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TECHNICAL PAPERS

H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers

[+] Author and Article Information
Toshihiko Asami

Mechanical Engineering, Himeji Inst. of Tech., 2167 Shosha, Himeji, Hyogo 671-2201, Japan

Osamu Nishihara

Systems Science, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan

J. Vib. Acoust 124(4), 583-592 (Sep 20, 2002) (10 pages) doi:10.1115/1.1501286 History: Received January 01, 2002; Revised May 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Asami,  T., Nishihara,  O., and Baz,  A. M., 2002, “Analytical Solutions to H and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems,” ASME J. Vibr. Acoust., 124(2), pp. 284–295.
Ormondroyd,  J., and Den Hartog,  J. P., 1928, “The Theory of the Dynamic Vibration Absorber,” ASME J. Appl. Mech., 50(7), pp. 9–22.
Crandall, S. H., and Mark, W. D., 1963, Random Vibration in Mechanical Systems, Academic Press.
Yamaguchi,  H., 1988, “Damping of Transient Vibration by a Dynamic Absorber,” Trans. Jpn. Soc. Mech. Eng., Ser. C, 54(499), Ser C, pp. 561–568 (in Japanese).
Satoh,  Y., 1991, “The Reductive Performance of the Dynamic Absorbers and Dynamic Properties of the Viscoelastic Absorber Elements,” Trans. Jpn. Soc. Mech. Eng., Ser. C, 57(534), Ser C, pp. 446–452 (in Japanese).
Asami,  T., and Nishihara,  O., 1999, “Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model,” ASME J. Vibr. Acoust., 121(3), pp. 334–342.
Gatade, Y., Misawa, H., Seto, K., and Doi, F., 1996, “Optimal Design of Notch Type Dynamic Absorber,” Prepr. of Jpn. Soc. Mech. Eng., No. 95-5(I), Vol. B, pp. 569–572 (in Japanese).
Kawashima,  T., 1992, “Vibration Prevention by a Three-Element Dynamic Vibration Absorber,” Trans. Jpn. Soc. Mech. Eng., Ser. C, 58(548), Ser C, pp. 1024–1029 (in Japanese).
Kreyszig, E., 1999, Advanced Engineering Mathematics, 8th ed., John Wiley & Sons, Inc.
Warburton,  G. B., 1982, “Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters,” Earthquake Eng. Struct. Dyn., 10, pp. 381–401.
Kowalik, J., and Osborne, M. R., 1968, Methods for Unconstrained Optimization Problems, American Elsevier Publishing Company.

Figures

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Comparison of the optimum design parameters and frequency response curves between the three-element and Voigt type DVAs (a ) Optimum design parameters (absolute displacement); (b) Optimum design parameters (relative displacement); (c) Optimized frequency response curves (absolute disp.); (d) Optimized frequency response curves (relative disp.)
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Analytical model of a system with an air damper (a) Schematic sketch; (b) Equivalent system
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Systems with the three-element type DVA (a) Force excitation system; (b) Motion excitation system
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Systems with the Voigt type DVA (a) Force excitation system; (b) Motion excitation system
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Graphical representation of the optimum parameters of the three-element type DVA based on the H2 criterion (absolute displacement-based design) (a) Optimum tuning νopt; (b) Optimum spring ratio κopt; (c) Optimum damping ζ2opt
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Graphical representation of the optimum parameters of the three-element type DVA based on the H2 criterion (relative displacement-based design) (a) Optimum tuning νopt; (b) Optimum spring ratio κopt; (c) Optimum damping ζ2opt
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Minimized performance indices for H2 optimization (a) Force excitation system (b) Motion excitation system (absolute displacement-based design); (c) Motion excitation system (relative displacement-based design)
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Comparison of the optimum design parameters and frequency response curves between the H2 and H optimization criterions (a) Optimum design parameters (absolute displacement); (b) Optimum design parameters (relative displacement); (c) Optimized frequency response curves (absolute disp.); (d) Optimized frequency response curves (relative disp.)

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