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Research Papers

Nonlinear Energy Sink for Whole-Spacecraft Vibration Reduction

[+] Author and Article Information
Kai Yang

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China

Ye-Wei Zhang, Tian-Zhi Yang

Shanghai Institute of Applied
Mathematics and Mechanics,
Shanghai University,
Shanghai 200072, China;
Faculty of Aerospace Engineering,
Shenyang Aerospace University,
Shenyang 110136, China

Hu Ding

Shanghai Institute of Applied
Mathematics and Mechanics;
Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai University,
Shanghai 200072, China

Yang Li

Faculty of Aerospace Engineering,
Shenyang Aerospace University,
Shenyang 110136, China

Li-Qun Chen

Shanghai Institute of Applied
Mathematics and Mechanics;
Shanghai Key Laboratory of Mechanics in
Energy Engineering,
Shanghai University,
Shanghai 200072, China;
Department of Mechanics,
Shanghai University,
Shanghai 200444, China

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 28, 2016; final manuscript received November 18, 2016; published online February 17, 2017. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 139(2), 021011 (Feb 17, 2017) (19 pages) Paper No: VIB-16-1326; doi: 10.1115/1.4035377 History: Received June 28, 2016; Revised November 18, 2016

A nonlinear energy sink (NES) approach is proposed for whole-spacecraft vibration reduction. Frequency sweeping tests are conducted on a scaled whole-spacecraft structure without or with a NES attached. The experimental transmissibility results demonstrate the significant reduction of the whole-spacecraft structure vibration over a broad spectrum of excitation frequency. The NES attachment hardly changes the natural frequencies of the structure. A finite element model is developed, and the model is verified by the experimental results. A two degrees-of-freedom (DOF) equivalent model of the scaled whole-spacecraft is proposed with the two same natural frequencies as those obtained via the finite element model. The experiment, the finite element model, and the equivalent model predict the same trends that the NES vibration reduction performance becomes better for the increasing NES mass, the increasing NES viscous damping, and the decreasing nonlinear stiffness. The energy absorption measure and the energy transition measure calculated based on the equivalent model reveals that an appropriately designed NES can efficiently absorb and dissipate broadband-frequency energy via nonlinear beats, irreversible targeted energy transfer (TET), or both for different parameters.

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Figures

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Fig. 1

The computer-aided design preliminary design of the NES

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Fig. 2

The scaled whole-spacecraft structure

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Fig. 3

Transmissibility results under excitation A1 = 0.3 g: (a) measure point #1 and (b) measure point #2

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Fig. 4

Transmissibility results under excitation A2 = 0.4 g: (a) measure point #1 and (b) measure point #2

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Fig. 5

Transmissibility results with NES mass ms = 4 kg: (a) measure point #1 and (b) measure point #2

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Fig. 6

Transmissibility results with NES mass ms = 6 kg: (a) measure point #1 and (b) measure point #2

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Fig. 7

Transmissibility results with NES cubic nonlinear stiffness ks = 500 N/m3: (a) measure point #1 and (b) measure point #2

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Fig. 8

Transmissibility results with NES cubic nonlinear stiffness ks = 1000 N/m3: (a) measure point #1 and (b) measure point #2

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Fig. 9

Transmissibility results with NES damping ratio ξs = 2.29%: (a) measure point #1 and (b) measure point #2

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Fig. 10

Transmissibility results with NES damping ratio ξs = 3.9%: (a) measure point #1 and (b) measure point #2

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Fig. 11

The FEM model of the scaled whole-spacecraft

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Fig. 12

The first mode shape at f1 = 20.33 Hz

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Fig. 13

The first mode shape at f2 = 94.03 Hz

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Fig. 14

Transmissibility results obtained through FEM analysis: (a) measure point #1 and (b) measure point #2

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Fig. 15

The equivalent simplified model of the whole spacecraft with NES attached

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Fig. 16

The NOFRFs of the nonlinear system (5) under a harmonic loading. (a) G1(jωF), (b) G2(j2ωF), (c) G3(jωF), (d) G3(j3ωF), (e) G4(j2ωF), and (f) G4(j4ωF).

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Fig. 17

The first four order output frequency response of the nonlinear system under a harmonic loading: (a) |X(jω)|, (b) |X(j2ω)|, (c) |X(j3ω)|, and (d) |X(j4ω)|

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Fig. 18

The transmissibility of the system with and without NES

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Fig. 19

Percentage of input energy absorbed by NES and dissipated by primary system damping under harmonic excitation: (a) driving frequency ωF1 = 20 Hz and (b) driving frequency ωF2 = 94 Hz

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Fig. 20

The effects of NES parameters on the energy absorption performance under harmonic excitation with driving frequency ωF1 = 20 Hz: (a) different values of NES mass m3 and (b) optimization of k3 and c3

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Fig. 21

The effects of NES parameters on the energy absorption performance under harmonic excitation with driving frequency ωF2 = 94 Hz: (a) different values of NES mass m3 and (b) optimization of k3 and c3

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Fig. 22

Percentage of impulsive energy absorbed by NES and dissipated by primary system damping under instantaneous excitation

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Fig. 23

The effects of NES parameters on the energy absorption performance under instantaneous excitation: (a) different values of NES mass m3 and (b) optimization of k3 and c3

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Fig. 24

Instantaneous transition of mechanical energy and energy dissipated by damping under harmonic excitation with driving frequency ωF1 = 20 Hz

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Fig. 25

Instantaneous transition of energy in the NES under harmonic excitation with driving frequency ωF1 = 20 Hz

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Fig. 26

Etrans of the compound system under harmonic excitation with driving frequency ωF1 = 20 Hz

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Fig. 27

The effects of NES parameters on Etrans under harmonic excitation with driving frequency ωF1 = 20 Hz. (a) contour plots for varying m3, (b) contour plots for varying k3, and (c) contour plots for varying c3.

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Fig. 28

Instantaneous transition of mechanical energy and energy dissipated by damping under harmonic excitation with driving frequency ωF2 = 94 Hz

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Fig. 29

Instantaneous transition of energy in the NES under harmonic excitation with driving frequency ωF2 = 94 Hz

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Fig. 30

Etrans of the compound system under harmonic excitation with driving frequency ωF2 = 94 Hz

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Fig. 31

The effects of NES parameters on the ETM Etrans under harmonic excitation with driving frequency ωF2 = 94 Hz. (a) contour plots for varying m3, (b) contour plots for varying k3, and (c) contour plots for varying c3.

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Fig. 32

Instantaneous transition of mechanical energy and energy dissipated by damping under instantaneous excitation

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Fig. 33

Instantaneous transition of energy in the NES under instantaneous excitation

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Fig. 34

The ETM Etrans of the compound system and the effects of NES parameters on the ETM Etrans under instantaneous excitation. (a) The ETM Etrans of the compound system, (b) different values of NES mass m3, (c) different values of NES nonlinear stiffness k3, and (d) different values of NES damping coefficient c3.

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