  Longitudinal wave propagation is considered in a pair of waveguides connected
by bilinear spring systems. The nature of the nonlinearity causes the
compressive and tensile force-displacement relations of the bilinear spring to
behave in a piece-wise linear manner, and all transmitted and reflected waves
scale linearly with the incident wave amplitude. We first concentrate on a
single bilinear spring connecting two waveguides. By controlling the bilinear
stiffness parameters it is possible to convert a time harmonic incident wave
into a transmitted wave of the same period but with particle displacement of a
single sign, positive or negative, an effect we call unilateral transmission.
Nonreciprocal wave phenomena are obtained by introducing spatial asymmetry. A
simple combination of a single bilinear spring with a mass and a linear spring
shows significant nonreciprocity with transmission relatively high in one
direction and low in the opposite direction.
