The viscous damping of fracton vibrations in 2D percolation clusters i
s computed. It is found that the anomalous damping is due to the local
irregular distribution of the vibration amplitudes. There exists a lo
calization of the damping within the usual localization of fractons. T
his effect is strongly enhanced by nonlinear dissipation. This is the
first evidence of the damping power of fractal structures.