Couette flow of viscoelastic fluid with constitutive relation involving general Caputo‐type fractional derivative

2020 ◽  
Vol 43 (5) ◽  
pp. 2090-2105 ◽  
Author(s):  
Chung‐Sik Sin ◽  
Hyok‐Chol In
Keyword(s):  
Fractional Derivative ◽  
Couette Flow ◽  
Constitutive Relation ◽  
Viscoelastic Fluid

scholarly journals The transversal creeping vibrations of a fractional derivative order constitutive relation of nonhomogeneous beam

2006 ◽  
Vol 2006 ◽  
pp. 1-18 ◽  
Author(s):  
Katica (Stevanovic) Hedrih
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Constitutive Relation ◽  
Continuous Functions ◽  
Beam Dynamic ◽  
Fractional Differential ◽  
Elastic Form ◽  
Partial Fractional Differential Equation ◽  
Derivative Order

We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to thenth shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.

Annular Couette Flow of a Suddenly Pressurized Viscoelastic Fluid

1973 ◽  
Vol 12 (1) ◽  
pp. 31-33 ◽  
Author(s):  
Shang J. Chang ◽  
Kenneth J. De Witt ◽  
John G. Fikioris
Keyword(s):  
Couette Flow ◽  
Viscoelastic Fluid
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