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Research Papers

Exact Optimization of a Three-Element Dynamic Vibration Absorber: Minimization of the Maximum Amplitude Magnification Factor

[+] Author and Article Information
Osamu Nishihara

Mem. ASME
Graduate School of Informatics,
Department of Systems Science,
Kyoto University,
Yoshida-honmachi, Sakyo-ku,
Kyoto 606-8501, Japan
e-mail: nishihara@i.kyoto-u.ac.jp

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 25, 2017; final manuscript received June 11, 2018; published online July 24, 2018. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 141(1), 011001 (Jul 24, 2018) (7 pages) Paper No: VIB-17-1470; doi: 10.1115/1.4040575 History: Received October 25, 2017; Revised June 11, 2018

In this study, the maximum amplitude magnification factor for a linear system equipped with a three-element dynamic vibration absorber (DVA) is exactly minimized for a given mass ratio using a numerical approach. The frequency response curve is assumed to have two resonance peaks, and the parameters for the two springs and one viscous damper in the DVA are optimized by minimizing the resonance amplitudes. The three-element model is known to represent the dynamic characteristics of air-damped DVAs. A generalized optimality criteria approach is developed and adopted for the derivation of the simultaneous equations for this design problem. The solution of the simultaneous equations precisely equalizes the heights of the two peaks in the resonance curve and achieves a minimum amplitude magnification factor. The simultaneous equations are solvable using the standard built-in functions of numerical computing software. The performance improvement of the three-element DVA compared to the standard Voigt type is evaluated based on the equivalent mass ratios. This performance evaluation is highly accurate and reliable because of the precise formulation of the optimization problem. Thus, the advantages of the three-element type DVA have been made clearer.

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References

Ormondroyd, J. , and Den Hartog, J. P. , 1928, “ The Theory of the Dynamic Vibration Absorber,” ASME J. Appl. Mech., 50(7), pp. 9–22.
Brock, J. E. , 1946, “ A Note on the Damped Vibration Absorber,” ASME J. Appl. Mech., 13(4), p. A-284.
Nishihara, O. , and Asami, T. , 2002, “ Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors),” Trans. ASME, J. Vib. Acoust., 124(4), pp. 576–582. [CrossRef]
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. Vib. Acoust., 121(3), pp. 334–342. [CrossRef]
Asami, T. , and Nishihara, O. , 2002, “ H2 Optimization of the Three-Element Type Dynamic Vibration Absorbers,” ASME J. Vib. Acoust., 124(4), pp. 583–592. [CrossRef]
Snowdon, J. C. , 1974, “ Dynamic Vibration Absorbers That Have Increased Effectiveness,” ASME J. Eng. Ind., 96(3), pp. 940–945. [CrossRef]
Den Hartog, J. P. , 1956, Mechanical Vibrations, 4th ed., McGraw-Hill, New York.
Anh, N. D. , Nguyen, N. X. , and Hoa, L. T. , 2013, “ Design of Three-Element Dynamic Vibration Absorber for Damped Linear Structures,” J. Sound Vib., 332(19), pp. 4482–4495. [CrossRef]
Anh, N. D. , Nguyen, N. X. , and Quan, N. H. , 2016, “ Global-Local Approach to the Design of Dynamic Vibration Absorber for Damped Structures,” J. Vib. Control, 22(14), pp. 3182–3201. [CrossRef]
Nishihara, O. , 2017, “ Minimization of Maximum Amplitude Magnification Factor in Designing Double-Mass Dynamic Vibration Absorbers, Application of Optimality Criteria Method to Parallel and Series Types,” Trans. JSME, 83(849), p. 16-00549 (in Japanese).
Asami, T. , Mizukawa, Y. , and Ise, T. , 2018, “ Optimal Design of Double-Mass Dynamic Vibration Absorbers Minimizing the Mobility Transfer Function,” ASME J. Vib. Acoust., 140(6), p. 061012. [CrossRef]
Asami, T. , 2016, “ Optimal Design of Double-Mass Dynamic Vibration Absorbers Arranged in Series or in Parallel,” ASME J. Vib. Acoust., 139(1), p. 011015. [CrossRef]

Figures

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Fig. 1

Schematic diagram of three-element DVA

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Fig. 2

Frequency response curves

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Fig. 3

Performance evaluation of the proposed method

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Fig. 4

Comparison of the fixed-point and proposed methods for tuning ratio

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Fig. 5

Comparison of the fixed-point and proposed methods for damping ratio

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Fig. 6

Comparison of the fixed-point and proposed methods for spring ratio

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Fig. 7

Optimized transmissibility curves for damped primary systems

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