  The bulk-boundary or bulk-edge correspondence is a principle relating surface
confined states to the topological classification of the bulk. By combining
non-Hermitian ingredients in terms of gain or loss with media that violate
reciprocity, an unconventional non-Bloch bulk-boundary correspondence leads to
unusual localization of bulk states at boundaries$-$a phenomenon coined
non-Hermitian skin effect. Here we \textcolor{black}{numerically} employ the
acoustoelectric effect in electrically biased and layered piezophononic media
as a solid framework for non-Hermitian and nonreciprocal topological mechanics
in the MHz regime. Thanks to a non-Hermitian skin effect for mechanical
vibrations, we find that the bulk bands of finite systems are highly sensitive
to the type of crystal termination, which indicates a failure of using
traditional Bloch bands to predict the wave characteristics. More surprisingly,
when reversing the electrical bias, we unveil how topological edge and bulk
vibrations can be harnessed either at the same or opposite interface. Yet,
while bulk states are found to display this unconventional skin effect, we
further discuss how in-gap edge states in the same instant, counterintuitively
are able to delocalize along the entire layered medium. We foresee that our
predictions will stimulate new avenues in echo-less ultrasonics based on exotic
wave physics.
