0
Research Papers

Wave Propagation in Sandwich Structures With Multiresonators

[+] Author and Article Information
J. S. Chen

Department of Engineering Science,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: jschen273@mail.ncku.edu.tw

Y. J. Huang

Department of Engineering Science,
National Cheng Kung University,
No. 1, University Road,
Tainan City 701, Taiwan
e-mail: n96034285@mail.ncku.edu.tw

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received September 14, 2015; final manuscript received March 2, 2016; published online May 23, 2016. Assoc. Editor: Mahmoud Hussein.

J. Vib. Acoust 138(4), 041009 (May 23, 2016) (10 pages) Paper No: VIB-15-1385; doi: 10.1115/1.4033197 History: Received September 14, 2015; Revised March 02, 2016

A new sandwich beam with embedded multiresonators is presented. Two continuum Timoshenko beam models are adopted for modeling sandwich beams. Numerical results show that multiple resonators can lead to multiple resonant-type bandgaps with remarkable wave attenuation. The effective mass is found to become negative for frequencies in the bandgaps where the wave is greatly attenuated. With two identical resonators connected in parallel, only one single bandgap can be found. If two resonators with equal masses and springs are connected in series, the central frequency of the second bandgap is approximated twice of the central frequency of the first gap. For the beam with series-connected resonators, a simple two degrees-of-freedom system is proposed and used for predicting the initial frequencies of the bandgaps while for the beam with resonators in parallel, two separate single degree-of-freedom systems are introduced.

