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Research Papers

Study of Targeted Energy Transfer Inside Three-Dimensional Acoustic Cavity by Two Nonlinear Membrane Absorbers and an Acoustic Mode

[+] Author and Article Information
Xian Wu

School of Automotive Studies,
Tongji University,
Shanghai 201804, China
e-mail: wuxian@tongji-auto.cn

Jianwang Shao

Institute for Advanced Study,
Tongji University,
Shanghai 201804, China
e-mail: shaojianwang@tongji.edu.cn

Bruno Cochelin

Professor
Laboratory of Mechanics and Acoustics,
Ecole Centrale Marseille,
Marseille 13451, France
e-mail: bruno.cochelin@centrale-marseille.fr

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 15, 2015; final manuscript received February 21, 2016; published online April 15, 2016. Assoc. Editor: Sheryl M. Grace.

J. Vib. Acoust 138(3), 031017 (Apr 15, 2016) (9 pages) Paper No: VIB-15-1387; doi: 10.1115/1.4033057 History: Received September 15, 2015; Revised February 21, 2016

As a new approach to passive sound control in low-frequency domain, the targeted energy transfer (TET) phenomenon has been investigated inside a three-dimensional (3D) acoustic cavity by considering a two degrees-of-freedom (DOF) system with an acoustic mode and a membrane nonlinear energy sink (NES). The beginning of TET phenomenon of the 2DOF system and the desired working zone for the membrane NES have been defined. In order to enhance the robustness and the effective TET range in acoustic cavities, a 3DOF system with two membranes and one acoustic mode is studied in this paper. We consider two different membranes and two almost identical membranes to analyze the TET phenomenon, respectively. The desired working zone which was obtained by the 2DOF system is applied to analyze the 3DOF system. We observe that two membranes can enlarge the desired working zone.

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Figures

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Fig. 1

Schema of the acoustic cavity with several membranes

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Fig. 2

Schema of the membrane

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Fig. 3

(a) Scheme of a linear mass–spring oscillator and (b) characteristic of the linear oscillator. A is the amplitude, and ω is the angular frequency.

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Fig. 4

(a) Scheme of a nonlinear mass–spring oscillator and (b) characteristic of the nonlinear oscillator. A is the amplitude, and ω is the angular frequency.

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Fig. 5

Superposition of characteristics of the linear oscillator and the nonlinear oscillator. Blue lines stand for the nonlinear oscillator. Red line stands for the linear oscillator. A is the amplitude, and ω is the angular frequency. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 6

Superposition of characteristics of several linear oscillators and several nonlinear oscillators. A is the amplitude, and ω is the angular frequency. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 7

The NNMs of the system. Red curves: u(t), blue curves: q1(t), and green curves: q2(t). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 8

The periodic forced responses of the system for five excitation levels of forcing F1=0.05 (blue curve), 0.55 (red curve), 4.05 (green curve), 10.05 (pink curve), and 14.05 (black curve): (a) u(t), (b) q1(t), and (c) q2(t). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 9

Stability of the NNMs. Solid lines refer to the periodic regime solutions, and dotted lines refer to the unstable solutions. (a) u(t), (b) q1(t), and (c) q2(t).

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Fig. 10

The periodic forced responses of u(t), q1(t), and q2(t) with stability for F1=4.05. Solid lines refer to the periodic regime solutions, and dotted lines refer to the unstable solutions. (a) u(t), (b) q1(t), and (c) q2(t).

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Fig. 11

The periodic forced responses of the system and the respective NNM of the system with the mode P010 and each membrane. Red-dashed curves: the NNM. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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Fig. 12

The periodic forced responses of the system with F1=0.15 : (a) u(t), (b) q1(t), and (c) q2(t)

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Fig. 13

The periodic forced responses of the system with F1=1 : (a) u(t), (b) q1(t), and (c) q2(t)

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Fig. 14

The periodic forced responses of the system with F1=2 : (a) u(t), (b) q1(t),and (c) q2(t)

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Fig. 15

The periodic forced responses of the system with F1=2.8 : (a) u(t), (b) q1(t), and (c) q2(t)

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Fig. 16

The periodic forced responses of the system with F1=3.3 : (a) u(t), (b) q1(t), and (c) q2(t)

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Fig. 17

The curve of the periodic forced response surface crest. Blue curve: one membrane q1. Red curve: two membranes q1 and q2. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this paper.)

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