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

Unilateral and nonreciprocal transmission through bilinear spring systems