The analysis of nonlinear vibrations of a pipe conveying an ideal fluid

SINIR B. G., Demir D. D.

European Journal of Mechanics, B/Fluids, vol.52, pp.38-44, 2015 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52
  • Publication Date: 2015
  • Doi Number: 10.1016/j.euromechflu.2015.01.005
  • Journal Name: European Journal of Mechanics, B/Fluids
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.38-44
  • Keywords: Nonlinear vibrations, Pipes conveying fluid, Method of multiple time scales, Fractional derivative
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study, the non-linear vibrations of fixed-fixed tensioned pipe with vanishing flexural stiffness and conveying fluid with constant velocity are considered. The fractional calculus approach is introduced in the constitutive relationship of viscoelastic material. The pipe is on fixed support and the immovable end conditions result in the extension of the pipe during vibration and hence are introduced further nonlinear terms to the equation of motion. Analytical solutions are obtained by using the method of multiple scales. Nonlinear frequencies versus the amplitude of deflection are calculated. For frequencies close to one times the natural frequency, stability of steady-state solutions is analysed.