Relationship between second- and third-order acoustic nonlinear parameters in relative measurement

The higher-order acoustic nonlinear parameters are considered effective damage indices in the field of nondestructive evaluation (NDE). They are defined by using the displacement amplitudes of the fundamental frequency and the harmonics, which are called the absolute nonlinear parameters. Generally, however, it is difficult to measure the very small displacement amplitudes of high-frequency harmonics. Therefore, the simplified parameters using the detected wave signal amplitudes, which are known as the relative nonlinear parameters, have been widely used, although their applications are limited to the relative comparison of before and after damage of a single material under consistent experimental circumstances. In this paper, in order to make clear the concept of relative parameter, we presented first that the relative ratio of the simplified parameters is identical to that of the absolute parameters when the detected signal amplitudes are linearly proportional to the actual displacement amplitudes with respect to the fundamental frequency and the harmonics. In addition, the new relationship between the relative ratio of simplified second-order parameter and the relative ratio of simplified third-order parameter was derived from the relationship between the absolute second- and third-order parameters. This new relationship was successfully verified based on experimental results obtained from Al 6061-T6 processed for different heat treatment times, where it was confirmed in advance that the PZT detection signal amplitudes at the fundamental frequency and its second- and third-order harmonics were linearly proportional to the displacement amplitudes.