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Research Papers

Three-Element Vibration Absorber–Inerter for Passive Control of Single-Degree-of-Freedom Structures

[+] Author and Article Information
Abdollah Javidialesaadi

Department of Civil and Environmental
Engineering,
The University of Tennessee,
Knoxville, TN 37996-2313
e-mail: ajavidia@vols.utk.edu

Nicholas E. Wierschem

Department of Civil and Environmental
Engineering,
The University of Tennessee,
Knoxville, TN 37996-2313
e-mail: nwiersch@utk.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 6, 2017; final manuscript received April 16, 2018; published online May 10, 2018. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 140(6), 061007 (May 10, 2018) (11 pages) Paper No: VIB-17-1532; doi: 10.1115/1.4040045 History: Received December 06, 2017; Revised April 16, 2018

In this study, a novel passive vibration control device, the three-element vibration absorber–inerter (TEVAI) is proposed. Inerter-based vibration absorbers, which utilize a mass that rotates due to relative translational motion, have recently been developed to take advantage of the potential high inertial mass (inertance) of a relatively small mass in rotation. In this work, a novel configuration of an inerter-based absorber is proposed, and its effectiveness at suppressing the vibration of a single-degree-of-freedom system is investigated. The proposed device is a development of two current passive devices: the tuned-mass-damper–inerter (TMDI), which is an inerter-base tuned mass damper (TMD), and the three-element dynamic vibration absorber (TEVA). Closed-form optimization solutions for this device connected to a single-degree-of-freedom primary structure and loaded with random base excitation are developed and presented. Furthermore, the effectiveness of this novel device, in comparison to the traditional TMD, TEVA, and TMDI, is also investigated. The results of this study demonstrate that the TEVAI possesses superior performance in the reduction of the maximum and root-mean-square (RMS) response of the underlying structure in comparison to the TMD, TEVA, and TMDI.

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Figures

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Fig. 1

Schematic representation of a two-terminal inerter device (b is equivalent rotational mass)

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Fig. 2

Schematic representation of physical mechanisms used to produce an inerter: (a) ball-screw mechanism and (b) rack and pinion mechanism

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Fig. 3

Schematic configuration of a traditional TMD attached to a single-degree-of-freedom structure

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Fig. 4

Schematic configuration of a TMDI attached to a single-degree-of-freedom structure

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Fig. 5

Schematic configuration of a TEVAI attached to a single-degree-of-freedom structure

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Fig. 6

Effect of inertance mass ratio on the TEVAI H2 optimum design values: (a) optimum tuning frequency ratio, (b) optimum spring ratio, and (c) optimum damping ratio

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Fig. 7

H2 norm versus inertance mass ratio for the H2 optimal TEVAI and TMDI

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Fig. 8

Peak DMF versus inertance mass ratio for systems with the H2 optimal TEVAI and TMDI

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Fig. 9

Frequency response function for systems with H2 optimal TMDI and TEVAI at different inertance mass ratios with a main mass ratio = 10%

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Fig. 10

Effect of changes to inertance mass ratio on the DMF of a system with an H2 optimal TEVAI with a main mass ratio = 10%

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Fig. 11

H Optimum design values of TMDI at different mass ratios: (a) optimum tuning frequency ratio and (b) optimum damping ratio

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Fig. 12

H Optimum design values of TEVAI at different mass ratios: (a) optimum tuning frequency ratio, (b) optimum damping ratio, and (c) optimum spring ratio

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Fig. 13

Peak DMF versus inertance mass ratio for systems with the H optimal TEVAI and TMDI

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Fig. 14

Peak DMF Improvement index (R)

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Fig. 15

Effect of inertance mass ratio on the DMF for H optimal systems with a TEVAI with a main mass ratio = 10%

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Fig. 16

Frequency domain response of primary structure with H optimal TMDI and TEVAI with mass ratio = 10%

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