A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams

Ebrahimi, Farzad; Barati, Mohammad Reza

doi:10.1007/s13369-015-1930-4

Cited by 133 publications

(30 citation statements)

References 33 publications

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“…in which ( , , ) are the unknown Fourier coefficients that will be calculated for each value of . Boundary conditions for a simply supported beam are as follows [37]:…”

Section: Power-low Functionally Graded Beams With Porositiesmentioning

confidence: 99%

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Ebrahimi

Jafari

2016

Journal of Engineering

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In the present paper, thermomechanical vibration characteristics of functionally graded (FG) Reddy beams made of porous material subjected to various thermal loadings are investigated by utilizing a Navier solution method for the first time. Four types of thermal loadings, namely, uniform, linear, nonlinear, and sinusoidal temperature rises, through the thickness direction are considered. Thermomechanical material properties of FG beam are assumed to be temperature-dependent and supposed to vary through thickness direction of the constituents according to power-law distribution (P-FGM) which is modified to approximate the porous material properties with even and uneven distributions of porosities phases. The governing differential equations of motion are derived based on higher order shear deformation beam theory. Hamilton’s principle is applied to obtain the governing differential equations of motion which are solved by employing an analytical technique called the Navier type solution method. Influences of several important parameters such as power-law exponents, porosity distributions, porosity volume fractions, thermal effects, and slenderness ratios on natural frequencies of the temperature-dependent FG beams with porosities are investigated and discussed in detail. It is concluded that these effects play significant role in the thermodynamic behavior of porous FG beams.

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“…in which ( , , ) are the unknown Fourier coefficients that will be calculated for each value of . Boundary conditions for a simply supported beam are as follows [37]:…”

Section: Power-low Functionally Graded Beams With Porositiesmentioning

confidence: 99%

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

Ebrahimi

Jafari

2016

Journal of Engineering

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“…Based on parabolic third order beam theory, the displacement field at any point of the beam are supposed to be in the form [34]:…”

Section: Nonlocal Fg Piezoelectric Nanobeam Modelmentioning

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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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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“…Boukhari et al [39] proposed a thermal study on wave propagation in FGM functionally graded materials plates based on the neutral surface position. Ebrahimi and Barati [40] have studied the influence of the environment on the damping vibration of nano-beams in functionally graded materials. Ahouel et al [41] investigated the size-dependent mechanical behavior of trigonometrically shear functional and trigonometric shear nano-beams, including the concept of the neutral surface position.…”

Section: Introductionmentioning

confidence: 99%

Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory

Hebbar

Ouinas

et al. 2020

Frattura Ed Integrità Strutturale

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The objective of this work is to analyze the behavior beams functionally graded, simply supported, under different conditions such as bending, buckling, and vibration and this by use shear deformation theories a two-dimensional (2D) and quasi-three-dimensional (quasi-3D). The proposed theories take into account a new field of displacement which includes indeterminate whole terms and contains fewer unknowns, compared to other theories of the literature; by taking account of the effects of the transverse shears and the thickness stretching. In this theory, the distribution of the transverse shear stress is hyperbolic and satisfies the boundary conditions on the upper and lower surfaces of the beam without the need for a shear correction factor. In this type of beam the properties of the materials vary according to a distribution of the volume fraction, the Hamilton principle is used to calculate the equations of motion, and in order to check the accuracy of the theory used comparison is made with the studies existing in the literature.

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A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams

Cited by 133 publications

References 33 publications

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities

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

Numerical modeling of bending, buckling, and vibration of functionally graded beams by using a higher-order shear deformation theory

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