  Significant amplitude-independent and passive non-reciprocal wave motion can
be achieved in a one dimensional (1D) discrete chain of masses and springs with
bilinear elastic stiffness. Some fundamental asymmetric spatial modulations of
the bilinear spring stiffness are first examined for their non-reciprocal
properties. These are combined as building blocks into more complex
configurations with the objective of maximizing non-reciprocal wave behavior.
The non-reciprocal property is demonstrated by the significant difference
between the transmitted pulse displacement amplitudes and energies for
incidence in opposite directions. Extreme non-reciprocity is realized when
almost-zero transmission is achieved for the propagation from one direction
with a noticeable transmitted pulse for incidence from the other. These models
provide the basis for a class of simple 1D non-reciprocal designs and can serve
as the building blocks for more complex and higher dimensional non-reciprocal
wave systems.
