Forced vibration of nanorods using nonlocal elasticity

Aydoğdu, Metin; Arda, Mustafa

doi:10.12989/anr.2016.4.4.265

Cited by 24 publications

(15 citation statements)

References 33 publications

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“…Longitudinal displacement terms in equation (32) will be defined after the solution of longitudinal equation of motion of the nanorod. Longitudinal equation of motion and boundary conditions were obtained in previous studies (Aydogdu and Arda, 2016; Arda and Aydogdu, 2017b) and are written below. The governing equation of motion for longitudinal vibration is and boundary conditions …”

Section: Discussionmentioning

confidence: 99%

Dynamic stability of harmonically excited nanobeams including axial inertia

Arda

Aydoğdu

2018

Journal of Vibration and Control

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This article is concerned with the dynamic stability problem of a nanobeam under a time-varying axial loading. The nonlocal Euler–Bernoulli beam model has been used for the continuum modeling of the nanobeam structure. This problem leads to a time-dependent Mathieu-Hill equation and has been solved by using the Lindstedt–Poincaré perturbation expansion method. The effect of a small-scale parameter on the dynamic displacement and critical dynamic buckling load of nanobeams has been investigated. Stability regions have been obtained from the local and nonlocal elasticity theories. The effect of the longitudinal vibration of nanobeams on instability regions has been included in the present analysis. Amplitudes of an arbitrary point of a nanobeam due to harmonic loads have been determined. Nonlocal and longitudinal vibration effects reduce the area of the instability region and increase amplitudes.

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Section: Discussionmentioning

confidence: 99%

Dynamic stability of harmonically excited nanobeams including axial inertia

Arda

Aydoğdu

2018

Journal of Vibration and Control

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“…In perspective on Eq. 14, the end conditions of the nonlocal simple shear deformation theory are (12)…”

Section: Governing Equationsmentioning

confidence: 99%

“…(6), (7) and (11), the stress resultants may be expressed in terms of the displacements in the form where Substituting Eq. (12) into Eq. (10) yields the accompanying nonlocal governing partial differential equations in terms of w and only,…”

Section: Governing Equationsmentioning

confidence: 99%

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A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

Zenkour

2020

J Braz. Soc. Mech. Sci. Eng.

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The present article presents a simple nonlocal two-unknown shear and normal deformation beam theory to discuss the buckling response of nanorods. The theory uses two variables only and takes under consideration the small-scale impact as well as the inclusion of both shear and normal deformations. The equilibrium equations and end conditions are gained utilizing the principle of virtual work. Different end conditions like pinned, clamped and free are studied. The critical buckling loads are obtained for axially loaded nanorods with different end conditions. The significant of small-scale, shear and normal deformation parameters are investigated. Some validation examples are presented, and the sensitivity of all parameters on the critical and other buckling loads of nanorods may be observed.

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“…It is shown that the point of attachment of the spring has differing effect on the different modes of the vibration. Also forced vibration of nanorod by using nonlocal elasticity and considering linear and sinusoidal axial loads is investigated by Aydogdu and Arda 19 and dynamic displacements are obtained for nano-rods with different geometrical properties, boundary conditions, and nonlocal parameters. It is shown that nonlocal effect increases dynamic displacement and frequency when compared with local elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear longitudinal forced vibration of a rod undergoing finite strain

Roody

Fotuhi

Jalili

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Rods are one of significant engineering’s structures and vibration analysis of a rod because of extended application of it in engineering is very important. Due to large amplitude or to excitations at frequencies close to their resonance frequencies, these structural elements can experience large amplitude, hence nonlinear vibration. Therefore, understanding of longitudinal nonlinear vibration of rods with different boundary conditions and large amplitude is very useful to reach an appropriate designing. In this paper, vibration of a rod with different boundary conditions undergoing finite strain, without simplification in strain–displacement equation, is investigated. For obtaining governing equation, Green–Lagrange strain, structural damping and Hamilton principle are used and then Galerkin method is employed to convert nonlinear partial differential equation to nonlinear ordinary differential equation. In spite of many papers that only use of cubic term for nonlinearity, the governing equation has quadratic and cubic terms. At the first, free vibration equations are solved with multiple time scales method and for verifying the accuracy of this method, the results are compared with results of Runge–Kutta numerical method, which have good accuracy. Then, forced vibration is investigated in the cases of primary resonance and hard excitation including sub-harmonic and super-harmonic resonances. Analytical expressions for frequency responses are derived, and the effects of different parameters including nonlinear coefficients, damping coefficient and external excitation are discussed.

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Forced vibration of nanorods using nonlocal elasticity

Cited by 24 publications

References 33 publications

Dynamic stability of harmonically excited nanobeams including axial inertia

Dynamic stability of harmonically excited nanobeams including axial inertia

A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods

Nonlinear longitudinal forced vibration of a rod undergoing finite strain

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