Research Papers

H2 Optimization of Damped-Vibration Absorbers for Suppressing Vibrations in Beams With Constrained Minimization

[+] Author and Article Information
Murat Tursun

Department of Mechanical Engineering,
Bogazici University,
Bebek, Istanbul 34342, Turkey
e-mail: mtursun1@ford.com

Department of Mechanical Engineering,
Bogazici University,
Bebek, Istanbul 34342, Turkey
e-mail: eskinat@boun.edu.tr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 8, 2012; final manuscript received December 8, 2013; published online January 15, 2014. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 136(2), 021012 (Jan 15, 2014) (14 pages) Paper No: VIB-12-1193; doi: 10.1115/1.4026246 History: Received July 08, 2012; Revised December 08, 2013

Vibration absorbers are efficient and robust tools for reducing vibration and noise. Researchers use various alternative approaches and validate their methods with examples consisting of mass-spring-damper systems. Focusing on the minimization of the vibration amplitudes via passive absorber approach, a new and efficient method for calculating the optimum parameters of N absorbers attached to a uniform beam with M mode shapes (where N and M are any positive integers) has been developed. First, for the most general case, dissipation due to damping, kinetic, and potential energy and the effects of external forces are analyzed. The Lagrange's equation is used to provide the state space representation of the system. State space representation of a system with N absorbers and M mode shapes is composed. On the basis of the state space representation and the Lyapunov function, the H2 norm of the transfer function of the system is utilized in the newly developed optimization package. The system output is minimized by the optimization algorithm and displayed with a comparison between cases without an absorber and with randomly selected absorber parameters. As a conclusion, with the help of this method for calculation of optimal absorber parameters, one can easily design a mechanical system according to design criteria.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Ormondroyd, J., and Den Hartog, J. P., 1928, “The Theory of the Dynamic Vibration Absorber,” ASME J. Appl. Mech., 50, pp. 9–22.
Ozturk, L., 1997, “Vibration Absorbers as Controllers,” M.S. thesis, Bogazici University, Istanbul, Turkey.
Wang, B. P., Kitis, L., Pilkey, D., and Palazzolo, A., 1985, “Synthesis of Dynamic Vibration Absorbers,” ASME J. Vib. Acoust., Stress, Reliab. Des., 107, pp. 161–166. [CrossRef]
Herzog, R., 1994, “Active Versus Passive Vibration Absorbers,” ASME J. Dyn. Syst., Meas., Control, 116, pp. 367–371. [CrossRef]
Jacquot, R. G., 1978, “Optimal Dynamic Vibration Absorbers for General Beam Systems,” J. Sound Vib., 60, pp. 535–542. [CrossRef]
Thompson, D. J., 2008, “A Continuous Damped Vibration Absorber to Reduce Broad-Band Wave Propagation in Beams,” J. Sound Vib., 311, pp. 824–842. [CrossRef]
Jacquot, R. G., 2001, “Suppression of Random Vibration in Plates Using Vibration Absorbers,” J. Sound Vib., 248, pp. 585–596. [CrossRef]
Cheung, Y. L., and Wong, W. O., 2009, “H and H2 Optimizations of a Dynamic Vibration Absorber for Suppressing Vibrations in Plates,” J. Sound Vib., 320, pp. 29–42. [CrossRef]
Cheung, Y. L., Wong, W. O., and Cheng, L., 2012, “Design Optimization of a Damped Hybrid Vibration Absorber,” J. Sound Vib., 331, pp. 750–766. [CrossRef]
Huang, Y. M., and Fuller, C. R., 1997, “The Effects of Dynamic Absorbers on the Forced Vibration of a Cylindrical Shell and Its Coupled Interior Sound Field,” J. Sound Vib., 200, pp. 401–418. [CrossRef]
Wong, W. O., Tang, S. L., Cheung, Y. L., and Cheng, L., 2007, “Design of a Dynamic Vibration Absorber for Vibration Isolation of Beams Under Point or Distributed Loading,” J. Sound Vib., 301, pp. 898–908. [CrossRef]
Wu, J. J., 2005, “Use of Equivalent Damper Method for Free Vibration Analysis of a Beam Carrying Multiple Two Degree of Freedom Spring Damper Mass Systems,” J. Sound Vib., 281, pp. 275–293. [CrossRef]
Burdisso, R. A., and Heilmann, J. D., 1998, “A New Dual Reaction Mass Dynamic Vibration Absorber Actuator for Active Vibration Control,” J. Sound Vib., 214, pp. 817–831. [CrossRef]
Gurgoze, M., Erdogan, G., and Inceoglu, S., 2001, “Bending Vibrations of Beams Coupled by a Double Spring Mass System,” J. Sound Vib., 243, pp. 361–369. [CrossRef]
Manikanahally, D. N., and Crocker, M. J., 1991, “Vibration Absorber for Hysterically Damped Mass-Loaded Beams,” ASME J. Vibr. Acoust., 113, pp. 116–122. [CrossRef]
Meirovitch, L., 1975, Elements of Vibration Analysis, McGraw-Hill, New York.
Zhou, K., and Doyle, J. C., 1998, Essentials of Robust Control, Prentice-Hall, Englewood Cliffs, NJ.
Skogestad, S., and Postlethwaite, I., 2005, Multivariable Feedback Control, Wiley, New York.
Candir, B., and Ozguven, H. N., 1986, “Suppressing the First and Second Resonances of Beams by Dynamic Vibration Absorbers,” J. Sound Vib., 111, pp. 377–390. [CrossRef]
Warburton, G. B., and Ayorinde, E. O., 1980, “Optimum Absorber Parameters for Simple Systems,” Earthquake Eng. Struct. Dyn., 8, pp. 197–217. [CrossRef]
Rade, D. A., and Steffen, V., 2000, “Optimization of Dynamic Vibration Absorbers Over a Frequency Band,” Mech. Syst. Signal Process., 14(5), pp. 679–690. [CrossRef]


Grahic Jump Location
Fig. 1

Vibration absorbers attached to a beam

Grahic Jump Location
Fig. 2

Transfer function diagram

Grahic Jump Location
Fig. 3

Flow chart of the optimization process

Grahic Jump Location
Fig. 4

Comparison with the displacement of the beam studied by Warburton and Ayorinde at x = lbeam/2

Grahic Jump Location
Fig. 5

One absorber attached to a pinned–pinned beam (five mode shapes)

Grahic Jump Location
Fig. 6

Displacement of the beam at x = lbeam/2

Grahic Jump Location
Fig. 7

Optimum absorber locations versus forcing frequency

Grahic Jump Location
Fig. 8

Optimum value of absorber damping versus forcing frequency

Grahic Jump Location
Fig. 9

Optimum value of absorber stiffness versus forcing frequency

Grahic Jump Location
Fig. 10

Minimized H2 norm versus forcing frequency

Grahic Jump Location
Fig. 11

Five absorbers attached to a pinned–pinned beam (two mode shapes)

Grahic Jump Location
Fig. 12

Displacement of the beam at x = lbeam/2

Grahic Jump Location
Fig. 13

Three absorbers attached to a fixed-free beam (two mode shapes)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In