Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment

Shafiei, Navvab; Ghadiri, Majid; Mahinzare, Mohammad

doi:10.1080/15376494.2017.1365982

Cited by 44 publications

(15 citation statements)

References 60 publications

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“…Ebrahimi and Barati (2016) investigated free vibrational behavior of FGM nanobeams based on the higher order shear deformation theory. Shafiei et al (2016Shafiei et al ( , 2017 used Hamilton's principle and generalized differential quadrature element method (GDQEM) and GDQM for obtaining governing equations of rotating FGM Timoshenko and Euler-Bernoulli micro/nanobeams and their size-dependent vibrational behaviors. Lee and Chang (2012) studied natural frequency behavior of nanotubes by considering surface effects based on the Timoshenko beam theory and Mohammadi et al (2013) investigated free vibration of a circular graphene single sheet subjected to in-plane pre-loading through nonlocal elasticity and Kirchhoff plate theory.…”

Section: Introductionmentioning

confidence: 99%

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Shojaeefard

Googarchin

Mahinzare

et al. 2018

Journal of Intelligent Material Systems and Structures

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This article investigates free vibration of a functionally graded piezomagnetic material cylindrical nanoshell embedded in viscoelastic media under rotational, external electric and magnetic loadings. The governing equations of the nanoshell are derived based on Eringen’s nonlocal theory. It is found that, magnetic and piezoelectric properties of the structure change exponentially along the thickness. The rotational loading is calculated considering initial hoop tension. The results are obtained by applying generalized differential quadrature method to the governing equations and associated boundary conditions. Results also include those achieved for clamped-clamped and simply hinged-hinged boundary conditions. It is found that free vibration characteristics of functionally graded piezomagnetic material cylindrical nanoshell are influenced by several factors including angular velocity, length scale parameter, external voltage, external amperage, functionally graded power index, and viscoelastic media parameters.

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Section: Introductionmentioning

confidence: 99%

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Shojaeefard

Googarchin

Mahinzare

et al. 2018

Journal of Intelligent Material Systems and Structures

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“…Shafiei et al [31] analysed transverse vibration of rotary functionally graded size-dependent tapered Euler-Bernoulli nanobeam in thermal environment. Nonlocal equations of motions were yielded by Hamilton's principle, and they were solved by the differential quadrature method.…”

Section: Thermal Environmentmentioning

confidence: 99%

Nanostructural Members in Various Fields: A Literature Review

Awrejcewicz

Krysko

Zhigalov

et al. 2020

Advanced Structured Materials

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Guo and Zhao [1] developed a theoretical background aimed at a study of the sizedependent bending elastic properties of nanobeams with surface effects.Lim and Wang [2] employed the exact variational nonlocal stress modelling with asymptotic higher order strain gradients for nanobeams.Wang et al.[3] analysed vibrations of initially stressed micro-and nanobeams. Challamel and Wang [4] solved a paradox associated with the small-scale effect for a nonlocal cantilever beam. Lim et al. [5] illustrated the stiffness strengthening effects of nonlocal stress and axial tension on free vibration of cantilever nanobeams.Aydogdu [6] proposed a general nonlocal beam theory to analyse bending, buckling and free vibration of nanobeams based on the classical Euler-Bernoulli, Timoshenko, Reddy and Levinson theories.Zhang et al.[7] analysed bending and vibration of hybrid nonlocal beams. Murmu and Adhikari [8] studied nonlocal transverse vibration of doublenanobeam systems within the framework of Eringen's nonlocal elasticity theory. The following results were reported: nonlocal natural frequencies are smaller than the corresponding local frequencies, small-scale effects are higher with increasing values of nonlocal parameter, whereas increase of stiffness of coupling springs reduces the nonlocal effects.Li et al.[9] derived a sixth-order PDE governing dynamics of simply supported nanobeams under initial axial force based on nonlocal elasticity theory. The effects of the nonlocal nanoscale and dimensionless axial force on the first twice mode frequencies were presented and discussed.Hosseini-Hashemi et al.[10] investigated the surface effects (elasticity, stress and density) of free vibrations of the Euler-Bernoulli and Timoshenko nanobeams employing the nonlocal elasticity theory. The governing PDEs were studied with regard to three different boundary conditions, i.e. simple-simple, clamped-simple and clamped-clamped. In particular, it was shown that rotary inertia and shear deformation had more effects on the surface than the nonlocal parameter.Simsek [11] proposed a novel size-dependent beam model for nonlinear free vibration of a functionally graded nanobeam by matching the nonlocal strain gradient theory and the Euler-Bernoulli beam theory with an account of the von Kármán's nonlinearity. Hamilton's principle yielded the governing PDEs and boundary conditions. A few case studies were supplemented pointing out the important features of the strain gradient length scale, the nonlocal parameters, vibration amplitude and various material compositions.Hashemi and Khaniki [12] studied free vibrations of a Timoshenko nanobeam with variable cross section in frame of the nonlocal elasticity theory. The smallscale effects were modelled by Eringen's nonlocal elasticity theory. They derived an analytical solution with regard to the Timoshenko nanobeams for three different

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“…Ebrahimi and Barati [31] studied the vibrational behavior of higher-order FG nanobeams using a nonlocal MCST. Shafiei et al [32] proposed flap-wise bending vibration analysis of a rotary tapered FG nanobeam in a thermal environment. They employed ENT and EBT models, utilized the differential quadrature method (DQM), and carefully imposed the cantilever boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

Rahmani

Faroughi

Friswell

2020

Mechanical Systems and Signal Processing

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A comprehensive vibrational analysis of bi-directional functionally graded (2D-FG) rotating nanobeams with porosities is studied for the first time. The beam is modeled based on general nonlocal theory (GNT) where the beam governing equations are derived depending on two different nonlocal parameters. Unlike Eringen's conventional form of nonlocal theory, the general nonlocal theory can reveal both hardening and softening behaviors of the material. Here, the attenuation functions are altered in both transverse and longitudinal directions of 2D-FG nanobeam. This feature, which has a significant effect on the vibrational characteristics, has not been considered in previous studies. Moreover, to estimate the effects of the higher-order transverse shear strains on the vibration of the nanobeam, Reddy's beam theory (RBT), which includes higher-order shear deformation, is employed. The material properties of the 2D-FG rotating nanobeam vary both in the length and thickness directions according to a power law.The generalized differential quadrature method (GDQM) is used to predict the vibration response. Also, the effects of material variation along the length and thickness directions, the rotating velocity of the nanobeam, the porosity volume fraction and the length to thickness ratio of the rotating nanobeam are illustrated and discussed in detail. The investigations performed in this study expose new phenomena for the vibration of nanobeams.

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Flapwise bending vibration analysis of rotary tapered functionally graded nanobeam in thermal environment

Cited by 44 publications

References 60 publications

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media

Nanostructural Members in Various Fields: A Literature Review

The vibration of two-dimensional imperfect functionally graded (2D-FG) porous rotating nanobeams based on general nonlocal theory

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