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Research Papers

Enhancing Broadband Vibration Energy Suppression Using Local Buckling Modes in Constrained Metamaterials

[+] Author and Article Information
Ryan L. Harne

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210
e-mail: harne.3@osu.edu

Daniel C. Urbanek

Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received January 2, 2017; final manuscript received May 10, 2017; published online July 26, 2017. Assoc. Editor: Stefano Lenci.

J. Vib. Acoust 139(6), 061004 (Jul 26, 2017) (9 pages) Paper No: VIB-17-1004; doi: 10.1115/1.4036888 History: Received January 02, 2017; Revised May 10, 2017

Studies on dissipative metamaterials have uncovered means to suppress vibration and wave energy via resonant and bandgap phenomena through such engineered media, while global post-buckling of the infinitely periodic architectures is shown to tailor the attenuation properties and potentially magnify the effective damping effects. Yet, despite the promise suggested, the practical aspects of deploying metamaterials necessitates a focus on finite, periodic architectures, and the potential to therefore only trigger local buckling features when subjected to constraints. In addition, it is likely that metamaterials may be employed as devices within existing engineering systems, so as to motivate investigation on the usefulness of metamaterials when embedded within excited distributed or multidimensional structures. To illuminate these issues, this research undertakes complementary computational and experimental efforts. An elastomeric metamaterial, ideal for embedding into a practical engineering structure for vibration control, is introduced and studied for its relative change in broadband damping ability as constraint characteristics are modified. It is found that triggering a greater number of local buckling phenomena provides a valuable balance between stiffness reduction, corresponding to effective damping magnification, and demand for dynamic mass that may otherwise be diminished in globally post-buckled metamaterials. The concept of weakly constrained metamaterials is also shown to be uniformly more effective at broadband vibration suppression of the structure than solid elastomeric dampers of the same dimensions.

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References

Cummer, S. A. , Christensen, J. , and Alù, A. , 2016, “ Controlling Sound With Acoustic Metamaterials,” Nat. Rev., 1, p. 16001.
Liu, Y. , Shen, X. , Su, X. , and Sun, C. T. , 2016, “ Elastic Metamaterials With Low-Frequency Passbands Based on Lattice System With on-Site Potential,” ASME J. Vib. Acoust., 138(2), p. 021011. [CrossRef]
Liu, X. N. , Hu, G. K. , Sun, C. T. , and Huang, G. L. , 2011, “ Wave Propagation Characterization and Design of Two-Dimensional Elastic Chiral Metacomposite,” J. Sound Vib., 330(11), pp. 2536–2553. [CrossRef]
Chen, J. S. , and Wang, R. T. , 2014, “ Wave Propagation and Power Flow Analysis of Sandwich Structures With Internal Absorbers,” ASME J. Vib. Acoust., 136(4), p. 041003. [CrossRef]
Popa, B. I. , and Cummer, S. A. , 2014, “ Non-Reciprocal and Highly Nonlinear Active Acoustic Metamaterials,” Nat. Commun., 5, p. 3398. [CrossRef] [PubMed]
Haberman, M. R. , and Guild, M. D. , 2016, “ Acoustic Metamaterials,” Phys. Today, 69(6), pp. 42–48. [CrossRef]
Hussein, M. I. , Leamy, M. J. , and Ruzzene, M. , 2014, “ Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook,” ASME Appl. Mech. Rev., 66(4), p. 040802. [CrossRef]
Nouh, M. , Aldraihem, O. , and Baz, A. , 2014, “ Vibration Characteristics of Metamaterials Beams With Periodic Local Resonances,” ASME J. Vib. Acoust., 136(6), p. 061012. [CrossRef]
Baravelli, E. , and Ruzzene, M. , 2013, “ Internally Resonating Lattices for Bandgap Generation and Low-Frequency Vibration Control,” J. Sound Vib., 332(25), pp. 6562–6579. [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]
Hussein, M. I. , and Frazier, M. J. , 2013, “ Metadamping: An Emergent Phenomenon in Dissipative Metamaterials,” J. Sound Vib., 332(20), pp. 4767–4774. [CrossRef]
Ba'ba'a, H. A. , and Nouh, M. , 2017, “ An Investigation of Vibrational Power Flow in One-Dimensional Dissipative Phononic Structures,” ASME J. Vib. Acoust., 139(2), p. 021003. [CrossRef]
Shan, S. , Kang, S. H. , Wang, P. , Qu, C. , Shian, S. , Chen, E. R. , and Bertoldi, K. , 2014, “ Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves,” Adv. Funct. Mater., 24(31), pp. 4935–4942. [CrossRef]
Shim, J. , Wang, P. , and Bertoldi, K. , 2015, “ Harnessing Instability-Induced Pattern Transformation to Design Tunable Phononic Crystals,” Int. J. Solids Struct., 58, pp. 52–61. [CrossRef]
Antoniadis, I. , Chronopoulos, D. , Spitas, V. , and Koulocheris, D. , 2015, “ Hyper-Damping Peroperties of a Stiff and Stable Linear Oscillator With a Negative Stiffness Element,” J. Sound Vib., 346, pp. 37–52. [CrossRef]
Harne, R. L. , Song, Y. , and Dai, Q. , 2017, “ Trapping and Attenuating Broadband Vibroacoustic Energy With Hyperdamping Metamaterials,” Extreme Mech. Lett., 12, pp. 41–47. [CrossRef]
Bishop, J. , Dai, Q. , Song, Y. , and Harne, R. L. , 2016, “ Resilience to Impact by Extreme Energy Absorption in Lightweight Material Inclusions Constrained Near a Critical Point,” Adv. Eng. Mater., 18(11), pp. 1871–1876. [CrossRef]
Kochmann, D. M. , 2014, “ Stable Extreme Damping in Viscoelastic Two-Phase Composites With Non-Positive-Definite Phases Close to the Loss of Stability,” Mech. Res. Commun., 58, pp. 36–45. [CrossRef]
Virgin, L. N. , and Wiebe, R. , 2013, “ On Damping in the Vicinity of Critical Points,” Philos. Trans. R. Soc. A, 371(1993), p. 20120426. [CrossRef]
Fahy, F. , and Gardonio, P. , 1987, Sound and Structural Vibration: Radiation, Transmission and Response, Academic Press, Oxford, UK.
Cremer, L. , Heckl, M. , and Petersson, B. A. T. , 2005, Structure-Borne Sound: Structural Vibrations and Sound Radiation at Audio Frequencies, Springer, Berlin.
Ungar, E. E. , 1992, “ Structural Damping,” Noise and Vibration Control Engineering, L. L. Beranek , and I. L. Ver , eds., Wiley, New York. [CrossRef]
Celli, P. , and Gonella, S. , 2014, “ Laser-Enabled Experimental Wavefield Reconstruction in Two-Dimensional Phononic Crystals,” J. Sound Vib., 333(1), pp. 114–123. [CrossRef]
Overvelde, J. T. B. , and Bertoldi, K. , 2014, “ Relating Pore Shape to the Non-Linear Response of Periodic Elastomeric Structures,” J. Mech. Phys. Solids, 64, pp. 351–366. [CrossRef]
Wang, P. , Casadei, F. , Shan, S. , Weaver, J. C. , and Bertoldi, K. , 2014, “ Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials,” Phys. Rev. Lett., 113(1), p. 014301. [CrossRef] [PubMed]
Virgin, L. N. , 2007, Vibration of Axially Loaded Structures, Cambridge University Press, Cambridge, UK. [CrossRef]
Avitabile, P. , 2001, “ Experimental Modal Analysis: A Simple Non-Mathematical Presentation,” Sound Vib., 35(1), pp. 20–31. http://classes.engineering.wustl.edu/2009/fall/mase431/PDF/modalana.pdf

