  The motive of this work is to understand the complex spatial characteristics
of finite-amplitude elastic wave propagation in periodic structures and
leverage the unique opportunities offered by nonlinearity to activate
complementary functionalities and design adaptive spatial wave manipulators.
The underlying assumption is that the magnitude of wave propagation is small
with respect to the length scale of the structure under consideration, albeit
large enough to elicit the effects of finite-deformation. We demonstrate that
the interplay of dispersion, nonlinearity and modal complexity involved in the
generation and propagation of higher harmonics gives rise to secondary wave
packets that feature multiple characteristics, one of which conforms to the
dispersion relation of the corresponding linear structure. This provides an
opportunity to engineer desired wave characteristics through a geometric and
topological design of the unit cell, and results in the ability to activate
complementary functionalities, typical of high frequency regimes, while
operating at low frequencies of excitation - an effect seldom observed in
linear periodic structures. The ability to design adaptive switches is
demonstrated here using lattice configurations whose response is characterized
by geometric and/or material nonlinearities.
