, Volume 47, Issue 5, pp 1059–1078 | Cite as

Vibration analysis of undamped, suspended multi-beam absorber systems

  • R. T. Faal
  • M. B. Amiri
  • A. A. Pirmohammadi
  • A. S. Milani


The vibration analysis of an Euler-Bernoulli beam with an attached rotary unit is first carried out assuming no unbalance. For comparison purposes, two different beam end boundary conditions are considered: a simply-supported and a clamped-clamped condition. The problem is then extended to the vibration behavior of the initial beam when subjected to a harmonic load due to an unbalance in the rotary unit. To absorb the ensuing vibrations, a secondary passive beam system is suspended from the primary beam which consists of two continuous leaf springs and three discrete masses. The absorption frequency is obtained by exploring the deflection norm of the primary beam versus dimensionless frequencies of the system. To ensure the appropriateness of the procedure for similar multi-beam absorber systems, an experimental set-up is established and analytical results are verified.


Vibration Continuous system Multi-beam absorber Dimensionless frequency Natural mode 



offset from the clamp of the absorber to the midpoint of the main beam


distance of the unbalance mass from the rotating axis (eccentricity)


flexural moduli of the main and two absorber beams


equivalent spring constants of the main and absorber beams


length of the main beam


lengths of the absorber beams


unbalance mass


unit length mass of the main and absorber beams


bending moment


masses attached at each end of the absorber beams


mass installed in the middle point of the absorber system


total mass of the attached rotary unit




shear force


absolute displacement of masses M r +M 3,M 1 and M 2, respectively


location of a given point on the beam


deflection of the main beam


deflections of the absorber beams relative to the moving clamped point at M 3


circular frequency


dimensionless natural frequency


norm of …


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • R. T. Faal
    • 1
  • M. B. Amiri
    • 1
  • A. A. Pirmohammadi
    • 1
  • A. S. Milani
    • 2
  1. 1.Faculty of EngineeringUniversity of ZanjanZanjanIran
  2. 2.School of EngineeringUniversity of British Columbia OkanaganKelownaCanada

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