Interaction Dynamics of Elastic Waves with a Complex Nonlinear Scatterer through the Use of a Time Reversal Mirror

This Letter reports on work performed to locate and interrogate a nonlinear scatterer in a linearly elastic medium through the use of a time reversal mirror in combination with nonlinear dynamics. Time reversal provides the means to spatially and temporally localize elastic energy on a scattering feature while the nonlinear dynamics spectrum allows one to determine whether the scatterer is nonlinear (e.g., mechanical damage). Here elastic waves are measured in a solid and processed to extract the nonlinear elastic response. The processed elastic signals are then time reversed, rebroadcast, and found to focus on the nonlinear scatterer, thus defining a time-reversed nonlinear elastic wave spectroscopy process. Additionally, the focusing process illuminates the complexity of the nonlinear scatterer in both space and time, providing a means to image and investigate the origins and physical mechanisms of the nonlinear elastic response.