  We propose a method for manipulating wave propagation in phononic lattices by
employing local vibro-impact (VI) nonlinearities to \textit{scatter} energy
across the underling linear band structure of the lattice, and
\textit{transfer} energy from lower to higher optical bands.Inspired by recent
developments in the field of nonlinear targeted energy transfer (TET) using
\textit{non-resonant} energy exchanges, we achieve this using spatially
localized VI forces that redistribute energy across the linear spectrum of the
lattice in a non-resonant fashion.First, a 1-dimensional (1D), 2-band phononic
lattice with embedded VI unit cells is computationally studied to demonstrate
that energy is scattered in the wavenumber domain, and this nonlinear
scattering mechanism depends on the energy of the propagating wave. Next, a
4-band lattice is studied with a similar technique to demonstrate the concept
of inter-band targeted energy transfer (IBTET) and to establish analogous
scaling relations with respect to energy. To interpret the results of IBTET, we
study the nonlinear normal modes (NNMs) of a reduced order model (ROM) of the
VI unit cell in the 4-band lattice, using the method of numerical continuation.
Interestingly, the slope of the frequency-energy branches of the ROM
corresponding to the 1:1 resonance NNM matches remarkably well with the
dependence of IBTET to input energy in the 4-band lattice. Moreover, relations
between the dynamics of the VI lattice and the NNMs of the underlying
Hamiltonian system provide physical interpretations for the relative energy
transfers.
