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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.

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Figures

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Fig. 1

Vibration absorbers attached to a beam

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Fig. 2

Transfer function diagram

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Fig. 3

Flow chart of the optimization process

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Fig. 4

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

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Fig. 5

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

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Fig. 6

Displacement of the beam at x = lbeam/2

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Fig. 7

Optimum absorber locations versus forcing frequency

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Fig. 8

Optimum value of absorber damping versus forcing frequency

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Fig. 9

Optimum value of absorber stiffness versus forcing frequency

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Fig. 10

Minimized H2 norm versus forcing frequency

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Fig. 11

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

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Fig. 12

Displacement of the beam at x = lbeam/2

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Fig. 13

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

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