graded materials (FGMs) in the radial tube direction, giving rise to nanotubes with varying properties. The Hamilton principle is employed to formulate the governing differential equations and precise boundary conditions. These equations are subsequently solved using the generalized differential quadrature element technique (GDQEM). This research not only advances our understanding of the dynamic behavior of nanotubes but also reveals the intriguing phenomena of both hardening and softening in the nonlocal parameter within cantilever nanostructures. Moreover, the findings hold promise for practical applications, including drug delivery, where the controlled vibrations of nanotubes can enhance the precision and efficiency of medication transport within the human body. By exploring the multifaceted characteristics of nanotubes, this study not only contributes to the design and manufacturing of rotating nanostructures but also offers insights into their potential role in revolutionizing drug delivery systems.

• 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.

• 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.

• Biomaterials and Biomechanics in Bioengineering
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• v.5 no.1
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• pp.1-10
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• 2020

This paper investigated vibrational behavior of the osteon as bone unit in the different situations. This study can lead to increase our knowledge of our body. In this paper free vibration of the osteon with considering it as composite material has been studied. The effect of numbers of lamellae and radius of those on natural frequency of osteon are subtle; while thickness of lamellae have decreasing trend on natural frequency of osteon. The presence of nerve and blood in haversian canal change trend of natural frequency, absolutely. Using the nonlocal strain gradient theory(NSGT) leads to effectiveness of scale parameter on equations of motion and the obtained results. The governing equations are derived by Hamilton's principles. A parametric study is presented to examine the effect of various parameters on vibrational behaviour of osteon. The results can also be regarded as a benchmark in vibration analysis behavior of osteon as bone unite.

• Structural Engineering and Mechanics
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• v.72 no.1
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• pp.71-81
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• 2019

The objective of this paper is to develop a size-dependent nonlinear model of beams for fluid-conveying nanotubes with an initial deflection. The nonlinear frequency response of the nanotube is analysed via an Euler-Bernoulli model. Size influences on the behaviour of the nanosystem are described utilising the nonlocal strain gradient theory (NSGT). Relative motions at the inner wall of the nanotube is taken into consideration via Beskok-Karniadakis model. Formulating kinetic and elastic energies and then employing Hamilton's approach, the nonlinear motion equations are derived. Furthermore, Galerkin's approach is employed for discretisation, and then a continuation scheme is developed for obtaining numerical results. It is observed that an initial deflection significantly alters the frequency response of NSGT nanotubes conveying fluid. For small initial deflections, a hardening nonlinearity is found whereas a softening-hardening nonlinearity is observed for large initial deflections.

• Advances in nano research
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• v.7 no.1
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• pp.51-61
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• 2019

This paper develops a four-unknown refined plate theory and the Galerkin method to investigate the size-dependent stability behavior of functionally graded material (FGM) under the thermal environment and the FGM having temperature-dependent material properties. In the current study two scale coefficients are considered to examine buckling behavior much accurately. Reuss micromechanical scheme is utilized to estimate the material properties of inhomogeneous nano-size plates. Governing differential equations, classical and non-classical boundary conditions are obtained by utilizing Hamiltonian principles. The results showed the high importance of considering temperature-dependent material properties for buckling analysis. Different influencing parametric on the buckling is studied which may help in design guidelines of such complex structures.

• Advances in nano research
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• v.13 no.3
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• pp.233-245
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• 2022

Resently, the use of smart structures has been heightened up rapidly. For this issue, vibration analysis related to a graphene nanoplatelet composite (GPLRC) nanodisk which is attached to a piezoelectric layer and is subjected to thermal loads is explored in the current paper. The formulation of this study is obtained through the energy method and nonlocal strain gradient theory, and then it is solved employing generalized differential quadrature method (GDQM). Halpin-Tsai model in addition to the mixture's rule are utilized to capture the material properties related to the reinforced composite layer. The compatibility conditions are presented for exhibiting the perfect bounding between two layers. The results of this study are validated by employing the other published articles. The impact of such parameters as external voltage, the radius ratio, temperature difference, and nonlocality on the vibrational frequency of the system is investigated in detail.