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

Abstract

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.

E. Cartan’s and A. Connnes’ Supersymmetry and Differences of Understanding Physical Phenomena

“…A superposition of a non linear sound wave and time reversed non-linear sound wave can reduce improper superposition of lobes around the proper peak produced by a superposition of reflected waves [19][20][21][22][23][24]38]. …”

Nonlinear Time Reversal Tomography of Structural Defects

“…This procedure requires measurement of inter-element response matrices for excitations necessary for ESAM application (Eqs (6-9)). From these matrices K (E) (t), K (A) (t), K (B1) (t) and K (B2) (t), the nonlinear terms corresponding to each trajectory |T k R m | are extracted according to Eqs (13)(14)(15). Matrices K (1) (t), K (2) (t) and K (3) (t) are obtained on which DORT is applied, as described previously.…”

“…For the extraction of nonlinear parameters corresponding to the scatterers S 1 and S 2 , DORT is applied on the separated nonlinear terms of direct responses provided by ESAM (Eqs (13)(14)(15)). This procedure requires measurement of inter-element response matrices for excitations necessary for ESAM application (Eqs (6-9)).…”

“…Using all synergy aspects of Symmetry Analysis (TR, reciprocity, ESAM, chirp-coded ESAM, etc.) and NEWS, TR-NEWS concepts [3,15] is recognized as extremely reliable [11]. In this paper, the straightforward ESAM-DORT technique is proposed.…”

A high amplitude, time reversal acoustic non-contact excitation (trance)

“…[1][2][3][4] They have been proven to be far more sensitive to early damage than standard linear acoustic techniques such as C-scans, time of flight, etc. Unfortunately, nonlinear techniques often require high amplitude waves to be generated within the sample.…”