Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method

Ebrahimi, Farzad; Salari, Erfan

doi:10.1016/j.compositesb.2015.04.010

Cited by 90 publications

(35 citation statements)

References 40 publications

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“…In the literature, various theories have been proposed to describe damage evolution in composites embedding different types of inclusions, including CNTs [4,5,6,7,8,9,10]. The literature on linear and nonlinear models of carbon nanotube nanocomposite materials employed for micronano plates or beams is wide and covers diverse fields such as homogenization [14], gradient/nonlocal elasticity [16,17,18,19], elasto-plasticity [20].…”

Section: A C C E P T E Dmentioning

confidence: 99%

A nonlinear mechanical model for the fatigue life of thin-film carbon nanotube supercapacitors

Formica

Lacarbonara

2015

Composites Part B: Engineering

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Section: A C C E P T E Dmentioning

confidence: 99%

A nonlinear mechanical model for the fatigue life of thin-film carbon nanotube supercapacitors

Formica

Lacarbonara

2015

Composites Part B: Engineering

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“…simply supported-simply supported (SS) and simply supportedclamped (SC), using the nonlocal elasticity within the frame work of Euler-Bernoulli beam theory (EBT) with von Kármán type nonlinearity is studied by Nazemnezhad and Hosseini-Hashemi [14]. Also, Ebrahimi et al [15][16][17] examined the applicability of differential transformation method in investigations on vibrational characteristics of FG size-dependent nanobeams. In another work, Ebrahimi and Salari [16,17] presented a semi-analytical method for vibrational and buckling analysis of FG nanobeams considering the position of neutral axis.…”

Section: Introductionmentioning

confidence: 99%

“…Also, Ebrahimi et al [15][16][17] examined the applicability of differential transformation method in investigations on vibrational characteristics of FG size-dependent nanobeams. In another work, Ebrahimi and Salari [16,17] presented a semi-analytical method for vibrational and buckling analysis of FG nanobeams considering the position of neutral axis. An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory in presented by Ansari et al [18].…”

Section: Introductionmentioning

confidence: 99%

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

Ebrahimi

Barati

2016

J Braz. Soc. Mech. Sci. Eng.

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119

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to suit the functionality of structures. The gradually composition variations of the material constituents from one surface to another provide a proper solution to the problem of induced transverse shear stresses due to the two bonded dissimilar materials with high difference in material properties. Also, due to containing outstanding mechanical properties, FGMs are appropriate for design of engineering structures [1][2][3][4][5][6][7].In recent years, FGMs have been extensively utilized in micro-electromechanical and nano-electromechanical systems and devices [8]. On the other hand, size-dependent structures such as micro and nano scale beams are key components in many systems. Therefore, mechanical analysis of micro/nano beams has received striking attention from research communities. The classical continuum theory which is extensively used in mechanical analysis of macroscopic structures should be extended to consider the size effect on mechanical behaviors of micro/nano structures. Therefore, this can be attained by the nonlocal elasticity theory proposed by Eringen in which a stress state at a reference point is suggested as a function of the strain of all neighbor points. It is noted that some studies are published on mechanical behavior of size-dependent FG beams. Among them, Simsek and Yurtcu [9] investigated bending and buckling behavior of size-dependent FG nanobeam using analytical method and Timoshenko and EulerBernoulli beam models. Also, the static and stability behavior of FG nanobeams based on nonlocal continuum theory studied by Eltaher et al. [10]. Nonlinear free vibration of functionally graded nanobeams within the framework of Euler-Bernoulli beam model including the von Kármán geometric nonlinearity studied by Sharabiani and Yazdi [11]. Also, forced vibration analysis of FG nanobeams based on the nonlocal elasticity theory and using Navier method for various shear deformation theories studied by Abstract This paper investigates buckling response of higher-order shear deformable nanobeams made of functionally graded piezoelectric (FGP) materials embedded in an elastic foundation. Material properties of FGP nanobeam change continuously in thickness direction based on power-law model. To capture small size effects, Eringen's nonlocal elasticity theory is adopted. Employing Hamilton's principle, the nonlocal governing equations of FGP nanobeams embedded in elastic foundation are obtained. To predict buckling behavior of embedded FGP nanobeams, the Navier-type analytical solution is applied to solve the governing equations. Numerical results demonstrate the influences of various parameters such as elastic foundation, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on the buckling loads of sizedependent FGP nanobeams.

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“…They addressed the effects of power law index, small scale coefficient, aspect ratio, side-to-thickness ratio, loading types, and elastic medium parameter on the buckling load of S-FGM nanoplates. Ebrahimi and Salari [32] employed the nonlocal Euler-Bernoulli beam theory for vibration analysis of functionally graded (FG) size-dependent nanobeams by using Navier-based analytical method and investigated the effects of systems parameters on the normalized natural frequencies of the FG nanobeams. In another research [33] they studied the thermal effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams subjected to an in-plane thermal loading using the same method of solution.…”

Section: Introductionmentioning

confidence: 99%

Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect

Sedighi

Keivani

Abadyan

2015

Composites Part B: Engineering

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Size-dependent free flexural vibrational behavior of functionally graded nanobeams using semi-analytical differential transform method

Cited by 90 publications

References 40 publications

A nonlinear mechanical model for the fatigue life of thin-film carbon nanotube supercapacitors

A nonlinear mechanical model for the fatigue life of thin-film carbon nanotube supercapacitors

Buckling analysis of nonlocal third-order shear deformable functionally graded piezoelectric nanobeams embedded in elastic medium

Modified continuum model for stability analysis of asymmetric FGM double-sided NEMS: Corrections due to finite conductivity, surface energy and nonlocal effect

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