Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid

Farokhi

Applied Mathematical Modelling

2019

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights  Chaos in fluid-conveying nanotubes with initial deflections is analysed.  A scale-dependent model of nanobeams with large deformations is developed.  To comprehensively simulate size effects, the NSGT is utilised.

Section: Accepted Manuscriptmentioning

confidence: 99%

Chaos in fluid-conveying NSGT nanotubes with geometric imperfections

Farokhi

Applied Mathematical Modelling

2019

“…In another study, Ghasemi et al [49] utilised the Euler-Bernoulli theory of nonlocal nanobeams for predicting size influences on the post-buckling of multi-walled CNTs conveying fluid at nanoscales. Moreover, Oveissi et al [50] presented a PNE-based scale-dependent model to analyse the longitudinal vibrations and instability of fluid-conveying CNTs. In another paper, Bahaadini and Hosseini [17] have recently explored the influence of a magnetic field on the flutter instability of fluidconveying nanoscale tubes.…”

Section: Introductionmentioning

confidence: 99%

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

Farokhi

2019

Microfluid Nanofluid

A coupled continuum model incorporating size influences and geometric nonlinearity is presented for the coupled motions of viscoelastic nonlinear nanotubes conveying nanofluid.A modified model of nanobeams incorporating nonlocal strain gradient effects is utilised for describing size influences on the bifurcation behaviour of the fluid-conveying nanotube. Furthermore, size influences on the nanofluid are taken into account via Beskok-Karniadakis theory. To model the geometric nonlinearity, nonlinear strain-displacement relations are employed. Utilising Hamilton's principle and the Kelvin-Voigt model, the coupled equations of nonlinear motions capturing the internal energy loss are derived. A Galerkin procedure with a high number of shape functions and a direct time-integration scheme are then employed to extract the bifurcation characteristics of the nanofluid-conveying nanotube with viscoelastic properties. A specific attention is paid to the chaotic response of the viscoelastic nanosystem. It is found that the coupled viscoelastic bifurcation behaviour is very sensitive to the flow velocity.

“…The nonlocal version of the Euler-Bernoulli theory was also used by Ghasemi et al (Ghasemi et al, 2013) for capturing size effects on the nonlinear stability of a system of nanotubes conveying fluid. Moreover, the wave propagation characteristics (Li and Hu, 2016), axial vibration (Oveissi et al, 2016), flutter instability (Bahaadini and Hosseini, 2016) of fluidconveying nanoscale tubes have recently been studied via several size-dependent models of elasticity.…”

Section: Introductionmentioning

confidence: 99%

A nonlinear viscoelastic model for NSGT nanotubes conveying fluid incorporating slip boundary conditions

Farokhi²,

Journal of Vibration and Control

2019

A nonlinear viscoelastic model is developed for the dynamics of nanotubes conveying fluid. The influences of strain gradients and stress nonlocality are incorporated via a nonlocal strain gradient theory (NSGT). Since at nanoscales, the assumptions of no-slip boundary conditions are not valid, the Beskok-Karniadakis theory is used to overcome this problem. The coupled nonlinear differential equations are derived via performing an energy/work balance. The derived equations along the transverse and axial axes are simultaneously solved to obtain the nonlinear frequency response. For this purpose, Galerkin's technique together with a continuation method are utilised. The frequency response is investigated in both subcritical and supercritical flow regimes.