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Propagation of primary pulse through an un-compressed granular chain subjectto external on-site perturbation is studied. Analytical procedure predictingthe evolution of the primary pulse is devised for the general form of theon-site perturbation applied on the chain. The validity of the analytical modelis confirmed with several specific granular setups such as, chains mounted onthe nonlinear elastic foundation, chains perturbed by the dissipative forces aswell as randomly perturbed chains. Additional interesting finding made in thepresent study corresponds to the chains subject to a special type ofperturbations including the terms leading to dissipation and those acting as anenergy source. It is shown in the study that application of such perturbationmay lead to formation of stable stationary shocks acting as attractors for theinitially unperturbed, propagating Nesterenko solitary waves. Interestinglyenough the developed analytical procedure provides an extremely closeestimations for the amplitudes of these stationary shocks as well as predictszones of their stability. In conclusion we would like to stress that thedeveloped analytical model have demonstrated spectacular correspondence to theresults of direct numerical simulations for all the setups considered in thestudy.

Evolution of the Primary Pulse in 1D Granular Crystals Subject to On-Site Perturbations: Analytical Study