Modeling and simulation of backward combined harmonic generation induced by one-way mixing of longitudinal ultrasonic guided waves in a circular pipe.

Nonlinear guided wave has been recognized as a potential means to characterize the state of material microstructures in solids. However, nonlinear guided wave approaches based on second harmonic generation or combined harmonic generation induced by counter-directional wave mixing, are applicable only under the condition that transmitters and receivers are placed at two different ends of the tested structures. These approaches are not effective for characterization of the structures with only one accessible end. In this paper, modeling of the backward combined harmonic at difference frequency induced by one-way mixing of two primary co-directional guided waves is investigated in a circular pipe, where the transmitters and receivers are placed at the same end of the pipe. The backward combined harmonic, generated at difference frequency and propagating in the direction opposite to that of two primary co-directional guided waves, is successfully observed numerically. A strong frequency mixing response characterized by a cumulative growth effect of the generated backward combined harmonic is demonstrated. The use of the generated backward combined harmonic for localized material degradation characterization and location is numerically examined in the given pipe. The obtained results indicate that the use of the backward combined harmonic can locate and characterize the localized material degradations in the given pipe by controlling the mixing zone of two primary co-directional guided waves. This study provides a promising means for characterization of localized degradations in pipes.