  Periodic structures can be engineered to exhibit unique properties observed
at symmetry points, such as zero group velocity, Dirac cones and saddle points;
identifying these, and the nature of the associated modes, from a direct
reading of the dispersion surfaces is not straightforward, especially in
three-dimensions or at high frequencies when several dispersion surfaces fold
back in the Brillouin zone. A recently proposed asymptotic high frequency
homogenisation theory is applied to a challenging time-domain experiment with
elastic waves in a pinned metallic plate. The prediction of a narrow
high-frequency spectral region where the effective medium tensor dramatically
switches from positive definite to indefinite is confirmed experimentally; a
small frequency shift of the pulse carrier results in two distinct types of
highly anisotropic modes. The underlying effective equation mirrors this
behaviour with a change in form from elliptic to hyperbolic exemplifying the
high degree of wave control available and the importance of a simple and
effective predictive model.
