The complexity of harmonically scattered nonlinear waves from triangular, circular, and rectangular corners of the 2-D domain

Abstract

Considering recent advancements in the nonlinear pulse-echo technique, understanding reflected nonlinear waves from inaccessible edges and surfaces becomes important. A unique geometrical model solved numerically using the finite element method is proposed and studied via extensive numerical experiments to gain insight into harmonically scattered waves from different shapes of the 2-D spaced corners considering the challenges of theoretical solutions that can capture the interplay between multiple phenomena. Tang et al. (2012), Kube (2017-18), and Achenbach and Wang (2017-18) studied the harmonic scattering of waves from nonlinear inclusions using analytical techniques. Linear longitudinal waves scattered from the triangular, circular, and rectangular-shaped free and fixed edges of the 2-D spaced corner show mode conversion and energy transfer between bulk wave modes at fundamental frequencies. The interaction of nonlinear ultrasonic waves with the edges makes things complex due to an interplay between harmonic generation, linear scattering, harmonic scattering, bulk wave mode conversion, and harmonic energy redistribution between all harmonics of the scattered longitudinal and transverse waves. This results in non-intuitive interesting responses. These studies are extended to explore one-way and two-way two-wave mixing of longitudinal waves and their interesting nonlinear effects. Phase difference introduced during harmonic scattering distinguishes the sensitivity of fundamental harmonics.