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Research Papers

Optimal Design of Double-Mass Dynamic Vibration Absorbers Minimizing the Mobility Transfer Function

[+] Author and Article Information
Toshihiko Asami

Professor
Mem. ASME
Department of Mechanical Engineering,
University of Hyogo,
2167 Shosha,
Himeji 671-2280, Hyogo, Japan
e-mail: asami@eng.u-hyogo.ac.jp

Yoshito Mizukawa

Department of Mechanical Engineering,
University of Hyogo,
2167 Shosha,
Himeji-City 671-2280, Hyogo, Japan
e-mail: mz6911@yahoo.co.jp

Tomohiko Ise

Mem. ASME
Department of Mechanical Engineering,
Toyohashi University of Technology,
1-1 Hibarigaoka, Tempaku-cho,
Toyohashi, Aichi 441-8580, Japan
e-mail: ise@mech.kindai.ac.jp

1Present address: Kindai University, 3-4-1 Kowakae, Higashiosaka-City, Osaka 577-8502, Japan

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 10, 2017; final manuscript received February 7, 2018; published online June 18, 2018. Assoc. Editor: Lei Zuo.

J. Vib. Acoust 140(6), 061012 (Jun 18, 2018) (14 pages) Paper No: VIB-17-1198; doi: 10.1115/1.4040229 History: Received May 10, 2017; Revised February 07, 2018

Although the vibration suppression effects of precisely adjusted dynamic vibration absorbers (DVAs) are well known, multimass DVAs have recently been studied with the aim of further improving their performance and avoiding performance deterioration due to changes in their system parameters. One of the present authors has previously reported a solution that provides the optimal tuning and damping conditions of the double-mass DVA and has demonstrated that it achieves better performance than the conventional single-mass DVA. The evaluation index of the performance used in that study was the minimization of the compliance transfer function. This evaluation function has the objective of minimizing the absolute displacement response of the primary system. However, it is important to suppress the absolute velocity response of the primary system to reduce the noise generated by the machine or structure. Therefore, in the present study, the optimal solutions for DVAs were obtained by minimizing the mobility transfer function rather than the compliance transfer function. As in previous investigations, three optimization criteria were tested: the H optimization, H2 optimization, and stability maximization criteria. In this study, an exact algebraic solution to the H optimization of the series-type double-mass DVA was successfully derived. In addition, it was demonstrated that the optimal solution obtained by minimizing the mobility transfer function differs significantly at some points from that minimizing the compliance transfer function published in the previous report.

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References

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Figures

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Fig. 1

Analytical models of DVAs attached to an undamped primary system

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Fig. 2

Steady-state and transient responses of the primary system attached to the optimized single-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) Steady-state response to sinusoidal excitation and (b) transient response to the initial velocity υ0

Grahic Jump Location
Fig. 3

Optimized parameters and minimized or maximized performance indices for the single-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization (algebraic solution), (b) H2 optimization (algebraic solution), and (c) stability maximization (algebraic solution)

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Fig. 4

Optimized frequency response curves of a primary system with an attached single-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization, (b) H2 optimization, and (c) stability maximization

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Fig. 5

Optimized parameters and minimized or maximized performance indices for the series-type double-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization (algebraic and numerical solutions), (b) H2 optimization (algebraic and numerical solutions), and (c) stability maximization (algebraic solution)

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Fig. 6

Optimized frequency response curves of the primary system with an attached series-type double-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization, (b) H2 optimization, and (c) stability maximization

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Fig. 7

Enlarged view of the H2-optimal curves around μ = 0.495 for the series-type double-mass DVA: (a) Optimal curves of μBopt and νopt, (b) optimal curves of νBopt and ζ3opt, and (c) optimal curves of ζ2opt

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Fig. 8

Two H2-optimal curves of the primary system with an attached series-type double-mass DVA: (a) two optimal curves for μ = 0.492196 (ζ2opt is negative), (b) two optimal curves for μ = 0.6 (ζ2opt is positive), and (c) two optimal curves for μ = 1.0 (ζ2opt is positive)

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Fig. 9

Optimized parameters and minimized or maximized performance indices for the parallel-type double-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization (numerical solution), (b) H2 optimization (numerical solution), and (c) stability maximization (numerical solution)

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Fig. 10

Optimized frequency response curves of the primary system with an attached parallel-type double-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) H optimization, (b) H2 optimization, and (c) stability maximization

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Fig. 11

Minimized performance indices of systems containing the single- or double-mass DVA (Solid line: Mobility transfer function, Dashed line: Compliance transfer function): (a) resonance amplitude ratio hmin and (b) squared areas Iamin and Ibmin under the frequency response curve

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Fig. 12

Example of the mobility transfer function of an H-optimal vibration system

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Fig. 13

Example of the function fn defined by Eq. (A4) for μ = 0.1

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Fig. 14

When the total derivative dr becomes zero, the function r is at a local minimum

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Fig. 15

Characteristic roots of a three-degree-of-freedom vibratory system

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