Porosity-dependent asymmetric thermal buckling of inhomogeneous annular nanoplates resting on elastic substrate

Salari, Erfan,Ashoori, Alireza,Vanini, Seyed Ali Sadough Techno-Press 2019 Advances in nano research Vol.7 No.1

This research is aimed at studying the asymmetric thermal buckling of porous functionally graded (FG) annular nanoplates resting on an elastic substrate which are made of two different sets of porous distribution, based on nonlocal elasticity theory. Porosity-dependent properties of inhomogeneous nanoplates are supposed to vary through the thickness direction and are defined via a modified power law function in which the porosities with even and uneven type are approximated. In this model, three types of thermal loading, i.e., uniform temperature rise, linear temperature distribution and heat conduction across the thickness direction are considered. Based on Hamilton's principle and the adjacent equilibrium criterion, the stability equations of nanoporous annular plates on elastic substrate are obtained. Afterwards, an analytical solution procedure is established to achieve the critical buckling temperatures of annular nanoplates with porosities under different loading conditions. Detailed numerical studies are performed to demonstrate the influences of the porosity volume fraction, various thermal loading, material gradation, nonlocal parameter for higher modes, elastic substrate coefficients and geometrical dimensions on the critical buckling temperatures of a nanoporous annular plate. Also, it is discussed that because of present of thermal moment at the boundary conditions, porous nanoplate with simply supported boundary condition doesn't buckle.

Effect of non-uniform temperature distributions on nonlocal vibration and buckling of inhomogeneous size-dependent beams

Ebrahimi, Farzad,Salari, Erfan Techno-Press 2018 Advances in nano research Vol.6 No.4

In the present investigation, thermal buckling and free vibration characteristics of functionally graded (FG) Timoshenko nanobeams subjected to nonlinear thermal loading are carried out by presenting a Navier type solution. The thermal load is assumed to be nonlinear distribution through the thickness of FG nanobeam. Thermo-mechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and the material properties are assumed to be temperature-dependent. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling and vibration analysis of graded nanobeams including size effect. Moreover, in following a parametric study is accompanied to examine the effects of the several parameters such as nonlocal parameter, thermal effect, power law index and aspect ratio on the critical buckling temperatures and natural frequencies of the size-dependent FG nanobeams in detail. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared some cases in the literature. Also, it is found that the small scale effects and nonlinear thermal loading have a significant effect on thermal stability and vibration characteristics of FG nanobeams.

Thermo-mechanical vibration analysis of a single-walled carbon nanotube embedded in an elastic medium based on higher-order shear deformation beam theory

Farzad Ebrahimi,Erfan Salari 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.9

In this study, the thermal effect on the free vibration characteristics of embedded Single-walled carbon nanotubes (SWCNTs) based onthe size-dependent Reddy higher order shear deformation beam theory subjected to in-plane thermal loading is investigated by presentinga Navier-type solution and employing a semi-analytical Differential transform method (DTM) for the first time. In addition, the exactnonlocal Reddy beam theory solution presented here should be useful to engineers designing nanoelectromechanical devices. The smallscaleeffect is considered based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton’sprinciple, and they are solved by applying DTM. Numerical results reveal that the proposed modeling and semi-analytical approachcan provide more accurate frequency results of the SWCNTs compared to analytical results and some cases in the literature. The detailedmathematical derivations are presented, and numerical investigations are performed, whereas emphasis is placed on investigating theeffect of several parameters such as small-scale effects, boundary conditions, mode number, thickness ratio, temperature change, andWinkler spring modulus on the natural frequencies of the SWCNTs in detail. The vibration behavior of SWCNTs is significantly influencedby these effects. Results indicate that the inclusion of size effect results in a decrease in nanobeam stiffness and leads to a decreasein natural frequency. Numerical results are presented to serve as benchmarks for future analyses of SWCNTs.

Thermal loading effects on electro-mechanical vibration behavior of piezoelectrically actuated inhomogeneous size-dependent Timoshenko nanobeams

Ebrahimi, Farzad,Salari, Erfan Techno-Press 2016 Advances in nano research Vol.4 No.3

In the present study, thermo-electro-mechanical vibration characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and non-linear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect 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 FGP nanobeams as compared to some cases in the literature. In following a parametric study is accompanied to examine the effects of several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams.

Semi-analytical vibration analysis of functionally graded size-dependent nanobeams with various boundary conditions

Farzad Ebrahimi,Erfan Salari 국제구조공학회 2017 Smart Structures and Systems, An International Jou Vol.19 No.3

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.

Nonlocal vibration analysis of FG nano beams with different boundary conditions

Ehyaei, Javad,Ebrahimi, Farzad,Salari, Erfan Techno-Press 2016 Advances in nano research Vol.4 No.2

In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle and they are solved applying semi analytical differential transform method. 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 small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams

Farzad Ebrahimi,Majid Ghadiri,Erfan Salari,Seied Amir Hosein Hoseini,Gholam Reza Shaghaghi 대한기계학회 2015 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.29 No.3

In this study, the applicability of differential transformation method (DTM) in investigations on vibrational characteristics of functionallygraded (FG) size-dependent nanobeams is examined. The material properties of FG nanobeam vary over the thickness based on thepower law. The nonlocal Eringen theory, which takes into account the effect of small size, enables the present model to be effective in theanalysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton’s principle. The obtained resultsexactly match the results of the presented Navier-based analytical solution as well as those available in literature. The DTM is alsodemonstrated to have high precision and computational efficiency in the vibration analysis of FG nanobeams. The detailed mathematicalderivations are presented and numerical investigations performed with emphasis placed on investigating the effects of several parameters,such as small scale effects, volume fraction index, mode number, and thickness ratio on the normalized natural frequencies of the FGnanobeams. The study also shows explicitly that vibrations of FG nanobeams are significantly influenced by these effects. Numericalresults are presented to serve as benchmarks for future analyses of FG nanobeams.