• Geomechanics and Engineering
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• v.17 no.2
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• pp.175-180
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• 2019

This research is concerned with post-buckling investigation of nano-scaled beams constructed from porous functionally graded (FG) materials taking into account geometrical imperfection shape. Hence, two types of nanobeams which are perfect and imperfect have been studied. Porous FG materials are classified based on even or uneven porosity distributions. A higher order nonlinear refined beam theory is used in the present research. Both perfect and imperfect nanobeams are formulated based on this refined theory. A detailed study is provided to understand the effects of geometric imperfection, pore distribution, material distribution and small scale effects on buckling of FG nanobeams.

• Advances in nano research
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• v.7 no.3
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• pp.145-155
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• 2019

In this article, the influence of small scale effects on the free vibration response of curved magneto-electro-elastic functionally graded (MEE-FG) nanobeams has been investigated considering nonlocal elasticity theory. Power-law is used to judge the through thickness material property distribution of MEE nanobeams. The Euler-Bernoulli beam model has been adopted and through Hamilton's principle the Nonlocal governing equations of curved MEE-FG nanobeam are obtained. The analytical solutions are obtained and validated with the results reported in the literature. Several parametric studies are performed to assess the influence of nonlocal parameter, magnetic potential, electric voltage, opening angle, material composition and slenderness ratio on the dynamic behaviour of MEE curved nanobeams. It is believed that the results presented in this article may serve as benchmark results in accurate analysis and design of smart nanostructures.

• Steel and Composite Structures
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• v.42 no.6
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• pp.805-826
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• 2022

The free and live load-forced vibration behaviour of porous functionally graded (PFG) higher order nanobeams in the thermal and magnetic fields is investigated comprehensively through this work in the framework of nonlocal strain gradient theory (NLSGT). The porosity effects on the dynamic behaviour of FG nanobeams is investigated using four different porosity distribution models. These models are exploited; uniform, symmetrical, condensed upward, and condensed downward distributions. The material characteristics gradation in the thickness direction is estimated using the power-law. The magnetic field effect is incorporated using Maxwell's equations. The third order shear deformation beam theory is adopted to incorporate the shear deformation effect. The Hamilton principle is adopted to derive the coupled thermomagnetic dynamic equations of motion of the whole system and the associated boundary conditions. Navier method is used to derive the analytical solution of the governing equations. The developed methodology is verified and compared with the available results in the literature and good agreement is observed. Parametric studies are conducted to show effects of porosity parameter; porosity distribution, temperature rise, magnetic field intensity, material gradation index, non-classical parameters, and the applied moving load velocity on the vibration behavior of nanobeams. It has been showed that all the analyzed conditions have significant effects on the dynamic behavior of the nanobeams. Additionally, it has been observed that the negative effects of moving load, porosity and thermal load on the nanobeam dynamics can be reduced by the effect of the force induced from the directed magnetic field or can be kept within certain desired design limits by controlling the intensity of the magnetic field.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.721-736
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• 2017

In this paper, free vibration characteristics of functionally graded (FG) nanobeams embedded on elastic medium are investigated based on third order shear deformation (Reddy) beam theory by presenting a Navier type solution for the first time. The material properties of FG nanobeam are assumed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on third order shear deformation beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. The obtained results are presented for the vibration analysis of the FG nanobeams such as the influences of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Coupled systems mechanics
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• v.6 no.3
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• pp.251-272
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• 2017

In this paper, the thermo-mechanical vibration characteristics of functionally graded (FG) nanobeams subjected to three types of thermal loading including uniform, linear and non-linear temperature change are investigated in the framework of third-order shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. Hence, applying a third-order shear deformation beam theory (TSDBT) with more rigorous kinetics of displacements to anticipate the behaviors of FG nanobeams is more appropriate than using other theories. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. The obtained results are compared with those predicted by the nonlocal Euler-Bernoulli beam theory and nonlocal Timoshenko beam theory and it is revealed that the proposed modeling can accurately predict the vibration responses of FG nanobeams. The obtained results are presented for the thermo-mechanical vibration analysis of the FG nanobeams such as the effects of material graduation, nonlocal parameter, mode number, slenderness ratio and thermal loading in detail. The present study is associated to aerospace, mechanical and nuclear engineering structures which are under thermal loads.

