Primary and secondary resonances in pipes conveying fluid with the fractional viscoelastic model

Nonlinear forced vibrations of a fractional viscoelastic pipe conveying fluid exposed to the time-dependent excitations is investigated in the present work. Attention is focused in particular on the primary and secondary resonances with the Kelvin–Voigt fractional order constitutive relationship mod...

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Bibliographic Details
Published in:Meccanica (Milan) 2019-11, Vol.54 (14), p.2081-2098
Main Authors: Javadi, M., Noorian, M. A., Irani, S.
Format: Article
Language:English
Subjects:
Automotive Engineering
Beam theory (structures)
Civil Engineering
Classical Mechanics
Computational fluid dynamics
Constitutive relationships
Conveying
Damping
Differential geometry
Equations of motion
Euler-Bernoulli beams
Flow velocity
Fluid flow
Fluid-solid interactions
Forced vibration
Galerkin method
Mathematical models
Mechanical Engineering
Multiscale analysis
Nonlinear dynamics
Nonlinear equations
Ordinary differential equations
Partial differential equations
Physics
Physics and Astronomy
Plug flow
Stiffness
Time dependence
Viscoelasticity
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Summary:Nonlinear forced vibrations of a fractional viscoelastic pipe conveying fluid exposed to the time-dependent excitations is investigated in the present work. Attention is focused in particular on the primary and secondary resonances with the Kelvin–Voigt fractional order constitutive relationship model. The nonlinear geometric partial differential equations due to stretching effect have been expressed by assumptions with Von Karman’s strain-displacement relation and Euler–Bernoulli beam theory. Viscoelastic fractional model for damping and stiffness, and also plug flow model for fluid flow are considered to derive the equation of motion. Based on the Galerkin truncation, the coupled Fluid-Solid interaction nonlinear equation transferred to ordinary differential equations. The method of multiple scales is adopted to analyze steady-state solutions for the primary, superharmonic, and subharmonic resonances. Finally, the detailed parametric studies on the nonlinear dynamic behavior are discussed. Results delineate that the fractional derivative order and the retardation time have significant effects on the oscillation exhibited for different values of flow velocity.
ISSN:0025-6455
1572-9648
DOI:10.1007/s11012-019-01068-2