Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)-Reference-Cited by-同舟云学术

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

Published:2002-09-20 Issue:4 Volume:124 Page:576-582
ISSN:1048-9002
Container-title:Journal of Vibration and Acoustics
language:en
Short-container-title:

Author:

Nishihara Osamu¹,Asami Toshihiko²

Affiliation:

1. Department of Systems Science, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan

2. Department of Mechanical Engineering, Himeji Institute of Technology, Shosha, Himeji, Hyogo 671-2201, Japan

Abstract

A typical design problem for which the fixed-points method was originally developed is that of minimizing the maximum amplitude magnification factor of a primary system by using a dynamic vibration absorber. This is an example of usual cases for which their exact solutions are not obtained by the well-known heuristic approach. In this paper, more natural formulation of this problem is studied, and algebraic closed-form exact solutions to both the optimum tuning ratio and the optimum damping coefficient for this classic problem are derived under assumption of undamped primary system. It is also proven that the minimum amplitude magnification factor, resonance and anti-resonance frequencies are entirely algebraic.

Publisher

ASME International

Subject

General Engineering

Link

http://asmedigitalcollection.asme.org/vibrationacoustics/article-pdf/124/4/576/5827728/576_1.pdf

Reference15 articles.

1. Brock, J. E. , 1946, “A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13(4), p. A-284A-284.

2. Ormondroyd, J., and Den Hartog, J. P., 1928, “The Theory of the Dynamic Vibration Absorber,” Trans. ASME, 50(7), pp. 9–22.

3. Den Hartog, J. P., 1956, Mechanical Vibrations (4th ed.), McGraw-Hill, New York.

4. Korenev, B. G., and Reznikov, L. M., 1993, Dynamic Vibration Absorbers: Theory and Technical Applications, John Wiley & Sons, New York.

5. Ikeda, T., and Ioi, T., 1977, “On Dynamic Vibration Absorbers for Damped Vibration Systems,” Trans. Jpn. Soc. Mech. Eng., 43(369), pp. 1707–1715.

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