  Mathematical modeling of resonant waves propagating in 2D periodic infinite
lattices is conducted. Rectangular-cell, triangular-cell and hexagonal-cell
lattices are considered. Eigenvalues (here eigenfrequencies) of steady-state
problems are determined, and dispersion properties of free waves are described.
We show that the frequency spectra of the models possess several resonant
points located both at the boundary of pass/stop bands and in the interior of a
pass band. Boundary value problems with a local monochromatic source are
explored, and peculiarities of resonant waves are revealed. Asymptotic
solutions are compared with the results of computer simulation. Special
attention is given to line-localized primitive waveforms at the resonance
frequencies and to the wave beaming phenomena at a resonant excitation.
