Nonlinear Dynamics

, Volume 71, Issue 1–2, pp 109–120 | Cite as

Nonlinear vibration analysis of harmonically excited cracked beams on viscoelastic foundations

  • D. Younesian
  • S. R. Marjani
  • E. Esmailzadeh
Original Paper


The frequency response of a cracked beam supported by a nonlinear viscoelastic foundation has been investigated in this study. The Galerkin method in conjunction with the multiple scales method (MSM) is employed to solve the nonlinear governing equations of motion. The steady-state solutions are derived for the two different resonant conditions. A parametric sensitivity analysis is carried out and the effects of different parameters, namely the geometry and location of crack, loading position and the linear and nonlinear foundation parameters, on the frequency-response solution are examined.


Cracked beam Nonlinear vibration Multiple scales method Parameter sensitivity Resonant frequency Viscoelastic foundation 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Center of Excellence in Railway Transportation, School of Railway EngineeringIran University of Science and TechnologyTehranIran
  2. 2.Faculty of Engineering and Applied ScienceUniversity of Ontario Institute of TechnologyOshawaCanada

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