  We investigate non-reciprocal wave propagation in spatiotemporal phononic
plates. In particular, the first goal of this manuscript is to present a
general formulation of the Plane Wave Expansion Method (PWEM) that, in contrast
with previous works, is applicable to any class of 2D spatiotemporal unit cells
whose properties can be expanded in traveling plane waves. The second goal is
to exploit this analysis tool in order to study a new class of materials
capable of violating mirror symmetry in momentum space, therefore breaking
reciprocity principle along different wave propagation directions. This is
obtained by considering the plate elastic properties to be discretely modulated
in space and continuously in time. Theoretical dispersion profiles are
validated and compared with numerical simulations.
