Longitudinal Vibration of CNTs Viscously Damped in Span

Arda, Mustafa; Aydoğdu, Metin

doi:10.24107/ijeas.305348

Cited by 9 publications

(6 citation statements)

References 48 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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“…Their results showed that the small-scale effect and natural frequencies are inversely proportional. Arda ana Aydogdu [36] studied the longitudinal vibrations of a carbon nanotube (CNT) with an attached damper, taking into account the nonlocal stress gradient elasticity theory. They demonstrated that the nonlocal effects significantly influence the dynamical behavior of a CNT with an attached damper.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the vibration behavior of nano piezoelectric rod using surface effects and non-local elasticity theory

et al. 2023

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Due to the importance of the analysis of piezoelectric nanorods and their different conditions in engineering problems, in this research, for the first time, both nonlocal elasticity theory and surface energy theory have been used simultaneously to model the piezoelectric nanorod. the natural frequency values of the system have been extracted using the Galerkin weighted residual method. By applying an external excitation voltage, the forced vibrations of nonlocal nanorods with surface effects are presented. the results are reported for different vibrational modes, and the impact of different parameters such as dimensions, nonlocal parameters, and surface effects are investigated. the results of this study prove that the nonlocal elastic theory is more effective than the surface energy theory on the vibration behavior of piezoelectric nanorods. Also, the effect of piezoelectric properties is enhanced by the nano scaling of the rods.

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“…Aydogdu (2009b, 2014) proposed the analysis model and studied the longitudinal vibration characteristics of nanorod structure with an attached spring and clamped-free boundary condition. Arda and Aydogdu (2017) investigated the longitudinal vibration of a carbon nanotube attached to a damper by using the nonlocal stress gradient elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

Longitudinal vibration characteristics analysis of nonlocal rod structure with arbitrary internal elastic supports

Zhang

et al. 2022

Journal of Vibration and Control

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This manuscript obtained an exact solution for longitudinal vibrating characteristics of generally restrained nanorod structure with multiple internal elastic supports via an improved Fourier series method. Due to the nonlocal elasticity theory, the general boundary restraints have been formulated by introducing artificial springs. Then, classical boundary conditions can be easily realized by setting the restrained stiffness to zero or infinity accordingly. Energy formulation is derived for describing longitudinal vibration characteristics of generally restrained nanorod with multiple internal elastic supports. To improve the differential continuities at the elastically restrained boundary, nonlocal longitudinal vibrating displacement is expanded as the standard Fourier series combined with auxiliary polynomials, which makes the field function sufficiently smooth in the calculation region. By making use Rayleigh–Ritz procedure, the unknown coefficients can be obtained by solving the standard eigenvalue matrix. Then, numerical results are presented and compared with those in the literature to illustrate the reliability and effectiveness of the current model. The influence of parameters of the multiple internal elastic supports, nonlocal structural parameters, and boundary restraints on vibration characteristics are discussed and analyzed. This study provides an effective method for predicting longitudinal vibration characteristics of a generally restrained nanorod with multiple internal elastic supports, in which the nanorod has complex boundary and coupling conditions.

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Longitudinal Vibration of CNTs Viscously Damped in Span

Abstract: Abstract

Cited by 9 publications

References 48 publications

Dynamic stability of harmonically excited nanobeams including axial inertia

Dynamic stability of harmonically excited nanobeams including axial inertia

Investigation of the vibration behavior of nano piezoelectric rod using surface effects and non-local elasticity theory

Longitudinal vibration characteristics analysis of nonlocal rod structure with arbitrary internal elastic supports

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