  We investigate periodic optomechanical arrays as reconfigurable platforms for
engineering the coupling between multiple mechanical and electromagnetic modes
and for exploring many-body phonon dynamics. Exploiting structural resonances
in the coupling between light fields and collective motional modes of the
array, we show that tunable effective long-range interactions between
mechanical modes can be achieved. This paves the way towards the implementation
of controlled phononic walks and heat transfer on densely-connected graphs as
well as the coherent transfer of excitations between distant elements of
optomechanical arrays.