Figures

Grahic Jump Location
Fig. 1

(a) Metamaterial architecture subjected to compression, exhibiting local and global buckling behaviors; (b) load–displacement; (c) stiffness–displacement measurements for three nominally identical specimens; (d) schematic of impact hammer experiments on U-channel beam, comparison of metamaterial and solid specimens, and cross section dimensions of U-channel; and (e) photograph of experimental setup

Grahic Jump Location
Fig. 2

FE model results of eigenfrequency change for change in compressive engineering strain. At bottom is an image of the deformation of a local buckling mode highlighted in the plot.

Grahic Jump Location
Fig. 3

Transfer function measurements of beam global acceleration to impact force. (a)–(c) present results for the instance where the embedded dampers are positioned at the impact locations, while (d)–(f) present results when the embedded dampers are positioned at response measurements locations. (a) and (d) provide narrowband plots, (b) and (e) provide one-third octave band plots, and (c) and (f) provide octave band totals of TF reductions from the case of the global vibration of the bare beam.

Grahic Jump Location
Fig. 4

Representative time series of acceleration ring-down responses after hammer impact. Beam acceleration from the four accelerometers shown for the beam with (a) no dampers embedded, with (b) metamaterial dampers type C at impact locations, and with (c) metamaterial dampers type C at response measurement locations. (d) The exponential decay rates computed from three representative experimental series.

Grahic Jump Location
Fig. 5

Transfer function measurements of beam global acceleration to impact force. Data obtained for the second instance of impact location and response measurement location experimentally considered. Layout of subfigure parts and presentation are identical to those in Fig. 3.

Grahic Jump Location
Fig. 6

FE model results of one-third octave band global acceleration to force TF, considering the metamaterial dampers to possess ranges of damping ratios, from significant underdamping to critical damping. Results shown for metamaterials at (a) impact locations and (b) response measurement locations (see color figure online).

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