Vibration localization in multi-coupled and multi-dimensional near-periodic structures

The vibration localization of multi-coupled 2-D and 3-D lattices are parametrically investigated. The lattices are made of slightly randomly disordered masses embedded in an elastic medium, the nearest-neighbor interaction potential of the lattices gives rise to the weak central and angular coupling forces within neighboring masses of each mass. It is observed that the first normal mode of a 2-D lattice has a strong tendency to localize. Both free and forced vibration localization due to random mass disorder exist, but are otherwise abated with the increase of the dimension of the lattices. Disorder also tends to increase energy leakage from one degree-of-freedom to another degree-of-freedom at the vibration localization sites.