  We study pulse propagation in one-dimensional chains of spherical granules
decorated with small randomly-sized granules placed between bigger monodisperse
ones. Such "designer chains" are of interest in efforts to control the behavior
of the pulse so as to optimize its propagation or attenuation, depending on the
desired application. We show that a recently proposed effective description of
simple decorated chains can be extended to predict pulse properties in chains
decorated with small granules of randomly chosen radii. Furthermore, we also
show that the binary collision approximation can again be used to provide
analytic results for this system.
