Nonlinear reverberation spectroscopy with phase-sensitive superheterodyne reception

A technique is presented for determining elastic nonlinearity of materials from resonant frequency shifts as a function of signal amplitude during free vibrational decay after tone burst excitation. The technique differs from previous nonlinear reverberation spectroscopy (NRS) techniques in that it employs phase-sensitive superheterodyne reception. Time-dependent amplitudes of in-phase and out-of-phase components of signals, relative to a reference sinusoid at the excitation frequency, are provided through analog hardware processing in the absence of digitization of the signal from the vibrational sensor. The time-dependent phase and amplitude of the signal are determined through software analysis of these in-phase and out-of-phase components, and the instantaneous frequency during free decay is then determined from the time derivative of the phase. With this approach, superheterodyne reception and low-pass filtering of the phase-detector outputs lead to a great reduction in noise and computation effort, relative to direct digitization and software processing of the sensor signal, while retaining information on frequency shifts on a relevant time scale during ringdown. As with other NRS techniques, rapid acquisition of data on amplitude dependence of the resonant frequency during ringdown leads to minimization of systematic errors from temperature drift. The technique is demonstrated with noncontacting electromagnetic-acoustic transduction on custom alloyed Al (0.2 at.% Zn) and commercial Al 7075 cylinders with axial-shear resonant frequencies between 658 kHz and 659 kHz. The precision of measurements of relative frequency shifts is found to be on the order of 0.1 parts per million (ppm), exceeding by two orders of magnitude the best reported precision of nonlinear resonant ultrasound spectroscopy (NRUS).