Non-symmetric flexural wave scattering and one-way extreme absorption

Abstract

The possibility of asymmetric absorption and reflection for flexural waves is demonstrated though analytical and numerical examples. We focus on the 1D case of flexural motion of a beam and consider combinations of point scatterers which together provide asymmetric scattering. The scatterers are attached damped oscillators characterized by effective impedances, analogous to effective configurations in 1D acoustic waveguides. By selecting the impedances of a pair of closely spaced scatterers we show that it is possible to obtain almost total absorption for incidence on one side, with almost total reflection if incident from the other side. The one-way absorption is illustrated through numerous examples of impedance pairs that satisfy the necessary conditions for zero reflectivity for incidence from one direction. Examples of almost total and zero reflection for different incidences are examined in detail, showing the distinct wave dynamics of flexural waves as compared with acoustics.