Nonlinear vibration of fractional viscoelastic plate: Primary, subharmonic, and superharmonic response

Nonlinear vibrations of fractional viscoelastic plate with Kelvin–Voigt fractional order constitutive relationship is investigated in this paper. Based on the Kirchhoff hypothesis for thin shells and von Karman’s assumption, the structural dynamic of the plate is modeled by using the Newton’s second...

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Bibliographic Details
Published in:International journal of non-linear mechanics 2018-03, Vol.99, p.154-164
Main Authors: Permoon, M.R., Haddadpour, H., Javadi, M.
Format: Article
Language:English
Subjects:
Automobile industry
Constitutive relationships
Equations of motion
Fractional derivative
Fractional order constitutive relationship
Galerkin method
Multiscale analysis
Nonlinear equations
Nonlinear response
Nonlinear vibration
Nonlinearity
Partial differential equations
Plates (structural members)
Stress functions
Thin walled shells
Vibration
Viscoelastic plate
Viscoelasticity
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Summary:Nonlinear vibrations of fractional viscoelastic plate with Kelvin–Voigt fractional order constitutive relationship is investigated in this paper. Based on the Kirchhoff hypothesis for thin shells and von Karman’s assumption, the structural dynamic of the plate is modeled by using the Newton’s second law. The nonlinear coupled equations of motion are obtained by introducing the Airy stress function and the Galerkin method is used to discretize the partial differential equations. Analytical solutions for fully simply supported and clamped plate are obtained by using the method of multiple scales and finally the equations of amplitude–frequency and phase–frequency are obtained for primary, super-harmonic and sub-harmonic resonance. The obtained amplitude–frequency and phase–frequency equations are used for studying the effects of excitation, fractional parameters and nonlinearity on the frequency responses of the fractional viscoelastic plate and finally some conclusions are outlined. •Nonlinear vibrations of fractional viscoelastic plate with Kelvin–Voigt fractional order constitutive relationship.•Primary, super-harmonic and sub-harmonic resonance of fractional viscoelastic plate.•Kirchhoff hypothesis and von Karman’s assumption for modeling the forced vibration of viscoelastic plate.
ISSN:0020-7462
1878-5638
DOI:10.1016/j.ijnonlinmec.2017.11.010