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

References

Rivin, E. I. , 2003, Passive Vibration Isolation, ASME Press, New York.
Lane, S. A. , Griffin, S. , and Richard, R. E. , 2006, “ Fairing Noise Mitigation Using Passive Vibroacoustic Attenuation Devices,” J. Spacecr. Rockets, 43(1), pp. 31–44. [CrossRef]
Liu, Z. , Zhang, X. , Mao, Y. , Zhu, Y. Y. , Yang, Z. , Chan, C. T. , and Sheng, P. , 2000, “ Locally Resonant Sonic Materials,” Science, 289(5485), pp. 1734–1736. [CrossRef] [PubMed]
Ho, K. M. , Cheng, C. K. , Yang, Z. , Zhang, X. X. , and Sheng, P. , 2003, “ Broadband Locally Resonant Sonic Shields,” Appl. Phys. Lett., 83(26), pp. 5566–5568. [CrossRef]
Sheng, P. , Zhang, X. X. , Liu, Z. , and Chan, C. T. , 2003, “ Locally Resonant Sonic Materials,” Physica B, 338(1–4), pp. 201–205. [CrossRef]
Li, J. , and Chan, C. T. , 2004, “ Double-Negative Acoustic Metamaterial,” Phys. Rev. E, 70(5), p. 055602. [CrossRef]
Chen, H. , and Chan, C. T. , 2007, “ Acoustic Cloaking in Three Dimensions Using Acoustic Metamaterials,” Appl. Phys. Lett., 91(18), p. 183518. [CrossRef]
Fokin, V. , Ambati, M. , Sun, C. , and Zhang, X. , 2007, “ Method for Retrieving Effective Properties of Locally Resonant Acoustic Metamaterials,” Phys. Rev. B, 76(14), p. 144302. [CrossRef]
Meng, H. , Wen, J. , Zhao, H. , and Wen, X. , 2012, “ Optimization of Locally Resonant Acoustic Metamaterials on Underwater Sound Absorption Characteristics,” J. Sound Vib., 331(20), pp. 4406–4416. [CrossRef]
Yao, S. , Zhou, X. , and Hu, G. , 2008, “ Experimental Study on Negative Effective Mass in a 1D Mass-Spring System,” New J. Phys., 10(4), p. 043020. [CrossRef]
Huang, H. H. , Sun, C. T. , and Huang, G. L. , 2009, “ On the Negative Effective Mass Density in Acoustic Metamaterials,” Int. J. Eng. Sci., 47(4), pp. 610–617. [CrossRef]
Huang, H. H. , and Sun, C. T. , 2009, “ Wave Attenuation Mechanism in an Acoustic Metamaterial With Negative Effective Mass Density,” New J. Phys., 11(1), p. 013003. [CrossRef]
Manimala, J. M. , Huang, H. H. , Sun, C. T. , Snyder, R. , and Bland, S. , 2014, “ Dynamic Load Mitigation Using Negative Effective Mass Structures,” Eng. Struct., 80, pp. 458–468. [CrossRef]
Manimala, J. M. , and Sun, C. T. , 2014, “ Microstructural Design Studies for Locally Dissipative Acoustic Metamaterials,” J. Appl. Phys., 115(2), p. 023518. [CrossRef]
Mikoshiba, K. , Manimala, J. M. , and Sun, C. T. , 2013, “ Energy Harvesting Using an Array of Multifunctional Resonators,” J. Intell. Mater. Syst. Struct., 24(2), pp. 168–179. [CrossRef]
Huang, G. L. , and Sun, C. T. , 2010, “ Band Gaps in a Multiresonator Acoustic Metamaterial,” ASME J. Vib. Acoust., 132(3), p.031003. [CrossRef]
Tan, K. T. , Huang, H. H. , and Sun, C. T. , 2012, “ Optimizing the Band Gap of Effective Mass Negativity in Acoustic Metamaterials,” Appl. Phys. Lett., 101(24), p. 241902. [CrossRef]
Tan, K. T. , Huang, H. H. , and Sun, C. T. , 2014, “ Blast-Wave Impact Mitigation Using Negative Effective Mass Density Concept of Elastic Metamaterials,” Int. J. Impact Eng., 64, pp. 20–29. [CrossRef]
Xiao, Y. , Mace, B. R. , Wen, J. , and Wen, X. , 2011, “ Formation and Coupling of Band Gaps in a Locally Resonant Elastic System Comprising a String With Attached Resonators,” Phys. Lett. A, 375(12), pp. 1485–1491. [CrossRef]
Xiao, Y. , Wen, J. , and Wen, X. , 2012, “ Longitudinal Wave Band Gaps in Metamaterial-Based Elastic Rods Containing Multi-Degree-of-Freedom Resonators,” New J. Phys., 14(3), p. 033042. [CrossRef]
Liu, L. , and Hussein, M. I. , 2012, “ Wave Motion in Periodic Flexural Beams and Characterization of the Transition Between Bragg Scattering and Local Resonance,” ASME J. Appl. Mech., 79(1), p. 011003. [CrossRef]
Xiao, Y. , Wen, J. , and Wen, X. , 2012, “ Flexural Wave Band Gaps in Locally Resonant Thin Plates With Periodically Attached Spring-mass Resonators,” J. Phys. D: Appl. Phys., 45(19), p. 195401. [CrossRef]
Xiao, Y. , Wen, J. , Yu, D. , and Wen, X. , 2013, “ Flexural Wave Propagation in Beams With Periodically Attached Vibration Absorbers: Band-Gap Behavior and Band Formation Mechanisms,” J. Sound Vib., 332(4), pp. 867–893. [CrossRef]
Xiao, Y. , Wen, J. , Wang, G. , and Wen, X. , 2013, “ Theoretical and Experimental Study of Locally Resonant and Bragg Band Gaps in Flexural Beams Carrying Periodic Arrays of Beam-Like Resonators,” ASME J. Vib. Acoust., 135(4), p. 041006. [CrossRef]
Pai, P. F. , Peng, H. , and Jiang, S. , 2014, “ Acoustic Metamaterial Beams Based on Multi-Frequency Vibration Absorbers,” Int. J. Mech. Sci., 79, pp. 195–205. [CrossRef]
Karagiozova, D. , Nurick, G. N. , Langdon, G. S. , Yuen, S. C. K. , Chi, Y. , and Bartle, S. , 2009, “ Response of Flexible Sandwich-Type Panels to Blast Loading,” Compos. Sci. Technol., 69(6), pp. 754–763. [CrossRef]
Wang, D. , 2009, “ Impact Behavior and Energy Absorption of Paper Honeycomb Sandwich Panels,” Int. J. Impact Eng., 36(1), pp. 110–114. [CrossRef]
Grujicic, M. , Galgalikar, R. , Snipes, J. S. , Yavari, R. , and Ramaswami, S. , 2013, “ Multi-Physics Modeling of the Fabrication and Dynamic Performance of All-Metal Auxetic-Hexagonal Sandwich-Structures,” Mater. Des., 51, pp. 113–130. [CrossRef]
Chen, J. S. , and Sun, C. T. , 2011, “ Dynamic Behavior of a Sandwich Beam With Internal Resonators,” J. Sandwich Struct. Mater., 13(4), pp. 391–408. [CrossRef]
Wellstead, P. E. , 1979, Introduction to Physical System Modelling, Academic Press Ltd., London.
Hasebe, R. S. , and Sun, C. T. , 2000, “ Performance of Sandwich Structures With Composite Reinforced Core,” J. Sandwich Struct. Mater., 2(1), pp. 75–100. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Model I: a sandwich beam with resonators in series and (b) model II: a sandwich beam with resonators in parallel

