Pulse propagation in decorated granular chains: An analytical approach

Abstract

We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E in print (2009); Phys. Rev. E {\bf 69}, 037601 (2004)]

10 pages and 12 figures

References in corpus (4)

• How Hertzian solitary waves interact with boundaries in a 1-D granular medium
• Solitary wave trains in granular chains: Experiments, theory and simulations
• Pulse propagation in tapered granular chains: An analytic study
• Short Pulse Dynamics in Strongly Nonlinear Dissipative Granular Chains

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• Periodic Travelling Waves in Dimer Granular Chains
• Scattering of Waves by Impurities in Precompressed Granular Chains
• Binary collision approximation for multi-decorated granular chains
• Traveling Waves in 2D Hexagonal Granular Crystal Lattices