### Abstract

We report on a countable infinity of traveling solitary waves in a class of highly heterogeneous ordered one-dimensional granular media, in particular, granular dimers composed of an infinite number of periodic sets of heavy elastic spherical beads in contact with N light ones; these media are denoted as 1: N granular dimers. Perfectly elastic Hertzian interaction between beads is assumed and no dissipative forces are taken into account in our study; moreover, zero pre-compression is assumed, rendering the dynamics strongly nonlinear through complete elimination of linear acoustics from the problem. After developing a general asymptotic methodology for the 1: N granular dimer, we focus on the case N _{2} and prove numerically and asymptotically the existence of a countable infinity of traveling solitary waves in the 1:2 dimer chain. These solitary waves, which can be regarded as anti-resonances in these strongly nonlinear media, are found to be qualitatively different than those previously studied in homogeneous and 1:1 dimer chains (i.e., composed of alternating heavy and light beads) which possess symmetric velocity waveforms. In contrast, for traveling solitary waves in 1:2 dimers, the velocity waveforms of the responses of the heavy beads are symmetric, whereas those of the light beads are non-symmetric. Interestingly, we show that no such solitary waves can be realized in general 1: N granular dimers with N > 2, although near-solitary waves can exist in these systems based on slow-fast frequency approximations.

Original language | English (US) |
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Article number | 034908 |

Journal | Journal of Applied Physics |

Volume | 112 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1 2012 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Journal of Applied Physics*,

*112*(3), [034908]. https://doi.org/10.1063/1.4740060