  We investigate elastic-wave propagation in a spatially-dispersive
multilayered, totally passive metamaterial system. At oblique incidence a
longitudinal (acoustic) wave can convert to transverse in the solid material
comprising the layers, but when the incident wave enters the multilayer from a
solid as opposed to a liquid medium, the incident transverse component
supported by the solid medium indirectly causes the longitudinal transmission
response to be greatly modified and similarly for the transverse wave exiting
the multilayer into a solid medium in response to an incident longitudinal
wave. The conversion between longitudinal and transverse waves is found to lead
to the emulation of a characteristic non-reciprocal phenomenon at some
frequencies: a directionality in the transmission response, sometimes
simultaneously with the reflection response. The directionality can be
exploited for example in the construction of antiseismic structures or
breakwater structures. The inclusion of gain/loss elements can strongly enhance
the directionality. Periodicity-breaking defects can cause a great variability
in the response, enabling the use of devices based on this phenomenon as
sensors.
