Envelope correction for shear-longitudinal collinear wave mixing to extract absolute nonlinear acoustic parameters

This paper addresses the effect of the excitation envelope on the generated nonlinear resonant signal (NRS) for collinear wave mixing of shear and longitudinal waves. The aim is to explore how the absolute material nonlinearity can be extracted accurately for any enveloped sinusoidal excitation signal. A finite difference time domain (FDTD) model was built to simulate the effect of input waveforms on the NRS. A change in the measured nonlinearity was seen as the input waveforms were changed from rectangular to Hanning windowed tone burst. The required waveform correction was derived theoretically and validated against the FDTD simulation. Experimental measurements were carried out for different waveforms at several input amplitudes, demonstrating its influence over the NRS. The theoretically derived correction factor, which is required to map the small NRS to the rectangular tone burst resonant amplitude, was validated experimentally. The correction was then used to extract one the fundamental Murnaghan constant (m). Comparatively, Hanning tone burst inputs showed lower variance in the extracted material property due to better control of the frequency bandwidth, relative to that of the transducers. This opens the opportunity to using Hanning windowed tone burst inputs reliably for the measurement of the absolute nonlinearity parameter and m through collinear shear-longitudinal wave mixing.