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

Ebrahimi, Farzad; Ghadiri, Majid; Salari, Erfan; Hoseini, S. A. H.; Shaghaghi, Gholam Reza

doi:10.1007/s12206-015-0234-7

Cited by 85 publications

(21 citation statements)

References 24 publications

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“…Considering a harmonic displacement solution for the vibration problem, the flexural deflection wand the rotation angle ψ can be given by the following complex forms: [2,7,27,29,30,[53][54][55] …”

Section: Problem Formulationmentioning

confidence: 99%

“…Unlike the classical elasticity theory, nonlocal elasticity theory of Eringin [18][19][20] is a scale dependent theory accounts the nonlocal effects on resonance frequencies of simply supported beams at nanometric dimensions [21][22][23][24]. Nowadays, researchers have applied nonlocal elasticity theory for different materials [25][26][27][28][29][30] to predict linear and nonlinear [1,31] resonance frequency for uniform and nonuniform [32][33][34][35] nanostructures.…”

Section: Introductionmentioning

confidence: 99%

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Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads

Bourouina

Yahiaoui

Sahar

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads

Bourouina

Yahiaoui

Sahar

et al. 2016

Physica E: Low-dimensional Systems and Nanostructures

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“…(15) and (17) in Eq. (13) and integrating by parts, and gathering the coefficients of δu, δ w, δ ψ and δ φ, the following governing equations are obtained:…”

Section: Nonlocal Fg Piezoelectric Nanobeam Modelmentioning

confidence: 99%

“…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%

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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“…Rahmani and Pedram [22] analyzed the size effects on vibration of FG nanobeams based on nonlocal TBT. Most recently, Ebrahimi et al [23] examined the applicability of differential transformation method in investigations on vibrational characteristics of FG size-dependent nanobeams. Recently, Rahmani and Jandaghian [24] presented Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

Ebrahimi

Barati

2016

International Journal of Smart and Nano Materials

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In the present work, thermo-electro-mechanical buckling behavior of functionally graded piezoelectric (FGP) nanobeams is investigated based on higher-order shear deformation beam theory. The FGP nanobeam is subjected to four types of thermal loading including uniform, linear, and sinusoidal temperature rise as well as heat conduction through the beam thickness. Thermo-electromechanical properties of FGP nanobeam are supposed to change continuously in the thickness direction based on power-law model. To consider the influences of small-scale sizes, Eringen's nonlocal elasticity theory is adopted. Applying Hamilton's principle, the nonlocal governing equations of an FGP nanobeam in thermal environments are obtained and are solved using Naviertype analytical solution. The significance of various parameters, such as thermal loadings, external electric voltage, power-law index, nonlocal parameter, and slenderness ratio on thermal buckling response of size-dependent FGP nanobeams is investigated. ARTICLE HISTORY

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

Cited by 85 publications

References 24 publications

Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads

Analytical modeling for the determination of nonlocal resonance frequencies of perforated nanobeams subjected to temperature-induced loads

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

Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment

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