0
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.

Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gendelman, O. , Manevitch, L. , Vakakis, A. , and M’Closkey, R. , 2001, “ Energy Pumping in Nonlinear Mechanical Oscillators: Part I—Dynamics of the Underlying Hamiltonian Systems,” ASME J. Appl. Mech., 68(1), pp. 34–41. [CrossRef]
Vakakis, A. , and Gendelman, O. , 2001, “ Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture,” ASME J. Appl. Mech., 68(1), pp. 42–48. [CrossRef]
Gendelman, O. , Gourdon, E. , and Lamarque, C. , 2006, “ Quasiperiodic Energy Pumping in Coupled Oscillators Under Periodic Forcing,” J. Sound Vib., 294(4–5), pp. 651–662. [CrossRef]
Gourdon, E. , Alexander, N. , Taylor, C. , Lamarque, C. , and Pernot, S. , 2007, “ Nonlinear Energy Pumping Under Transient Forcing With Strongly Nonlinear Coupling: Theoretical and Experimental Results,” J. Sound Vib., 300(3–5), pp. 522–551. [CrossRef]
Nucera, F. , Vakakis, A. , McFarland, D. , Bergman, L. , and Kerschen, G. , 2007, “ Targeted Energy Transfers in Vibro-Impact Oscillators for Seismic Mitigation,” Nonlinear Dyn., 50(3), pp. 651–677. [CrossRef]
Starosvetsky, Y. , and Gendelman, O. , 2009, “ Vibration Absorption in Systems With a Nonlinear Energy Sink: Nonlinear Pumping,” J. Sound Vib., 324(3–5), pp. 916–939. [CrossRef]
Gourc, E. , Michon, G. , Seguy, S. , and Berlioz, A. , 2015, “ Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments,” ASME J. Vib. Acoust., 137(3), p. 031008. [CrossRef]
Cochelin, B. , Herzog, P. , and Mattei, P.-O. , 2006, “ Experimental Evidence of Energy Pumping in Acoustics,” C. R. Mec., 334(11), pp. 639–644. [CrossRef]
Bellet, R. , 2010, “ Vers une nouvelle technique de contrôle passif du bruit: Absorbeur dynamique non linéaire et pompage énergétique,” Ph.D. thesis, Université de Provence (AIX-MARSEILLE 1), Marseille, France.
Bellet, R. , Cochelin, B. , Côte, R. , and Mattei, P.-O. , 2012, “ Enhancing the Dynamic Range of Targeted Energy Transfer in Acoustics Using Several Nonlinear Membrane Absorbers,” J. Sound Vib., 331(26), pp. 5657–5668. [CrossRef]
Mariani, R. , Bellizzi, S. , Cochelin, B. , Herzog, P. , and Mattei, P.-O. , 2011, “ Toward an Adjustable Nonlinear Low Frequency Acoustic Absorber,” J. Sound Vib., 330(22), pp. 5245–5258. [CrossRef]
Vakakis, A. , Manevitch, L. , Musienko, A. , Kerschen, G. , and Bergman, L. , 2005, “ Transient Dynamics of a Dispersive Elastic Wave Guide Weakly Coupled to an Essentially Nonlinear End Attachment,” Wave Motion, 41(2), pp. 109–132. [CrossRef]
Georgiades, F. , Vakakis, A. , and Kerschen, G. , 2007, “ Broadband Passive Targeted Energy Pumping From a Linear Dispersive Rod to a Lightweight Essentially Non-Linear End Attachment,” Int. J. Non-Linear Mech., 42(5), pp. 773–788. [CrossRef]
Panagopoulos, P. , Vakakis, A. , and Tsakirtzis, S. , 2004, “ Multi-Scaled Analysis of the Damped Dynamics of an Elastic Rod With an Essentially Nonlinear End Attachment,” Int. J. Solids Struct., 41, pp. 6505–6528. [CrossRef]
Georgiades, F. , and Vakakis, A. , 2007, “ Dynamics of a Linear Beam With an Attached Local Nonlinear Energy Sink,” Commun. Nonlinear Sci. Numer. Simul., 12(5), pp. 643–651. [CrossRef]
Ahmadabadi, Z. N. , and Khadem, S. , 2012, “ Nonlinear Vibration Control of a Cantilever Beam by a Nonlinear Energy Sink,” Mech. Mach. Theory, 50, pp. 134–149. [CrossRef]
Georgiades, F. , and Vakakis, A. , 2009, “ Passive Targeted Energy Transfers and Strong Modal Interactions in the Dynamics of a Thin Plate With Strongly Nonlinear Attachments,” Int. J. Solids Struct., 42(11–12), pp. 773–788.
Kerschen, G. , Kowtko, J. , McFarland, D. , Bergman, L. , and Vakakis, A. , 2007, “ Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators,” Nonlinear Dyn., 47, pp. 285–309. [CrossRef]
Pham, T. , Pernot, S. , and Lamarque, C. , 2010, “ Competitive Energy Transfer Between a Two Degrees-of-Freedom Dynamic System and an Absorber With Essential Nonlinearity,” Nonlinear Dyn., 62(3), pp. 573–592. [CrossRef]
Manevitch, L. , Gendelman, O. , Musienko, A. , Vakakis, A. , and Bergman, L. , 2003, “ Dynamic Interaction of a Semi-Infinite Linear Chain of Coupled Oscillators With a Strongly Nonlinear End Attachment,” Physica D, 178(1–2), pp. 1–18. [CrossRef]
Lee, Y. , Vakakis, A. , Bergman, L. , McFarland, D. , and Kerschen, G. , 2008, “ Enhancing Robustness of Aeroelastic Instability Suppression Using MDOF Energy Sinks,” AIAA J., 46(6), pp. 1371–1394. [CrossRef]
Tsakirtzis, S. , Kerschen, G. , Panagopoulos, P. , and Vakakis, A. , 2005, “ Multi-Frequency Nonlinear Energy Transfer From Linear Oscillators to Mdof Essentially Nonlinear Attachments,” J. Sound Vib., 285(1–2), pp. 483–490. [CrossRef]
