Analysis of inhomogeneous anisotropic viscoelastic bodies described by multi-parameter fractional differential constitutive models

Nerantzaki, M. S.; Babouskos, Nick G.

doi:10.1016/j.camwa.2011.05.003

Cited by 23 publications

(8 citation statements)

References 27 publications

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“…The fractional Kelvin-Voigt viscoelastic model is employed to obtain the equations of motion. The fractional-order constitutive relationships are defined as [35]…”

Section: Equations Of Motionmentioning

confidence: 99%

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

2020

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Nonlinear vibrations of viscoelastic thin cylindrical shells are studied in this paper. The viscoelastic properties are modeled using the Kelvin-Voigt fractional-order constitutive relationship. Based on the nonlinear Love thin shell theory, the structural dynamics of the cylindrical shell is modeled by using the Newton's second law, and the Galerkin method is used to discretize the nonlinear partial differential equations into the set of nonlinear ordinary differential equations. The method of multiple scales is used to solve the nonlinear ordinary differential equations, and the amplitude-frequency and phase-frequency equations are extracted. The obtained results are verified with available investigations, and the effects of fractional parameters, excitation, and nonlinearity on the amplitude-frequency and phase-frequency responses of the viscoelastic cylindrical shells are outlined.

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“…The fractional Kelvin-Voigt viscoelastic model is employed to obtain the equations of motion. The fractional-order constitutive relationships are defined as [35]…”

Section: Equations Of Motionmentioning

confidence: 99%

Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

2020

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“…Without excluding other fractional differential models [36], the employed herein viscoelastic material is described by the Kelvin-Voigt type model with fractional-order derivative where E; n are the elastic material constants, the viscoelastic parameter, and D a c the Caputo fractional derivative of order a defined as…”

Section: Viscoelastic Membranes 541 Differential Viscoelastic Modelmentioning

confidence: 99%

BEM for Large Deflection Analysis of Membranes

Katsikadelis

2014

The Boundary Element Method for Plate Analysis

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“…Eqs. Another important advantage of this method is that it can be readily extended to solve evolution equations of order higher than two, such as those arising from the static or dynamic response of viscoelastic structures described with multi-term differential viscoelastic models [23,24]. In any case the user of these methods should be aware of the applicability of the employed method as well as of its advantages and drawbacks.…”

Section: Numerical Solution Of the Semi-discretized Equations Of Motionmentioning

confidence: 99%

“…A general method for establishing the redundant initial conditions has been proposed by Nerantzaki and Babouskos [23]. (4.65).…”

Section: Aem Solutionmentioning

confidence: 99%