Some Exceptional Features of Flexural Wave Scattering by a Cluster of Nonlinear Scatterers on a Beam

Abstract

The scattering of flexural waves on a beam can be manipulated by adding scatterers to it in the form of point attachments. A number of special scattering properties have previously been presented when only the linear properties of the scatterers are considered, such as asymmetric total reflection and asymmetric total absorption. More recently, scatterer clusters which also account for nonlinear properties of the attachments have been proposed, analyzed and simulated, using an analytical scheme based on perturbation theory. These models have predicted further exceptional features of scattering response which are not possible with only linear scatterers, such as non-reciprocal transmission and energy transfer to different frequency bands. In this paper, the established perturbation methodology is used to analyze the reflection and transmission coefficients for two different special configurations of scatterer clusters. The analytical results are also validated with those from Finite Element models. The particular characteristics of the scattering behavior of each configuration are highlighted. The potential for exploiting the exceptional response characteristics of such nonlinear scatterer clusters for applications is also briefly discussed.