Targeted energy transfers and passive acoustic wave redirection in a two-dimensional granular network under periodic excitation

We study passive pulse redirection and nonlinear targeted energy transfer in a granular network composed of two semi-infinite, ordered homogeneous granular chains mounted on linear elastic foundations and coupled by weak linear stiffnesses. Periodic excitation in the form of repetitive half-sine pulses is applied to one of the chains, designated as the “excited chain,” whereas the other chain is initially at rest and is regarded as the “absorbing chain.” We show that passive pulse redirection and targeted energy transfer from the excited to the absorbing chain can be achieved by macro-scale realization of the spatial analog of the Landau-Zener quantum tunneling effect. This is realized by finite stratification of the elastic foundation of the excited chain and depends on the system parameters (e.g., the percentage of stratification) and on the parameters of the periodic excitation. Utilizing empirical mode decomposition and numerical Hilbert transforms, we detect the existence of two distinct nonlinear phenomena in the periodically forced network; namely, (i) energy localization in the absorbing chain due to sustained 1:1 resonance capture leading to irreversible pulse redirection from the excited chain, and (ii) continuous energy exchanges in the form of nonlinear beats between the two chains in the absence of resonance capture. Our results extend previous findings of transient passive energy redirection in impulsively excited granular networks and demonstrate that steady state passive pulse redirection in these networks can be robustly achieved under periodic excitation.