Two Kinds of Localized Oscillating Modes in Strongly Nonlinear Hertzian Chains with Defect

We study mechanical energy localization, which has been experimentally observed by Job Phys. Rev. E 80 (2009) 025602(R), using computer simulations and the binary-collision approximation. We find interactions of a solitary wave with a light intruder exciting two kinds of localized modes. One is visible in the tail of the incident impulse, and the other is observed when the defect is loaded by the solitary wave. The frequency of localized oscillations is analytically obtained and is in excellent agreement with the numerical results.