<p style="text-align: justify">Theories and experiments related to the measurement of quadratic nonlinear parameters capable of evaluating the degree of damage or nonlinear material properties through the generation and measurement of second harmonics are relatively well established. In contrast, measurement of cubic nonlinear parameters using third harmonics is limited to relative measurement, and theories and experiments for absolute measurement have not been well developed. This paper deals with the theoretical aspects for accurately measuring cubic nonlinear parameters using third harmonics in isotropic materials. First, the amplitude of the third harmonic is obtained by applying the perturbation solution to the displacement-based wave equation, and the nonlinear parameter formula is defined. Since the amplitude of the ultrasonic wave actually measured deviates from the plane wave due to diffraction and attenuation, corrections of these effects are required. The attenuation and diffraction corrections are obtained from the multi-Gaussian beam model based on the integral solutions for the three-dimensional Westervelt equation. We present a formula for the cubic nonlinear parameter corrected for diffraction and attenuation. Harmonic generation measurements have been conducted to obtain the cubic nonlinear parameter as well as the quadratic nonlinear parameter. The theoretical relationship between these two parameters was confirmed through experiments and the possible application area will be proposed.</p>

Theoretical and Experimental Study of the Cubic Nonlinear Parameter for Metallic Materials

Paper Proceedings: https://asmedigitalcollection.asme.org/qnde/QNDE2021/volume/85529

ASME 2021 48th Annual Review of Progress in Quantitative Nondestructive Evaluation (QNDE2021)

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