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Vibration analysis of undamped, suspended multi-beam absorber systems

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Abstract

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.

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Abbreviations

e :

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

e 1 :

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

E 1 I 1,E 2 I 2,E 3 I 3 :

flexural moduli of the main and two absorber beams

k 1,k 2,k 3 :

equivalent spring constants of the main and absorber beams

L :

length of the main beam

L 1,L 2 :

lengths of the absorber beams

m :

unbalance mass

m 1,m 2,m 3 :

unit length mass of the main and absorber beams

M :

bending moment

M 1,M 2 :

masses attached at each end of the absorber beams

M 3 :

mass installed in the middle point of the absorber system

M r :

total mass of the attached rotary unit

t :

time

V :

shear force

w 1,w 2,w 3 :

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

x :

location of a given point on the beam

y 1 :

deflection of the main beam

y 2,y 3 :

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

ω :

circular frequency

β 1 L :

dimensionless natural frequency

∥…∥:

norm of …

References

  1. de Silva CW (1999) Vibration fundamentals and practice. CRC Press, New York

    Book  Google Scholar 

  2. Watts P (1883) On a method of reducing the rolling of ships at sea. Trans Inst Nav Archit 24:165–190

    Google Scholar 

  3. Frahm H (1909) Device for damping vibration of bodies. US Patent No 989958

  4. Ormondroyd J, Hartog JPD (1928) The theory of the dynamic vibration absorber. Trans ASME 50:9–15

    Google Scholar 

  5. Hartog JPD (1985) Mechanical vibration, 4th edn. Dover, New York (1st edition 1934)

    Google Scholar 

  6. Sevin E (1961) On the parametric excitation of a pendulum-type vibration absorber. J Appl Mech 28:330–334

    Article  MATH  Google Scholar 

  7. Haxton RS, Barr ADS (1972) The autoparametric vibration absorber. J Eng Ind 94:119–125

    Article  Google Scholar 

  8. Balachandran B, Magrab EB (2004) Vibrations. Thomson International, New York

    Google Scholar 

  9. Pennestri E (1998) An application of Chebyshev’s min-max criterion to the optimal design of a damped dynamic vibration absorber. J Sound Vib 217(4):757–765

    Article  MathSciNet  ADS  Google Scholar 

  10. Mitchiner RG, Leonard RG (1991) Centrifugal pendulum vibration absorbers-theory and practice. J Vib Acoust 113:503–507

    Article  Google Scholar 

  11. Haddowand AG, Shaw SW (2003) Centrifugal pendulum vibration absorbers: an experimental and theoretical investigation. Nonlinear Dyn 34:293–307

    Article  Google Scholar 

  12. Gus’kov AM, Panovko GYa, Bin CV (2008) Analysis of the dynamics of a pendulum vibration absorber. J Mach Manuf Reliab 37(4): 321–329

    Article  Google Scholar 

  13. Hosek M, Elmali H, Olgac N (1997) A tunable vibration absorber: The centrifugal delayed resonator. J Sound Vib 205(2):151–165

    Article  ADS  Google Scholar 

  14. Bachmann H, Ammann WJ, Deischl F, Eisenmann J, Floegl I, Hirsch GH, Klein GK, Lande GJ, Mahrenholtz O, Natke, Nussbaumer H, Pretlove AJ, Rainer JH, Saemann E-U, Steinbeisser L (1995) Vibration problems in structures: practical guidelines. Birkhäuser, Berlin

    Book  Google Scholar 

  15. Thompson DJ (2008) A continuous damped vibration absorber to reduce broad-band wave propagation in beams. J Sound Vib 311(3–5):824–842

    Article  ADS  Google Scholar 

  16. Juang JN (1984) Optimal design of a passive vibration absorber for a truss beam. J Guid Control Dyn 7(6):733–739

    Article  Google Scholar 

  17. Aida T, Toda S, Ogawa N, Imada Y (1992) Vibration control of beams by beam-type dynamic vibration absorbers. J Eng Mech 118(2):248–258

    Article  Google Scholar 

  18. Ellakany AM, Tablia HA (2010) A numerical model for static and free vibration analysis of elastic composite beams with end shear restraint. Meccanica 45:463–474

    Article  MathSciNet  Google Scholar 

  19. Fasana A, Giorcelli E (2010) A vibration absorber for motorcycle handles. Meccanica 45:79–88

    Article  MATH  Google Scholar 

  20. Avramov KV, Gendelman OV (2010) On interaction of vibrating beam with essentially nonlinear absorber. Meccanica 45:355–365

    Article  MathSciNet  Google Scholar 

  21. Sathyamoorthy M, Rllebracht JF (1986) Effect of nonlinear constitutive equation on vibrations of beams. Meccanica 21:159–163

    Article  MATH  Google Scholar 

  22. Jakšic N (2009) Numerical algorithm for natural frequencies computation of an axially moving beam model. Meccanica 44:687–695

    Article  MathSciNet  Google Scholar 

  23. Ozgumus OO, Kaya MO (2006) Flapwise bending vibration analysis of double tapered rotating Euler–Bernoulli beam by using the differential transform method. Meccanica 41:661–670

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering, University of Zanjan, P.O. Box 45195-313, Zanjan, Iran

    R. T. Faal, M. B. Amiri & A. A. Pirmohammadi

  2. School of Engineering, University of British Columbia Okanagan, Kelowna, Canada

    A. S. Milani

Authors
  1. R. T. Faal
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  2. M. B. Amiri
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  3. A. A. Pirmohammadi
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  4. A. S. Milani
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Correspondence to R. T. Faal.

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Faal, R.T., Amiri, M.B., Pirmohammadi, A.A. et al. Vibration analysis of undamped, suspended multi-beam absorber systems. Meccanica 47, 1059–1078 (2012). https://doi.org/10.1007/s11012-011-9493-2

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