Resonance and Anti-Resonance phenomenon in Granular Dimer Chains with no Pre-Compression

It is a well known fact that many interesting phenomena in the theory of waves in nonlinear lattices, e.g., the significant reduction of the amplitude of a propagating primary pulse or the essential growth of the phase velocity, may be explained in terms of various resonant mechanisms existing in the system (e.g. Frankel-Kontorova model). Recently, we have demonstrated analytically and numerically that similar resonant mechanisms also exist in periodically disordered granular chains with no pre-compression. Moreover, these mechanisms are responsible for the aforementioned phenomena of intensive pulse attenuation as well as speeding up of solitary waves in periodic granular chains. In our studies we have considered regular dimer chains consisting of pairs of ‘heavy ’ and ‘light’ beads with no pre compression and with elastic Hertzia