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TECHNICAL PAPERS

Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)

[+] Author and Article Information
Osamu Nishihara

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

Toshihiko Asami

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

J. Vib. Acoust 124(4), 576-582 (Sep 20, 2002) (7 pages) doi:10.1115/1.1500335 History: Received August 01, 2000; Revised April 01, 2002; Online September 20, 2002
Copyright © 2002 by ASME
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References

Brock,  J. E., 1946, “A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13(4), p. A-284.
Ormondroyd,  J., and Den Hartog,  J. P., 1928, “The Theory of the Dynamic Vibration Absorber,” Trans. ASME, 50(7), pp. 9–22.
Den Hartog, J. P., 1956, Mechanical Vibrations (4th ed.), McGraw-Hill, New York.
Korenev, B. G., and Reznikov, L. M., 1993, Dynamic Vibration Absorbers: Theory and Technical Applications, John Wiley & Sons, New York.
Ikeda,  T., and Ioi,  T., 1977, “On Dynamic Vibration Absorbers for Damped Vibration Systems,” Trans. Jpn. Soc. Mech. Eng., 43(369), pp. 1707–1715.
Soom,  A., and Ming-San,  Lee., 1983, “Optimal Design of Linear and Nonlinear Vibration Absorbers for Damped Systems,” ASME J. Vibr. Acoust., 105(1), pp. 112–1193.
Haddad,  W. M., and Razavi,  A., 1998, “H2, Mixed H2/H, and H2/L1 Optimally Tuned Passive Isolators and Absorbers,” ASME J. Dyn. Syst., Meas., Control, 120(2), pp. 282–287.
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.
Nishihara,  O., Asami,  T., and Watanabe,  S., 2000, “Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response (1st Report, Viscous Damped Absorber),” Trans. Jpn. Soc. Mech. Eng., Ser. C, 66(642), pp. 420–426.
Asami,  T., Nishihara,  O., and Watanabe,  S., 2000, “Exact Algebraic Optimization of a Dynamic Vibration Absorber for Minimization of Maximum Amplitude Response (2nd Report, Hysteretic Damped Absorber),” Trans. Jpn. Soc. Mech. Eng., Ser. C, 66(644), pp. 1186–1193.
Azuma, T., Nishihara, O., Honda, Y., and Matsuhisa, H., 1997, “Design of a Passive Gyroscopic Damper for Minimization of Maximum Amplitude Magnification Factor,” Preprint of JSME (in Japanese), No. 974-2, pp. 53–54.
Wolfram, S., 1991, Mathematica—A System for Doing Mathematics by Computer (Second Edition), Addison-Wesley, Reading, MA.
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.
Nishihara, O., Asami, T., and Kumamoto, H., 1999, “Design Optimization of Dynamic Vibration Absorber for Minimization of Maximum Amplitude Magnification Factor (Consideration of Primary System Damping by Numerical Exact Solution),” Preprint of JSME (in Japanese), No. 99-7 (I), pp. 365–368.
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.

Figures

Grahic Jump Location
Dynamic vibration absorber attached to single-degree-of-freedom system
Grahic Jump Location
General view of compliance curves (μ=0.05), (Optimum parameter values for undamped primary system [–], Fixed-points method [[[dashed_line]]], Primary system (z=∞) [- ⋅ -])
Grahic Jump Location
Close-ups of point A and B(μ=0.05), (Optimum parameter values for undamped primary system [–], Fixed-points method [[[dashed_line]]], Primary system (z=∞) [- ⋅ -])
Grahic Jump Location
Close-up of point C(μ=0.05), (Optimum parameter values for undamped primary system [–], Fixed-points method [[[dashed_line]]])
Grahic Jump Location
Reduction of maximum amplitude magnification factors by numerical optimizations (μ=0.05). (Iterative solutions that take accounts of the primary system damping are displayed for several values of the primary system damping ratio [–]. The additional curves are provided only for comparison purposes, where the optimum parameter values for undamped primary system are diverted to the damped cases [[[dashed_line]]].)

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