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TECHNICAL PAPERS

Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems

[+] Author and Article Information
Toshihiko Asami

Department of Mechanical Engineering, Himeji Institute of Technology, 2167 Shosha, Himeji, Hyogo 671-2201, Japan e-mail: asami@mech.eng.himeji-tech.ac.jp

Osamu Nishihara

Department of Systems Science, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan e-mail: nishihara@i.kyoto-u.ac.jp

Amr M. Baz

Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, e-mail: baz@eng.umd.edu

J. Vib. Acoust 124(2), 284-295 (Mar 26, 2002) (12 pages) doi:10.1115/1.1456458 History: Received April 01, 2000; Revised December 01, 2001; Online March 26, 2002
Copyright © 2002 by ASME
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References

Frahm, H., 1911, “Device for Damping Vibrations of Bodies,” U.S. Patent, No. 989, 958, pp. 3576–3580.
Ormondroyd,  J., and Den Hartog,  J. P., 1928, “The Theory of the Dynamic Vibration Absorber,” ASME J. Appl. Mech., 50-7, pp. 9–22.
Hahnkamm,  E., 1932, “Die Dämpfung von Fundamentschwingungen bei veränderlicher Erregergrequenz,” Ing. Arch.,4, pp. 192–201, (in German).
Brock,  J. E., 1946, “A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13-4, p. A-284.
Den Hartog, J. P., 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York.
Nishihara, O., and Matsuhisa, H., 1997, “Design and Tuning of Vibration Control Devices via Stability Criterion,” Prepr. of Jpn. Soc. Mech. Eng., No. 97-10-1, pp. 165–168, (in Japanese).
Ikeda,  K., and Ioi,  T., 1978, “On the Dynamic Vibration Damped Absorber of the Vibration System,” Bull. JSME, 21-151, pp. 64–71.
Randall,  S. E., Halsted,  D. M., and Taylor,  D. L., 1981, “Optimum Vibration Absorbers for Linear Damped Systems,” ASME J. Mech. Des., 103-4, pp. 908–913.
Thompson,  A. G., 1981, “Optimum Tuning and Damping of a Dynamic Vibration Absorber Applied to a Force Excied and Damped Primary System,” J. Sound Vib., 77-3, pp. 403–415.
Soom,  A., and Lee,  M., 1983, “Optimal Design of Linear and Nonlinear Vibration Absorbers for Damped Systems,” ASME J. Vibr. Acoust., 105-1, pp. 112–119.
Sekiguchi,  H., and Asami,  T., 1984, “Theory of Vibration Isolation of a System with Two Degrees of Freedom,” Bull. JSME, 27-234, pp. 2839–2846.
Asami,  T., and Hosokawa,  Y., 1995, “Approximate Expression for Design of Optimal Dynamic Absorbers Attached to Damped Linear Systems (2nd Report, Optimization Process Based on the Fixed-Points Theory),” Trans. Jpn. Soc. Mech. Eng., Ser. C, 61-583, pp. 915–921, (in Japanese).
Crandall, S. H., and Mark, W. D., 1963, Random Vibration in Mechanical Systems, Academic Press.
Iwata, Y., 1982, “On the Construction of the Dynamic Vibration Absorbers,” Prepr. of Jpn. Soc. Mech. Eng., No. 820-8, pp. 150–152, (in Japanese).
Asami,  T. , 1991, “Optimum Design of Dynamic Absorbers for a System Subjected to Random Excitation,” JSME Int. J., Ser. III, 34-2, pp. 218–226.
Asami,  T., Momose,  K., and Hosokawa,  Y., 1993, “Approximate Expression for Design of Optimal Dynamic Absorbers Attached to Damped Linear Systems (Optimization Process Based on the Minimum Variance Criterion),” Trans. Jpn. Soc. Mech. Eng., Ser. C, 59-566, pp. 2962–2967, (in Japanese).
Yamaguchi,  H., 1988, “Damping of Transient Vibration by a Dynamic Absorber,” Trans. Jpn. Soc. Mech. Eng., Ser. C, 54-499, pp. 561–568, (in Japanese).
Nishihara,  O., and Matsuhisa,  H., 1997, “Design of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Magnification Factor (Derivation of Algebraic Exact Solution),” Trans. Jpn. Soc. Mech. Eng., Ser. C, 63-614, pp. 3438–3445, (in Japanese).
Meirovitch, L., 1986, Elements of Vibration Analysis, McGraw-Hill, New York.

Figures

Grahic Jump Location
Comparison of three optimum frequency response curves based on different optimization criteria
Grahic Jump Location
Systems subjected to sinusoidal excitation
Grahic Jump Location
Graphical representation of the solutions for H optimization of the system subjected to force excitation
Grahic Jump Location
Graphical representation of the solutions for H optimization of the system subjected to motion excitation
Grahic Jump Location
Systems subjected to random excitation
Grahic Jump Location
Graphical representation of the solution for H2 optimization of the system subjected to force excitation
Grahic Jump Location
Graphical representation of the solution for H2 optimization of the system subjected to motion excitation

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