Technical Brief

Optimal Damped Vibration Absorber: Including Multiple Modes and Excitation Due to Rotating Unbalance

[+] Author and Article Information
Alok Sinha

Department of Mechanical and Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802
e-mail: axs22@psu.edu

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 14, 2014; final manuscript received April 8, 2015; published online July 9, 2015. Editor: I. Y. (Steve) Shen.

J. Vib. Acoust 137(6), 064501 (Dec 01, 2015) (6 pages) Paper No: VIB-14-1137; doi: 10.1115/1.4030714 History: Received April 14, 2014; Revised April 08, 2015; Online July 09, 2015

Optimal vibration absorbers are designed using the definition of H-infinity norm and numerical optimization. The cases of both constant amplitude excitation and rotating unbalance excitation are considered. The design procedure is quite general, and can easily handle multiple modes of vibration. A general procedure to construct a root loci plot is also developed. Using a cantilever beam, numerical results are presented.

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Fig. 1

A damped vibration absorber attached to cantilever and free-body diagram

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Fig. 2

Single-mode root loci plots for variations in the absorber damping ratio ξa, (μ=0.05)

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Fig. 3

Optimal absorber frequency ratio versus mass ratio

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Fig. 4

Optimal absorber damping ratio versus mass ratio

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Fig. 5

Minimum values of objective functions

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Fig. 6

Frequency response magnitude for an optimal absorber with constant excitation amplitude

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Fig. 7

Frequency response magnitude for an optimal absorber with rotating unbalance excitation

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Fig. 8

Two modes root loci plot for variations in the absorber damping ratio ξa, (μ=0.2)



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