Traveling waves in trimer granular lattice II: Asymptotic prediction of weakly attenuated pulses

In the present study we consider the impulsive response of perfectly aligned, uncompressed, tri-atomic (trimer) granular lattice. In this study, we demonstrate that under particular choice of the system parameters - impulsively loaded, trimer granular lattice can support formation of highly localized, weakly attenuated pulses. These pulses are manifested by the completely non-symmetric wave profiles and can be attributed to the special family of solitary like waves forming in the non-homogenous, periodic trimer granular lattice in the state of acoustic vacuum. Using the recently developed analytical procedure based on the singular, multi-scale perturbation analysis, we derive a simplified reduced order model predicting the special regions in the space of the system parameters corresponding to the formation of the weakly attenuated pulses. Predictions of the asymptotical model are found to be in very good agreement with the results of numerical simulations of the full trimer granular lattice. From a practical point of view, these results can have important implications in complex, structural optimization problems of wave manipulation in the repetitive granular metamaterials.