Bandgaps in two-dimensional high-contrast periodic elastic beam lattice materials

We consider elastic waves in a two-dimensional periodic lattice network of Timoshenko-type beams. We show that for general configurations involving certain highly-contrasting components a high-contrast modification of the homogenization theory is capable of accounting for bandgaps, explicitly relating those to low resonant frequencies of the `soft' components. An explicit example of a square-periodic network of beams with a single isolated resonant beam within a periodicity cell is considered in detail.