Unilateral and nonreciprocal transmission through bilinear spring systems

TL;DR

This paper investigates how bilinear spring systems can enable unilateral and nonreciprocal wave transmission in waveguides, demonstrating controllable wave directionality and significant nonreciprocity through simple nonlinear structures.

Contribution

It introduces a novel approach to achieve unilateral and nonreciprocal wave transmission using bilinear springs, highlighting the effects of nonlinearity and spatial asymmetry.

Findings

Bilinear springs can convert harmonic waves into unidirectional signals.

Spatial asymmetry induces nonreciprocal wave transmission.

Simple bilinear spring-mass systems exhibit high nonreciprocity.

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 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.