  By applying an unrestriced Hartree-Fock approximation and a Random Phase
approximation to multiband Peierls-Hubbard Hamiltonians, we determine the
phonon mode structure in models of transition metal oxides in the presence of
intrinsic nanoscale inhomogeneities induced by hole doping. We identify low
frequency $local$ vibrational modes pinned to the interface between regions of
distinct electronic structure and separated in frequency from the band of
extended phonons. A major characteristic of these ``edge'' modes is that their
energy is essentially insensitive to the doping level, while their intensity
increases with the density of interfaces (and thus doping level). We argue that
the presence of such modes is a typical feature of systems with phase
separation, including cuprates, nickelates, manganites, and bismuthates. We
specifically address the experimental signatures of these modes in lattice
inelastic neutron scattering.
