Description

Because of their inherent nonlinearity, granular materials have unique stress wave propagation characteristics which make them attractive for a wide range of applications including impact wave resistance systems, acoustic filters, lens, diodes, rectifiers, and so on. This work investigates the design of tunable granular chains for tailoring of impact waves. The system configuration under study consists of a chain of spheres in contact with cylinders placed on either side of the chain. Each cylinder is in contact with two spheres and the system is densely packed and constrained on either side by plane surfaces. From geometry considerations, the diameter ratio between the cylinders and spheres can vary between 0.25 and 1. By moving the plane surfaces toward each other, thus applying a uniform lateral precompression, contact forces are induced between the spheres and cylinders. The presence of these contact forces causes the elastic wave propagation characteristics to be significantly altered when the system is subjected to an axial impact. This property allows to tune the response of the system from a rapidly decaying leading wave to a quasi-solitary wave and thus can be used as a potential tunable energy filter. The system is modeled as a network of point masses connected by nonlinear springs with the stiffness derived from the Hertz contact, assuming elastic interactions. A systematic parametric study is conducted numerically over a wide range of geometric and material properties, and various regimes of behavior related to the nonlinear resonances and antiresonances of the system are identified. The resonances correspond to rapidly decaying waves, whereas the antiresonances result in quasi-solitary leading waves having almost constant amplitude. Their key features are captured by an asymptotic analysis. Finally, their existence is demonstrated experimentally where a system of steel spheres and aluminum cylinders is subjected to low velocity impacts.

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Tunable energy filter by laterally precompression in elastic granular chains

Because of their inherent nonlinearity, granular materials have unique stress wave propagation characteristics which make them attractive for a wide range of applications including impact wave resistance systems, acoustic filters, lens, diodes, rectifiers, and so on. This work investigates the design of tunable granular chains for tailoring of impact waves. The system configuration under study consists of a chain of spheres in contact with cylinders placed on either side of the chain. Each cylinder is in contact with two spheres and the system is densely packed and constrained on either side by plane surfaces. From geometry considerations, the diameter ratio between the cylinders and spheres can vary between 0.25 and 1. By moving the plane surfaces toward each other, thus applying a uniform lateral precompression, contact forces are induced between the spheres and cylinders. The presence of these contact forces causes the elastic wave propagation characteristics to be significantly altered when the system is subjected to an axial impact. This property allows to tune the response of the system from a rapidly decaying leading wave to a quasi-solitary wave and thus can be used as a potential tunable energy filter. The system is modeled as a network of point masses connected by nonlinear springs with the stiffness derived from the Hertz contact, assuming elastic interactions. A systematic parametric study is conducted numerically over a wide range of geometric and material properties, and various regimes of behavior related to the nonlinear resonances and antiresonances of the system are identified. The resonances correspond to rapidly decaying waves, whereas the antiresonances result in quasi-solitary leading waves having almost constant amplitude. Their key features are captured by an asymptotic analysis. Finally, their existence is demonstrated experimentally where a system of steel spheres and aluminum cylinders is subjected to low velocity impacts.