Dynamical stability of viscoelastic column with fractional derivative constitutive relation

根国,; 朱正佑,; 程昌钧,; Gen-guo, LI; Zhu, Zhihui; Chang-jun, Cheng

doi:10.1007/bf02437967

Cited by 12 publications

(6 citation statements)

References 6 publications

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“…Such relations may be used for the study of motion and stability of viscoelastic rods (see [9,10] and [12]). Following the standard procedure (plane cross section hypothesis), as was described in [11] we obtain…”

Section: Application IImentioning

confidence: 99%

See 1 more Smart Citation

On a distributed derivative model of a viscoelastic body

Atanacković

2003

Comptes Rendus. Mécanique

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Section: Application IImentioning

confidence: 99%

“…The linearized version of (33) was used in [12]. For the case φ σ = δ(γ ) + aδ(γ − α); φ ε = δ(γ ) + bδ(γ − α) + cδ(γ − β) (see (14)) we obtain…”

Section: Application IImentioning

confidence: 99%

On a distributed derivative model of a viscoelastic body

Atanacković

2003

Comptes Rendus. Mécanique

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“…Two classic models, the generalized Maxwell model and fractional derivative model, have been developed to solve this question. 21 , 22 …”

Section: Viscoelasticity Constitutive Relationsmentioning

confidence: 99%

“…Therefore, the Maxwell model and Kelvin model cannot be used to accurately describe the viscoelasticity characteristics of crude oil. Two classic models, the generalized Maxwell model and fractional derivative model, have been developed to solve this question. , …”

Section: Viscoelasticity Constitutive Relationsmentioning

confidence: 99%

Viscoelastic Behavior and Constitutive Relation of Heavy Crude Oils

Liu

Xu²,

Chen

et al. 2022

ACS Omega

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Heavy crude oil exhibits very complex viscoelastic behaviors due to its complex composition of resins, asphaltenes, saturates, and aromatics. It has a great influence on oil production and transportation. In this work, the viscoelastic behaviors of three different heavy crude oils were measured using a rotational rheometer. In conclusion, all of these heavy crude oils display linear viscoelastic behaviors in the experimental range. The loss modulus ( E ″) of the three crude oils decreased as the experimental temperature increased, and the variation trends of the three crude oils were basically the same. However, the experimental temperature has almost no effect on the storage modulus ( E ′), which always retained a constant value of 0.4 Pa. Furthermore, the storage modulus ( E′ ) and loss modulus ( E ″) increase as the angular frequency increases. To describe the physical deformation characteristics of viscoelastic materials, the generalized Maxwell model and the fractional derivative Maxwell model are used to establish the constitutive relation of heavy crude oil. In conclusion, the generalized Maxwell model and the fractional derivative Maxwell model can predict the experimental results very well. All of the square of the correlation coefficient ( R 2 ) values are greater than 0.95. However, the number of fitting parameters for the fractional derivative Maxwell model is less than that for the fourth-order generalized Maxwell model which can save the calculating time. Therefore, the fractional derivative Maxwell model is suggested to describe the viscoelastic behavior of heavy crude oil in industrial applications.

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“…On the basis of constitutive equation 3one can derive a moment curvature relation for a rod. Such relations may be used for the study of motion and stability of viscoelastic rods (see [9], [10] and [12]). Following the standard procedure (plane cross section hypothesis), as was described in [11] we obtain…”

Section: Examplesmentioning

confidence: 99%