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Nonlinear vibration analysis of fractional viscoelastic cylindrical shells

Permoon, M. R ; Sharif University of Technology | 2020

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-020-02785-6
  3. Publisher: Springer , 2020
  4. Abstract:
  5. 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. © 2020, Springer-Verlag GmbH Austria, part of Springer Nature
  6. Keywords:
  7. Control nonlinearities ; Cylinders (shapes) ; Frequency response ; Galerkin methods ; Ordinary differential equations ; Partial differential equations ; Shells (structures) ; Structural dynamics ; Vibration analysis ; Viscoelasticity ; Constitutive relationships ; Method of multiple scale ; Non-linear vibrations ; Nonlinear ordinary differential equation ; Nonlinear partial differential equations ; Nonlinear vibration analysis ; Thin cylindrical shell ; Viscoelastic properties ; Nonlinear equations
  8. Source: Acta Mechanica ; Volume 231, Issue 11 , 2020 , Pages 4683-4700
  9. URL: https://link.springer.com/article/10.1007/s00707-020-02785-6