Grahic Jump Location
Fig. 2

Sketch of a unit cell (left) and its equivalent model (right) for (a) model I and (b) model II

Grahic Jump Location
Fig. 3

A two degrees-of-freedom system

Grahic Jump Location
Fig. 4

Two spring–mass systems

Grahic Jump Location
Fig. 5

Attenuation factor β for the sandwich beam with resonators in series (model I) (a) m2/m1=0.5; (b) m2/m1=1.0; and (c) m2/m1=1.5 (a = 0.012 m, k2/k1=1.0)

Grahic Jump Location
Fig. 6

Attenuation factor β for the sandwich beam with resonators in series (model I) (a) k2/k1=0.5; (b) k2/k1=1.0; and (c) k2/k1=1.5 (a = 0.012 m, m2/m1=1.0)

Grahic Jump Location
Fig. 7

Effect of m2/m1 for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, k2/k1=1.0)

Grahic Jump Location
Fig. 8

Effect of k2/k1 for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, m2/m1=1.0)

Grahic Jump Location
Fig. 9

Effect of a for model I on edge frequencies of (a) the first bandgap and (b) the second bandgap (m2/m1=0.5, k2/k1=1.0)

Grahic Jump Location
Fig. 10

Dispersion curves for model I, obtained by the continuum model and finite element (FE) model (a = 0.012 m, m2/m1=1.5, k2/k1=1)

Grahic Jump Location
Fig. 11

Nondimensionalized wave number for model I as a function of dimensionless frequency ω¯, obtained by the continuum model with distributed masses and the one with effective mass (a = 0.012 m, m2/m1=1.5, k2/k1=1)

Grahic Jump Location
Fig. 12

Dimensionless effective mass per unit length for model I with varying (a) m2/m1 and (b) k2/k1 (a = 0.012 m)

Grahic Jump Location
Fig. 13

Attenuation factor β for the sandwich beam with resonators in parallel (model II) (a) m2/m1=0.5 and (b) m2/m1=1.5 (a = 0.012 m, k2/k1=1.0)

Grahic Jump Location
Fig. 14

Attenuation factor β for the sandwich beam with resonators in parallel (model II) (a) k2/k1=0.5 and (b) k2/k1=1.5 (a = 0.012 m, m2/m1=1.0)

Grahic Jump Location
Fig. 15

Comparison of attenuation factor β for the sandwich beam having a two-resonator system with m2/m1=1.0 and k2/k1=1.0 (model II) and for the beam with one spring–mass system (a = 0.012 m)

Grahic Jump Location
Fig. 16

Effect of m2/m1 for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, k2/k1=1.0)

Grahic Jump Location
Fig. 17

Effect of k2/k1 for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (a = 0.012 m, m2/m1=1.0)

Grahic Jump Location
Fig. 18

Effect of a for model II on edge frequencies of (a) the first bandgap and (b) the second bandgap (m2/m1=0.5, k2/k1=1.0)

Grahic Jump Location
Fig. 19

Dispersion curves for model II, obtained by the continuum model and FE model (a = 0.012 m, m2/m1=1.5, k2/k1=1.0)

Grahic Jump Location
Fig. 20

Nondimensionalized wave number for model II as a function of dimensionless frequency ω¯, obtained by the continuum model with distributed masses and the one with effective mass (a = 0.012 m, m2/m1=1.5, k2/k1=1.0)

Grahic Jump Location
Fig. 21

Dimensionless effective mass per unit length for model II with varying (a) m2/m1 and (b) k2/k1 (a = 0.012 m)

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