Determining Material Parameters with Resonant Acoustic Spectroscopy

While material parameters are fairly well known for conventional solids, more variability occurs with materials produced by additive manufacturing. A method is described to determine these parameters from the unique vibrational resonance-response spectra, which can be measured experimentally and predicted by simulations. The experimental spectra, obtained by excitation of the component with a piezo-electric transducer and measurement with a laser Doppler vibrometer, are defined by the actual values of material parameters although only some of the resonance modes are captured in any particular measurement. On the other hand, the simulated spectra, predicted by finite element analysis based on the CAD file of the part, contain all possible vibration peaks, but their specific frequencies, unlike the experimental values, depend on the assumed values of the material parameters. Thus, the two sets contain different number of peaks and are measured on two differently-scaled frequency scales. The main re-scaling factor is the ratio of elasticity to density, and a nonlinear least squares regression that maximizes the correlation between the two sets of peaks yields the optimal pairwise assignment. A linear regression over pairwise-assigned peaks yields the Young's modulus that gives the best match between the two spectra. Unlike the elasticity, the Poisson's ratio affects different modes differently, and inaccuracies in the Poisson ratio lead to increased deviations from linearity in the experiment vs. simulations regression, and maximization of the correlation coefficient yields the best-fitting value of the Poisson ratio as well. The accuracy, sources of errors, and potential limitations are discussed.