Theoretical investigation of nonlinear ultrasonic wave modulation spectroscopy at crack interface

• Crack described by a model combining classical and hysteretic nonlinearity.
• Spectral analysis on quasistatic response to two-frequency excitation was performed.
• General description of hysteretic response is based on amplitude and frequency ratios.
• Method of hysteretic parameter extraction from combined model response is proposed.

This paper studies theoretical results of a nonlinear ultrasonic method based on interaction of two elastic waves of different frequencies. A virtual Nonlinear Wave Modulation Spectroscopy experiment is performed in the vicinity of a crack described by a model combining classical and hysteretic nonlinearity. Quasistatic response to two frequency excitation was computed and harmonic and intermodulation components were studied. The influence of driving signal parameters and nonlinear parameters on the response is thoroughly discussed. A general way of hysteretic response description based on scaling properties is explained. In case of the combined nonlinear model, an analysis of nonlinear spectral components is performed in complex plane. Based on the complex interaction of classical and hysteretic parts, a method of their separation is proposed.