  We study the flexural wave modes existing in finite stacks of gratings
containing rigid, zero-radius pins. We group the modes into even and odd
classes, and derive dispersion equations for each. We study the recently
discovered EDIT (elasto-dynamically inhibited transmission) phenomenon, and
relate it to the occurrence of trapped waves of even and odd symmetries being
simultaneously resonant. We show how the EDIT interaction may be steered over a
wide range of frequencies and angles, using a strategy in which the
single-grating reflectance is kept high, so enabling the quality factors of the
even and odd resonances to be kept large.
