  The dispersive wave propagation in a periodic metamaterial with tetrachiral
topology and inertial local resonators is investigated. The Floquet-Bloch
spectrum of the metamaterial is compared with that of the tetrachiral beam
lattice material without resonators. The resonators can be designed to open and
shift frequency band gaps, that is, spectrum intervals in which harmonic waves
do not propagate. Therefore, an optimal passive control of the frequency band
structure can be pursued in the metamaterial. To this aim, a suitable
constrained nonlinear optimization problem on a compact set of admissible
geometrical and mechanical parameters is stated. According to functional
requirements, the particular set of parameters which determines the largest
low-frequency band gap between a pair of consecutive branches of the
Floquet-Bloch spectrum is obtained. The optimization problem is successfully
solved by means of a version of the method of moving asymptotes, combined with
a quasi-Monte Carlo multi-start technique.
