Nonlinear Dynamics

, Volume 60, Issue 1, pp 193–205

Non-linear vibration of variable speed rotating viscoelastic beams

Original Paper

DOI: 10.1007/s11071-009-9589-6

Cite this article as:
Younesian, D. & Esmailzadeh, E. Nonlinear Dyn (2010) 60: 193. doi:10.1007/s11071-009-9589-6


Non-linear vibration of a variable speed rotating beam is analyzed in this paper. The coupled longitudinal and bending vibration of a beam is studied and the governing equations of motion, using Hamilton’s principle, are derived. The solutions of the non-linear partial differential equations of motion are discretized to the time and position functions using the Galerkin method. The multiple scales method is then utilized to obtain the first-order approximate solution. The exact first-order solution is determined for both the stationary and non-stationary rotating speeds. A very close agreement is achieved between the simulation results obtained by the numerical integration method and the first-order exact solution one. The parameter sensitivity study is carried out and the effect of different parameters including the hub radius, structural damping, acceleration, and the deceleration rates on the vibration amplitude is investigated.


Non-linear vibrationViscoelastic beamRotating beamVariable speedMultiple scales methodGalerkin method

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.School of Railway EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Faculty of Engineering and Applied ScienceUniversity of Ontario Institute of TechnologyOshawaCanada