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Research Papers

Mechanism of Optimal Targeted Energy Transfer

[+] Author and Article Information
Y. M. Wei, X. J. Dong, W. M. Zhang, G. Meng

State Key Laboratory of
Mechanical System and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China

Z. K. Peng

State Key Laboratory of
Mechanical System and Vibration,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: z.peng@sjtu.edu.cn

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 22, 2015; final manuscript received October 5, 2016; published online October 24, 2016. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 84(1), 011007 (Oct 24, 2016) (9 pages) Paper No: JAM-15-1693; doi: 10.1115/1.4034929 History: Received December 22, 2015; Revised October 05, 2016

A novel nonlinear vibration reduction mechanism based on targeted energy transfer (TET) is proposed. Targeted energy transfer is a physical phenomenon that describes a one-way irreversible energy flow from a linear oscillator (LO) to a nonlinearizable (essentially) nonlinear auxiliary substructure, noted as nonlinear energy sink (NES). The optimal targeted energy transfer where NES is set on the optimal state is investigated in this study. Complexification-averaging methodology is used to derive the optimal TET of the undamped system for different initial conditions. It is revealed that the optimal TET is dependent on the energy, indicating that passive control of NES cannot be optimally set for arbitrary initial conditions. In addition, it is found that for the undamped system, the optimal phrase difference between the linear primary oscillator and the nonlinear attachment is π/2. From the perspective of active control, the NES can be taken as an actuator to keep the system vibrating on the optimal TET. An available modification form of the optimal equations is proposed for the impulse excitation with relatively small damping. The comparisons of the effectiveness of the optimal TET is validated by using numerical simulations with the excitations including impulse, harmonic, to input with sufficient bandwidth, and random signal. The design procedure would pave the way for practical implications of TET in active vibration control.

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Figures

Grahic Jump Location
Fig. 1

The proportion of energy stored in the NES, A = 0.8 m/s

Grahic Jump Location
Fig. 2

The proportion of energy stored in the NES, A = 1 m/s

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Fig. 3

The proportion of energy stored in the NES, A = 5 m/s

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Fig. 4

Displacement responses of LO and NES

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Fig. 5

Oscillation of H (λ1=λ2=0.1)

Grahic Jump Location
Fig. 6

Responses of LO and NES (λ1=λ2=0.1)

Grahic Jump Location
Fig. 7

Oscillation of H (λ1=λ2=0.2)

Grahic Jump Location
Fig. 8

Displacement responses of (a) normal NES, (b) optimal equations, (c) modified form by Eq. (34), and (d) the envelope, respectively

Grahic Jump Location
Fig. 9

Displacement responses of (a) normal NES, (b) optimal equations, (c) modified form by Eq. (39), and (d) the envelope (λ1=λ2=0.1)

Grahic Jump Location
Fig. 10

Energy dissipated in the NES along with impulse X

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Fig. 11

Displacement responses of LO and NES (λ1=λ2=0.2)

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Fig. 12

Displacement response of LO by optimal equations

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Fig. 13

Displacement response of LO by PID control

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Fig. 14

Relationship between average amplitude and amplitude of periodic loading

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Fig. 15

Relationship between energy of LO and amplitude of periodic loading

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Fig. 16

Responses of LO in normal NES and optimal equations (f=0.1* sin(wt),  λ1=λ2=0.04 )

Grahic Jump Location
Fig. 17

Responses of LO in normal NES and optimal equations (f=0.1* sin(wt), λ1=λ2=0.2)

Grahic Jump Location
Fig. 18

Integrate H of the system simulated above

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Fig. 19

Relationship between energy of LO and excitation frequency (λ1=λ2=0.2)

Grahic Jump Location
Fig. 20

Relationship between energy of LO and damping (λ=λ1=λ2)

Grahic Jump Location
Fig. 21

Displacement responses of LO in normal NES and optimal equations (λ1=λ2=0.04 N s/m)

Grahic Jump Location
Fig. 22

Displacement responses of LO: (a) original system, (b) normal NES, (c) optimal equations, and (d) the envelope, respectively

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