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Nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to mono-frequency excitation

Ahmadian, M. T ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. DOI: 10.1007/s00707-009-0277-x
  3. Publisher: 2010
  4. Abstract:
  5. In this paper, the nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to a mono-frequency excitation is considered. The model of the viscoelastic guide is a parallel combination of springs and viscous dampers. The governing equation of motion is developed using Hamilton's principle. Applying the method of multiple scales to the governing partial differential equation, the solvability condition and approximate solutions are derived. Three cases, namely primary, subharmonic and superharmonic resonances are studied and appropriate analytical solutions are obtained. The effect of mean value velocity, force amplitude, guide stiffness and viscosity coefficient of the string on the frequency-response and bifurcation points is investigated. Findings are in good agreement with results extracted from numerical modeling
  6. Keywords:
  7. Analytical solutions ; Approximate solution ; Bifurcation points ; Force amplitude ; Frequency excitation ; Governing equations ; Hamilton's principle ; Mean values ; Method of multiple scale ; Numerical modeling ; Parallel combination ; Solvability conditions ; Subharmonics ; Superharmonic resonance ; Transversal vibration ; Viscoelastic strings ; Viscosity coefficient ; Viscous dampers ; Equations of motion ; Frequency response
  8. Source: Acta Mechanica ; Volume 214, Issue 3-4 , November , 2010 , Pages 357-373 ; 00015970 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00707-009-0277-x