A resonant frequency retrieving method for low Q-factor materials based on resonant ultrasound spectroscopy

Shear and longitudinal attenuations and quality factors of poly(methyl metacrylate) (PMMA) from 20 kHz to 12 MHz investigation with ultrasonic spectroscopy

PMMA is often considered as a calibration material for experimental benches dedicated to viscoelasticity investigation. Nevertheless, regarding literature, data concerning attenuation coefficients and quality factors are essentially available in the MHz frequency range and results in the low-frequency range are scarce and scattered. In this communication, thanks to the use of high-frequency ultrasonic spectroscopy between 2 and 8 MHz in the range 6 °C - 45 °C, Time-Temperature Superposition principle and Resonant Ultrasonic Spectroscopy (RUS), we show that both longitudinal and shear quality factors of PMMA decrease considerably for low frequencies (<MHz), and that the classically accepted linear laws describing attenuation as a function of frequency are valid only beyond several MHz. This variation is attributed to secondary relaxation processes such as γ relaxation considering the activation energy deduced from experimental data. Power laws are proposed to describe the evolution of quality factors and attenuation coefficients versus frequency in the 20 kHz - 12 MHz range.

Inverse Problem in Resonant Ultrasound Spectroscopy With Sampling and Optimization: A Comparative Study on Human Cortical Bone

The Bayesian inference with prior knowledge has been proposed recently to solve the inverse problem in resonant ultrasound spectroscopy. It allows inferring the elastic properties of high damping materials, such as cortical bone with less dependence on the initial guessed values. In this method, the estimation of the stiffness coefficients is expressed as a probabilistic solution to the inverse problem, which can be achieved by sampling or optimization methods. However, the detailed performance comparison of these two strategies applied to high damping materials has not been fully studied. In this work, the full stiffness tensor of 52 transversely isotropic cortical bone specimens was obtained using Markov chain Monte Carlo (MCMC) sampling and particle swarm optimization (PSO), respectively. Results showed that the local probability distributions of stiffness coefficients estimated by the two methods are consistent. Compared with MCMC, the average calculation speed of PSO is ten times faster [614 s ± 59 s (MCMC) versus 53 s ± 22 s (PSO)]. The mean standard error between theoretical and experimental resonant frequencies was slightly smaller for PSO compared with MCMC. In conclusion, PSO, a global optimization strategy, is suitable to solve the inverse problem for high damping materials.

Application of differential evolution on elasticity measurement of low quality factor materials using FEM-based resonant ultrasound spectroscopy

Finite element method based resonant ultrasound spectroscopy (FEM-based RUS) allows elasticity measurement for a material with high quality factor (Q) and arbitrary geometry by minimizing the differences between its theoretically calculated resonant frequencies and the corresponding experimentally measured ones. As Q decreases, some experimental frequencies remain undetermined, which makes it difficult to pair the calculated and experimental frequencies and to correctly identify the elastic constants. Additional difficulty need be tackled for irregularly-shaped low-Q materials due to the adoption of time-consuming FEM, thus efficiency of the identification method needs to be focused on. To apply FEM-based RUS to low-Q materials, a new elastic constant identification method is proposed based on a differential evolution algorithm in this paper. This method can perform a global search combining with local optimizations in the elastic constant space, and improve the overall efficiency by limiting the number of the frequency calculations. By using numerical experiments, the effectiveness of the proposed method under different frequency missing situations was verified and its efficiency was measured from the required frequency calculation numbers, showing an approximate two third reduction compared with an existing method. Finally, the elastic constants of an actual irregular cortical bone-mimicking material (Q ≈ 25) were measured using the two methods, yielding consistent Young's moduli (calculated from the identified constants) with the data provided by the manufacturer and a similar improvement in computational efficiency of the proposed method.