Nonlinear elastic imaging using reciprocal time reversal and third order symmetry analysis

This paper presents a nonlinear imaging method for the detection of the nonlinear signature due to impact damage in complex anisotropic solids with diffuse field conditions. The proposed technique, based on a combination of an inverse filtering approach with phase symmetry analysis and frequency modulated excitation signals, 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 by exploiting its invariant properties with the phase angle of the input waveforms. Then, a "virtual" reciprocal time reversal imaging process, using only one broadcasting transducer and one receiving transducer, was used to insonify the defect taking advantage of multiple linear scattering as mode conversion and boundary reflections. The robustness of this technique was experimentally demonstrated on a damaged sandwich panel, and the nonlinear source, induced by low-velocity impact loading, was retrieved with a high level of accuracy. 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 behavior.