• Smart Structures and Systems
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• v.19 no.3
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• pp.243-257
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• 2017

In this paper, free vibration of functionally graded (FG) size-dependent nanobeams is studied within the framework of nonlocal Timoshenko beam model. It is assumed that material properties of the FG nanobeam, vary continuously through the thickness according to a power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The non-classical governing differential equations of motion are derived through Hamilton's principle and they are solved utilizing both Navier-based analytical method and an efficient and semi-analytical technique called differential transformation method (DTM). Various types of boundary conditions such as simply-supported, clamped-clamped, clamped-simply and clamped-free are assumed for edge supports. The good agreement between the presented DTM and analytical results of this article and those available in the literature validated the presented approach. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The obtained results show the significance of the material graduation, nonlocal effect, slenderness ratio and boundary conditions on the vibration characteristics of FG nanobeams.

• Proceedings of the Korean Vacuum Society Conference
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• 2014.02a
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• pp.424.1-424.1
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• 2014

Vanadium dioxide (VO2) is a strongly correlated oxide exhibiting a first-order metal-insulator transition (MIT) that is accompanied by a structural phase transition from a low temperature monoclinic phase to a high-temperature rutile phase. VO2 has attracted significant attention because of a variety of possible applications based on its ultrafast MIT. Interestingly, the transition nature of VO2 is significantly affected by stress due to doping and/or interaction with a substrate and/or surface tension as well as defects. Accordingly, there have been considerable efforts to understand the influences of such factors on the phase transition and the fundamental mechanisms behind the MIT behavior. Here, we present the influences of oxygen deficiency, hydrogen doping, and substrate-induced stress on MIT phenomena in single-crystalline VO2 nanobeams. Specifically, the work function and the electrical resistance of the VO2 nanobeams change with the compositional variation due to the oxygen-deficiency-related defects. In addition, the VO2 nanobeams during exposure to hydrogen gas exhibit the reduction of transition temperature and the complex phase inhomogenieties arising from both substrate-induced stress and the formation of the hydrogen doping-induced metallic rutile phase.

• Steel and Composite Structures
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• v.35 no.4
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• pp.555-566
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• 2020

This paper aims to present an analytical methodology to investigate influences of nanoscale and surface energy on buckling stability behavior of perforated nanobeam structural element, for the first time. The surface energy effect is exploited to consider the free energy on the surface of nanobeam by using Gurtin-Murdoch surface elasticity theory. Thin and thick beams are considered by using both classical beam of Euler and first order shear deformation of Timoshenko theories, respectively. Equivalent geometrical constant of regularly squared perforated beam are presented in simplified form. Problem formulation of nanostructure beam including surface energies is derived in detail. Explicit analytical solution for nanoscale beams are developed for both beam theories to evaluate the surface stress effects and size-dependent nanoscale on the critical buckling loads. The closed form solution is confirmed and proven by comparing the obtained results with previous works. Parametric studies are achieved to demonstrate impacts of beam filling ratio, the number of hole rows, surface material characteristics, beam slenderness ratio, boundary conditions as well as loading conditions on the non-classical buckling of perforated nanobeams in incidence of surface effects. It is found that, the surface residual stress has more significant effect on the critical buckling loads with the corresponding effect of the surface elasticity. The proposed model can be used as benchmarks in designing, analysis and manufacturing of perforated nanobeams.

• Advances in nano research
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• v.7 no.6
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• pp.379-390
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• 2019

Putting emphasis on the effect of existence of porosity in the functionally graded materials (FGMs) on the dynamic responses of waves scattered in FG nanobeams resulted in implementation of a novel porosity-based homogenization method for FGMs and show its applicability in a wave propagation problem in the presence of axial pre-load for the first time. In the employed porosity-dependent method, the coupling between density and Young's moduli is included to consider for the effective moduli of the FG nanobeam by the means of a more reliable homogenization technique. The beam-type element will be modeled via the classical theory of beams, namely Euler-Bernoulli beam theory. Also, the dynamic form of the principle of virtual work will be extended for such nanobeams to derive the motion equations. Applying the nonlocal constitutive equations of Eringen on the obtained motion equations will be resulted in derivation of the nanobeam's governing equations. Depicted results reveal that the dispersion responses of FG nanobeams will be decreased as the porosity volume fraction is increased which must be noticed by the designers of advanced nanosize devices who are interested in employment of wave dispersion approach in continuous systems for specific goals.

• Advances in nano research
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• v.4 no.2
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• pp.65-84
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• 2016

This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electro-magnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electro-magnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.