Abstract:

The reflected fundamental and second harmonic sound fields of finite amplitude are studied based on the quasilinear theory, and they are presented as the combinations of pure plane wave solutions, attenuation corrections and diffraction corrections with multi-Gaussian beams model. A modified equation for calculating nonlinear parameter using pulse-echo method is derived. These second harmonic components reflected from a stress-free interface at normal incidence are simulated, and the results show that the total second harmonic components will be reduced as the reflected component and the new generated one have inverse phases. However, it is found that when the thickness of the sample is larger than 1/2 of the Rayleigh distance, the pulse-echo method can be used to determine the nonlinear parameter as the transducer can receive effective total second harmonic components. The nonlinear parameter of Al-6061 sample is measured experimentally using pulse-echo method, and the measured value with consideration of diffractions and attenuations is close to that from pitch-catch method, which verifies the proposed method. Compared with pitch-catch method, the pulse-echo method is less limited by the experiment setup and it provides a useful tool to determine the nonlinear parameters of solids.

Key words: diffraction and attenuation corrections, multi-Gaussian beam model, nonlinear parameter of longitudinal wave, Ultrasonic pulse-echo method