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Research Papers

Experimental Evaluation of Structural Intensity in Two-Dimensional Plate-Type Locally Resonant Elastic Metamaterials

[+] Author and Article Information
H. Al Ba'ba'a, M. A. Attarzadeh

Mechanical and Aerospace
Engineering Department,
University at Buffalo (SUNY),
Buffalo, NY 14260

M. Nouh

Mechanical and Aerospace
Engineering Department,
University at Buffalo (SUNY),
Buffalo, NY 14260
e-mail: mnouh@buffalo.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 8, 2017; final manuscript received January 11, 2018; published online February 2, 2018. Assoc. Editor: Yihui Zhang.

J. Appl. Mech 85(4), 041005 (Feb 02, 2018) (9 pages) Paper No: JAM-17-1623; doi: 10.1115/1.4039042 History: Received November 08, 2017; Revised January 11, 2018

Elastic metamaterials utilize locally resonant mechanical elements to onset band gap characteristics that are typically exploited in vibration suppression and isolation applications. The present work employs a comprehensive structural intensity analysis (SIA) to depict the structural power distribution and variations associated with band gap frequency ranges, as well as outside them along both dimensions of a two-dimensional (2D) metamaterial. Following a brief theoretical dispersion analysis, the actual mechanics of a finite metamaterial plate undergoing flexural loading and consisting of a square array of 100 cells is examined experimentally using a fabricated prototype. Scanning laser Doppler vibrometer (SLDV) tests are carried out to experimentally measure the deformations of the metamaterial in response to base excitations within a broad frequency range. In addition to confirming the attenuation and blocked propagation of elastic waves throughout the elastic medium via graphical visualizations of power flow maps, the SIA reveals interesting observations, which give additional insights into energy flow and transmission in elastic metamaterials as a result of the local resonance effects. A drastic reduction in power flow magnitudes to the bulk regions of the plate within a band gap is noticeably met with a large amplification of structural intensity around and in the neighborhood of the excitation source as a compensatory effect. Finally, the theoretical and experimentally measured streamlines of power flow are presented as an alternative tool to predict the structural power patterns and track vortices as well as confined regions of energy concentrations.

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Figures

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Fig. 3

In-plane (dashed) and out-of-plane (solid) dispersion curves (and corresponding deformation modes) for the shown unit cell mesh obtained via a 3D model of solid elements. Kirchhoff predictions (circles) are shown for comparison.

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Fig. 2

(a) Discretization of the unit cell and the arrangement of the degrees-of-freedom groups and (b) the dispersion curves for the unit cell shown in Fig. 1

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Fig. 1

Schematic of the metamaterial plate and its unit cell along with their dimensions

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Fig. 12

Theoretical and experimental streamlines of power flow for the pass band frequency (500 Hz)

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Fig. 13

Theoretical and experimental streamlines of power flow for the band gap frequency (1700 Hz)

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Fig. 4

(a) The experimental setup consisting of the vibrometer, the magnifier, the electrodynamic shaker and the metamaterial plate and (b) a flow diagram of the experimental testing

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Fig. 5

(a) Schematic diagram illustrating the sensing and excitation locations on the metamaterial plate and (b) the numerical and experimental frequency response function at the sensing location

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Fig. 6

Numerical and experimental displacement fields at a (a) pass band frequency (500 Hz) and (b) a band gap frequency (1700 Hz)

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Fig. 7

Flow chart illustrating the procedure of the numerical and experimental SIA computations

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Fig. 8

Theoretical and experimental power flow maps for the pass band frequency (500 Hz)

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Fig. 9

Theoretical and experimental power flow maps for the band gap frequency (1700 Hz)

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Fig. 10

The frequency response of the active power magnitude |P| function at a point near the excitation source and select close-ups of the power flow map in its neighborhood

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Fig. 11

The frequency response of the active power magnitude |P| function at the sensing point and select close-ups of the power flow map in its neighborhood

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