  We study frequency conversion in nonlinear mechanical lattices, focusing on a
chain of magnets as a model system. We show that by inserting mass defects at
suitable locations, we can introduce localized vibrational modes that
nonlinearly couple to extended lattice modes. The nonlinear interaction
introduces an energy transfer from the high-frequency localized modes to a
low-frequency extended mode. This system is capable of autonomously converting
energy between highly tunable input and output frequencies, which need not be
related by integer harmonic or subharmonic ratios. It is also capable of
obtaining energy from multiple sources at different frequencies with a tunable
output phase, due to the defect synchronization provided by the extended mode.
Our lattice is a purely mechanical analog of an opto-mechanical system, where
the localized modes play the role of the electromagnetic field, and the
extended mode plays the role of the mechanical degree of freedom.
