Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: Upstream configuration. The experimental (symbols) and numerical (solid lines) values show that the output velocity decreases rapidly with increasing side pairs.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: 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.

Date of download: 10/12/2017 Copyright © ASME. All rights reserved. From: Tunable Wave Propagation in Granular Crystals by Altering Lattice Network Topology J. Eng. Mater. Technol. 2016;139(1):011005-011005-7. doi:10.1115/1.4034820 Figure Legend: Close-up of the loading area of the setup illustrating loading ramp, infrared-based velocity measurement system, and confining steel walls