Imaging non-classical elastic nonlinearities using reciprocal time reversal and phase symmetry analysis

In this research work, an imaging method of the nonlinear signature in a reverberant complex anisotropic structure with hysteretic behaviour is reported. The proposed technique relies on a combination of phase symmetry analysis with frequency modulation excitation and nonlinear time reversal, and it is applied to a number of waveforms containing the nonlinear impulse responses of the medium. Phase symmetry analysis was used to characterize the third order nonlinearity of the structure due to delamination and cracks, by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only two sensors in pitch-catch mode, was used to "illuminate" the damage. Taking advantage of multiple linear scattering, this methodology allows achieving the optimal focalization at the nonlinear source by a compensation of the distortion effects in a dissipative medium. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel undergone to low-velocity impact loading. The nonlinear source was retrieved with a high level of accuracy with little computational time (less than 1 sec). Its minimal processing requirements make this method a valid alternative to the traditional nonlinear elastic wave spectroscopy techniques for materials showing either classical or non-classical nonlinear behaviour.