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Research Papers

Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology

[+] Author and Article Information
Raj Kumar Pal

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Robert F. Waymel, Philippe H. Geubelle

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

John Lambros

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: lambros@illinois.edu

1Present address: Daniel Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332.

2Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 4, 2016; final manuscript received September 8, 2016; published online October 20, 2016. Assoc. Editor: Peter W. Chung.

J. Eng. Mater. Technol 139(1), 011005 (Oct 20, 2016) (7 pages) Paper No: MATS-16-1165; doi: 10.1115/1.4034820 History: Received June 04, 2016; Revised September 08, 2016

We develop a framework for wave tailoring by altering the lattice network topology of a granular crystal consisting of spherical granules in contact. The lattice topology can alternate between two stable configurations, with the spherical granules of the lattice held in stable equilibrium in each configuration by gravity. Under impact, the first configuration results in a wave with rapidly decaying amplitude as it propagates along a primary chain, while the second configuration results in a solitary wave propagating along the primary chain with no decay. The mechanism to achieve such tunability is by having energy diverted to the granules adjacent to the primary chain in the first case but not the second. The tunable design of the proposed network is validated using both numerical simulations and experiments. In terms of potential applications, the proposed bistable lattice network can be viewed either as a wave attenuator or as a device that allows higher amplitude wave propagation in one direction than in the opposite direction. The lattice is analogous to a crystal phase transformation due to the change in atomic configurations, leading to the change in properties at the macroscale.

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References

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Figures

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Fig. 1

The network of spheres is arranged on an inclined ramp. Gravity alters the lattice network topology between: (a) the downstream configuration, in which side spheres only contact the adjacent downstream axial sphere and (b) the upstream configuration. (c) Cross-sectional view of spheres resting on the Teflon ramp.

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Fig. 2

Close-up of the loading area of the setup illustrating loading ramp, infrared-based velocity measurement system, and confining steel walls

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Fig. 3

Downstream configuration. (a) The arrow indicates the direction of wave propagation through two unit cells. The lateral beads are only in contact with the downstream lateral beads. (b) Embedded sensor at the end of the chain to measure the solitary wave profile; additional beads are placed between the instrumented bead and the support to reduce the interference from reflections.

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Fig. 4

Upstream configuration. (a) Two unit cells, with the arrow indicating the direction of wave propagation. Note that the lateral beads are only in contact with the upstream primary chain beads. (b) Steel support that prevents the chain from rolling. (c) Infrared detector at the end of the chain that measures the output velocity.

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Fig. 5

Upstream configuration. The experimental (symbols) and numerical (solid lines) values show that the output velocity decreases rapidly with increasing side pairs.

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Fig. 6

Energy transferred to side beads. The total energy (solid line) remains constant as the leading wave transfers energy from the axial chain (dot-dashed curves) to the side spheres (dashed curves) when the leading pulse encounters the first, third, and fifth pair of side spheres.

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Fig. 7

Downstream configuration. Experimental (symbols) and numerical (solid line) values of peak forces show that the force experienced at the 18th bead is constant regardless of the number of side pairs.

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Fig. 8

Force and velocity profiles of the upstream configuration. (a) Contact forces on the first and last sphere for different side pairs. As the number of side pairs increases, both the peak force and the wave velocity decrease, but the wave profile associated with the propagating solitary wave remains the same. (b) Velocity of the 15th axial sphere along the chain and the impacting sphere. As the number of side spheres increases, the sphere velocity and wave velocity both decrease.

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Fig. 9

Force and velocity profiles of the downstream configuration. (a) Contact forces on the first and last sphere are independent of the number of side pairs. (b) Velocity of the 15th axial sphere along the chain and the impacting sphere. As the number of side spheres increases, the sphere velocity and wave velocity remain the same as the side spheres do not interact with the propagating wave.

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