Abstract
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 piecewise 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.
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