Tsakirtzis, S. , Vakakis, A. , and Panagopoulos, P. , 2007, “ Broadband Energy Exchanges Between a Dissipative Elastic Rod and a Multi-Degree-of-Freedom Dissipative Essentially Non-Linear Attachment,” Int. J. Non-Linear Mech., 42(1), pp. 36–57. [CrossRef]
Tsakirtzis, S. , Panagopoulos, P. , Kerschen, G. , Gendelman, O. , Vakakis, A. , and Bergman, L. , 2007, “ Complex Dynamics and Targeted Energy Transfer in Linear Oscillators Coupled to Multi-Degree-of-Freedom Essentially Nonlinear Attachments,” Nonlinear Dyn., 48(3), pp. 285–318. [CrossRef]
Musienko, A. , Lamarque, C. , and Manevitch, L. , 2006, “ Design of Mechanical Energy Pumping Devices,” J. Vib. Control, 12(4), pp. 355–371. [CrossRef]
Ma, X. , Vakakis, A. , and Bergman, L. , 2008, “ Karhunen–Loeve Analysis and Order Reduction of the Transient Dynamics of Linear Coupled Oscillators With Strongly Nonlinear End Attachments,” J. Sound Vib., 309(3–5), pp. 569–587. [CrossRef]
Gendelman, O. , Sapsis, T. , Vakakis, A. , and Bergman, L. , 2011, “ Enhanced Passive Targeted Energy Transfer in Strongly Nonlinear Mechanical Oscillators,” J. Sound Vib., 330(1), pp. 1–8. [CrossRef]
Wierschem, N. , Quinn, D. , Hubbard, S. , Al-Shudeifat, M. A. , Michael McFarland, D. , Luo, J. , Fahnestock, L. A. , Spencer, B. F., Jr. , Vakakis, A. F. , and Bergman, L. A. , 2012, “ Passive Damping Enhancement a Two-Degree-of-Freedom System Through a Strongly Nonlinear Two-Degree-of-Freedom Attachment,” J. Sound Vib., 331(25), pp. 5393–5407. [CrossRef]
Vaurigaud, B. , Savadkoohi, A. T. , and Lamarque, C. , 2011, “ Targeted Energy Transfer With Parallel Nonlinear Energy Sinks—Part I: Design Theory and Numerical Results,” Nonlinear Dyn., 66(4), pp. 763–780. [CrossRef]
Savadkoohi, A. , Vaurigaud, B. , Lamarque, C. , and Pernot, S. , 2012, “ Targeted Energy Transfer With Parallel Nonlinear Energy Sinks—Part II: Theory and Experiments,” Nonlinear Dyn., 67(1), pp. 37–46. [CrossRef]
Shao, J. , and Cochelin, B. , 2014, “ Theoretical and Numerical Study of Targeted Energy Transfer Inside an Acoustic Cavity by a Non-Linear Membrane Absorber,” Int. J. Non-Linear Mech., 64, pp. 85–92. [CrossRef]
Wu, X. , Shao, J. , and Cochelin, B. , 2016, “ Parameters Design of a Nonlinear Membrane Absorber Applied to 3D Acoustic Cavity Based on Targeted Energy Transfer (TET),” Noise Contr. Eng. J., 64(1), pp. 99–113.
Bellet, R. , Cochelin, B. , Herzog, P. , and Mattei, P.-O. , 2010, “ Experimental Study of Targeted Energy Transfer From an Acoustic System to a Nonlinear Membrane Absorber,” J. Sound Vib., 329(14), pp. 2768–2791. [CrossRef]
Gourdon, E. , and Lamarque, C. , 2005, “ Energy Pumping for a Larger Span of Energy,” J. Sound Vib., 285(3), pp. 711–720. [CrossRef]
Starosvetsky, Y. , and Gendelman, O. , 2008, “ Strongly Modulated Response in Forced 2DOF Oscillatory System With Essential Mass and Potential Asymmetry,” Physica D, 237(13), pp. 1719–1733. [CrossRef]
Kuether, R. , Renson, L. , Detroux, T. , Grappasonni, C. , Kerschen, G. , and Allen, M. , 2015, “ Nonlinear Normal Modes, Modal Interactions and Isolated Resonance Curves,” J. Sound Vib., 351, pp. 299–310. [CrossRef]
Shao, J. , Wu, X. , and Cochelin, B. , 2014, “ Targeted Energy Transfer in Two Degrees-of-Freedom Linear System Coupled by One Nonlinear Absorber,” 21st International Congress on Sound and Vibration, Beijing, China, July 13–17, Paper No. 850.
Karkar, S. , Cocheliln, B. , Vergez, C. , Thomas, O. , and Lazarus, A. , 2011, “ ManLab: An Interactive Path-Fllowing and Bifurcation Analysis Software,” available at: http://manlab.lma.cnrs-mrs.fr

Figures

Grahic Jump Location
Fig. 1

Schema of the acoustic cavity with several membranes

Grahic Jump Location
Fig. 2

Schema of the membrane

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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.)

Grahic Jump Location
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.)

Grahic Jump Location
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.)

Grahic Jump Location
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.)

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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.)

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
Fig. 13

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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
Fig. 15

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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
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.)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In