Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

Tang, Ye; Zhen, Yaxin; Fang, Bo

doi:10.1016/j.apm.2017.11.022

Cited by 70 publications

(14 citation statements)

References 30 publications

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“…According to the aforementioned reason, many remarkable achievements on dynamic analysis of pipes conveying fluid are available in [1][2][3][4][5][6][7][8]. The dynamic analysis of inclined supported pipes conveying fluid was addressed in [1].…”

Section: Introductionmentioning

confidence: 99%

“…Some physical and geometrical quantities were introduced in [7], and they were studied in how to influence dynamics properties. The non-linear vibration for viscoelastic pipes conveying fluid was investigated based on a fractional order model in [8]. A mount of works have been done, but still exist some issues needed to be further considered for pipes conveying fluid.…”

Section: Introductionmentioning

confidence: 99%

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Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Wang

Chen

2020

Applied Mathematical Modelling

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The dynamic analysis of viscoelastic pipes conveying fluid is investigated with the variable fractional order model in this article. The nonlinear variable fractional order integral-differential equation is established by introducing the model into the governing equation. Then the Shifted Legendre Polynomials algorithm is first presented for dealing with this kind of equations. The numerical example verifies that the algorithm is an effective and accurate technique for addressing this type complicated equation. Numerical results for dynamic analysis of viscoelastic pipes conveying fluid show the effect of parameters on displacement, acceleration, strain and stress. It also indicates that how dynamic properties are affected by the variable fractional order and fluid velocity varying. Most of all, the proposed algorithm has enormous potentials for the problem of high precision dynamics with the variable fractional order model.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Wang

Chen

2020

Applied Mathematical Modelling

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“…Studies were carried out on the stability of nanotubes conveying fluids 4 , 6 – 17 . The influence of the fluid flow on the free vibration of nanotubes has been investigated using linear models of the nanotube dynamics 11 – 14 , 18 – 20 .…”

Section: Introductionmentioning

confidence: 99%

“…Dong et al 10 investigated the wave propagation in multi-walled CNTs embedded in an elastic medium. Tang et al 7 , 16 , 17 studied the divergence instability of nonhomogeneous nanotubes conveying fluids. These studies revealed that the frequencies of the free vibration of nanotubes conveying fluids decrease as the fluid flow velocity increases 7 , 11 – 13 , 16 , 17 .…”

Section: Introductionmentioning

confidence: 99%

Wettability and confinement size effects on stability of water conveying nanotubes

Shaat

Javed

Faroughi

2020

Sci Rep

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This study investigates the wettability and confinement size effects on vibration and stability of water conveying nanotubes. We present an accurate assessment of nanotube stability by considering the exact mechanics of the fluid that is confined in the nanotube. Information on the stability of nanotubes in relation to the fluid viscosity, the driving force of the fluid flow, the surface wettability of the nanotube, and the nanotube size is missing in the literature. For the first time, we explore the surface wettability dependence of the nanotube natural frequencies and stability. By means of hybrid continuum-molecular mechanics (HCMM), we determined water viscosity variations inside the nanotube. Nanotubes with different surface wettability varying from super-hydrophobic to super-hydrophilic nanotubes were studied. We demonstrated a multiphase structure of nanoconfined water in nanotubes. Water was seen as vapor at the interface with the nanotube, ice shell in the middle, and liquid water in the nanotube core. The average velocity of water flow in the nanotube was obtained strongly depend on the surface wettability and the confinement size. In addition, we report the natural frequencies of the nanotube as functions of the applied pressure and the nanotube size. Mode divergence and flutter instabilities were observed, and the activation of these instabilities strongly depended on the nanotube surface wettability and size. This work gives important insights into understanding the stability of nanotubes conveying fluids depending on the operating pressures and the wettability and size of confinement. We revealed that hydrophilic nanotubes are generally more stable than hydrophobic nanotubes when conveying fluids.

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“…Wang et al [7] studied the effects of several physical and geometric parameters on the dynamic characteristics of infusion pipelines by using bifurcation diagram and phase diagram. Tang et al [8] considered a free vibration of viscoelastic pipes conveying fluid by a nonlinear fractional model and also investigated the effect of model parameters on the amplitudes and frequencies of pipes. Although a lot of research results have been contributed, there are still difficult problems in pipes conveying fluid aspects.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials

Wang

Chen

2019

Fractal Fract

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Viscoelastic pipeline conveying fluid is analyzed with an improved variable fractional order model for researching its dynamic properties accurately in this study. After introducing the improved model, an involuted variable fractional order, which is an unknown piecewise nonlinear function for analytical solution, an equation is established as the governing equation for the dynamic displacement of the viscoelastic pipeline. In order to solve this class of equations, a numerical method based on shifted Legendre polynomials is presented for the first time. The method is effective and accurate after the numerical example verifying. Numerical results show that how dynamic properties are influenced by internal fluid velocity, force excitation, and variable fractional order through the proposed method. More importantly, the numerical method has shown great potentials for dynamic problems with the high precision model.

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Nonlinear vibration analysis of a fractional dynamic model for the viscoelastic pipe conveying fluid

Cited by 70 publications

References 30 publications

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model

Wettability and confinement size effects on stability of water conveying nanotubes

Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials

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