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Research Papers

Band-Gap of a Soft Magnetorheological Phononic Crystal

[+] Author and Article Information
Alireza Bayat

Composite and Intelligent Materials Laboratory,
Department of Mechanical Engineering,
University of Nevada–Reno,
Reno, NV 89557

Faramarz Gordaninejad

Fellow ASME
Professor
Composite and Intelligent Materials Laboratory,
Department of Mechanical Engineering,
University of Nevada–Reno,
Reno, NV 89557
e-mail: faramarz@unr.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received April 1, 2014; final manuscript received September 5, 2014; published online November 12, 2014. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 137(1), 011011 (Feb 01, 2015) (8 pages) Paper No: VIB-14-1121; doi: 10.1115/1.4028556 History: Received April 01, 2014; Revised September 05, 2014; Online November 12, 2014

This paper presents the wave propagation in a tunable phononic crystal consisting of a porous hyperelastic magnetorheological elastomer (MRE) subjected to an external magnetic field. Finite deformations and magnetic induction influence phononic characteristics of the periodic structure through altering the geometry and material properties of the unit cell. The governing equations for incremental time-harmonic plane wave motions superimposed on a static predeformed media are derived. Analytical and finite element (FE) methods are used to investigate dispersion relation and band structure of the phononic crystal for different levels of deformation and applied magnetic induction. It is demonstrated that large deformations and magnetic induction could transform the location and width of band-gaps.

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Figures

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Fig. 1

The FE results for pattern transformation in the phononic crystal due to buckling instability under the applied deformation. (a) An undeformed 8 × 8 periodic structure, (b) the first buckling mode of the structure subjected to uniaxially compressive stretch in horizontal direction, and (c) the first buckling eigenmode of the enlarged unit cell.

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Fig. 2

Schematic diagram of the different state and coordinates chosen for study; Cr, reference or undeformed state (Lagrangian coordinate), Ct, deformed state (Eulerian coordinate), and Cd, incrementally deformed state due to the superimposed infinitesimal motion

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Fig. 3

(a) The representative unit cell selected for the uniaxial compression, (b) the corresponding deformed geometry for λ1 = 0.9, (c) the representative unit cell selected for equally biaxial compression, (d) the corresponding deformed geometry for λ = 0.9, and (e) reciprocal lattice's unit cell selected for the wave propagation study. IBZ is shown in the region bounded by Γ-X-M-Γ.

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Fig. 4

Inplane band diagrams for the phononic crystal subjected to uniaxial compression and unidirectionally applied magnetic induction: (a) no magnetic induction, (b) 1.0 T, (c) 2.0 T, and (d) 3.0 T. PBGs are shown in shaded regions.

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Fig. 5

Inplane band diagrams for the phononic crystal subjected to biaxial compression and unidirectionally applied magnetic induction: (a) no magnetic induction, (b) 1.0 T, (c) 2.0 T, and (d) 3.0 T. PBGs are shown in shaded regions.

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Fig. 6

PBG versus applied magnetic induction in y direction, for the square array phononic crystal in: (a) uniaxially compressive stretch λ1 = 0.9 and (b) in biaxially compressive stretch λ = 0.9

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