  The lattice dynamic properties and spin-phonon coupling in DyMn$_2$O$_5$ are
studied by using the density-functional theory. The calculated phonon
frequencies are in very good agreement with experiments. We then compare the
phonon modes calculated from different spin configurations. The results show
that the phonon frequencies change substantially in different spin
configurations, suggesting that the spin-phonon coupling in this material is
very strong. Especially, the short range spin ordering has drastic effects on
the highest Raman and IR phonon modes that might be responsible for the
observed phonon anomalies near and above the magnetic phase transitions.
