  In this paper, the 2D band structure of a mixed-mode metamaterial resonator
array for in-plane waves is investigated. The band structure in the interior
and on the boundary of the irreducible Brillouin zone as well as 1D dispersion
diagrams for different propagation angles are calculated numerically and
presented. Additionally, a reduced order analytical method is established to
compare and approximate the band structure. The studied metamaterial, with a
T-shaped cantilever beam as resonator in its square array repeating unit cells,
exhibits branches with mixed P and SV waves except at exactly one angle of
propagation. This paper also reports on the occurrence of avoided level
crossings, which are related to the existence of exceptional points in the
complex domain. A reduced order analytical approach is used that can generate
partial (low branches) band structure with relatively little computational
effort. The reduced order model agrees well with the numerical results for
these low branches and can provide support in mode identification and band
sorting. With proper adjustments in parameters, this analytical method will be
applicable for other metamaterials that have similar unit cell structure.
