  We use experiments, numerical simulations, and theoretical analysis to
investigate the propagation of highly nonlinear solitary waves in periodic
arrangements of dimer (two-mass) and trimer (three-mass) cell structures in
one-dimensional granular lattices. To vary the composition of the fundamental
periodic units in the granular chains, we utilize beads of different materials
(stainless steel, bronze, glass, nylon, polytetrafluoroethylene, and rubber).
This selection allows us to tailor the response of the system based on the
masses, Poisson ratios, and elastic moduli of the components. For example, we
examine dimer configurations with two types of heavy particles, two types of
light particles, and alternating light and heavy particles. Employing a model
with Hertzian interactions between adjacent beads, we find very good agreement
between experiments and numerical simulations. We find equally good agreement
between these results and a theoretical analysis of the model in the
long-wavelength regime that we derive for heterogeneous environments (dimer
chains) and general bead interactions. Our analysis encompasses
previously-studied examples as special cases and also provides key insights on
the influence of heterogeneous lattices on the properties (width and
propagation speed) of the nonlinear wave solutions of this system.
