This paper describes resonant ultrasound spectroscopy (RUS) as a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist. In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.

Separate signals from noise with this valuable introduction to signal processing by applied decomposition The decomposition of complex signals into their sub-signals or individual components is a crucial tool in signal processing. It allows each component of a signal to be analyzed individually and enables the signal to be isolated from noise and processed in full. Decomposition processes have not always been widely adopted due to the difficult underlying mathematics and complex applications. This text simplifies these obstacles. Signal Processing: An Applied Decomposition Approach demystifies these tools from a model-based perspective. This offers a mathematically informed, “step-by-step” analysis of the process by breaking down a composite signal/system into its constituent parts, while introducing both fundamental concepts and advanced applications. This comprehensive approach addresses each of the major decomposition techniques, making it an indispensable addition to any library specializing in signal processing. Signal Processing readers will find: Signal decomposition techniques developed from the data-based, spectral-based and model-based perspectives incorporate: statistical approaches (PCA, ICA, Singular Spectrum); spectral approaches (MTM, PHD, MUSIC); and model-based approaches (EXP, LATTICE, SSP) In depth discussion of topics includes signal/system estimation and decomposition, time domain and frequency domain techniques, systems theory, modal decompositions, applications and many more Numerous figures, examples, and tables illustrating key concepts and algorithms are developed throughout the text Includes problem sets, case studies, real-world applications as well as MATLAB notes highlighting applicable commands Signal Processing is ideal for engineering and scientific professionals, as well as graduate students seeking a focused text on signal/system decomposition with performance metrics and real-world applications.

Many significant achievements in new ultrasound technologies to measure bone and models to elucidate the interaction and the propagation of ultrasonic waves in complex bone structures have been reported over the past ten years. Impaired bone remodeling affects not only the trabecular compartment but also the cortical one. Despite the crucial contribution of the cortical structure to the whole bone mechanical competence, cortical bone was understudied for a long time. A paradigm shift occurred around 2010, with a special focus placed on the importance of cortical bone. This has sparkled a great deal of interest in new ultrasound techniques to assess cortical bone. While our book ‘Bone Quantitative Ultrasound’ published in 2011 emphasized techniques to measure trabecular bone, this new book is devoted for a large part to the technologies introduced recently to measure cortical bone. These include resonant ultrasound spectroscopy, guided waves, scattering, and pulse-echo and tomography imaging techniques. Instrumentation, signal processing techniques and models used are detailed. Importantly, the data accumulated in recent years such as anisotropic stiffness, elastic engineering moduli, compression and shear wave speeds of cortical bones from various skeletal sites are presented comprehensively. A few chapters deal with the recent developments achieved in quantitative ultrasound of trabecular bone. These include (i) scattering-based approaches and their application to measure skeletal sites such as the spine and proximal femur and (ii) approaches exploiting the poro-elastic nature of bone. While bone fragility and osteoporosis are still the main motivation for developing bone QUS, this Book also includes chapters reporting ultrasound techniques developed for other applications of high interest such as 3-D imaging of the spine, assessment of implant stability and transcranial brain imaging. This book, together with the book ‘Bone Quantitative Ultrasound’ published in 2011 will provide a comprehensive overview of the methods and principles used in bone quantitative ultrasound and will be a benchmark for all novice or experienced researchers in the field. The book will offer recent experimental results and theoretical concepts developed so far and would be intended for researchers, graduate or undergraduate students, engineers, and clinicians who are involved in the field. The book should be considered as a complement to the first book publisher in 2011, rather than a second edition, in the sense that basic notions already presented in the first book are not repeated.

Resonant Ultrasound Spectroscopy (RUS) has been used successfully to determine the elastic properties of single crystal and homogeneous materials. We have attempted to answer the following question. Under what conditions is RUS a useful tool for determining the moduli of macroscopic, inhomogeneous samples. We concentrated on identifying a sample geometry that will maximize success with RUS. The work consisted of numerical modeling of sample resonances under varying conditions, and empirical testing of rock samples. Numerical modeling and empirical testing indicate that RUS is a viable technique for characterizing the average isotropic elastic moduli of inhomogeneous materials, although larger RMS errors can be expected than for single crystal materials. Success with RUS can optimized by ensuring that the sample size is large compared to the scale of inhomogeneity and by using a high aspect ratio parallelepiped sample.

The objective of this thesis is to validate Resonant Ultrasound Spectroscopy (RUS) as a non-destructive evaluation tool that can be used to study effects of radiation on the mechanical properties of a material, mainly its elastic constants. RUS involves experimentally measuring the resonant frequencies of a sample and calculating the elastic constants based on these measurements. Finite Element Method (FEM) is used to get the frequencies of the modes of free vibration for the sample model. This result depends on the elastic constant values used in the FEM simulation. Studies were conducted to confirm the accuracy of the FEM model, and determine the right configuration and parameters to use for the simulation. Assuming uniform and isotropic elastic property changes, the effects of radiation damage can be quantified by obtaining a set of matching resonant frequencies between the experimental and FEM simulation results, before and after irradiating the sample. This is done by adjusting the elastic constant values used in the simulation so that the results match with the experimentally obtained resonant frequencies. With powerful enough equipment, even real time monitoring is possible in harsh environments, thus pointing out imminent failure.

All objects exhibit vibrational resonances when mechanically excited. These resonant frequencies are determined by density, geometry, and elastic moduli. Resonant ultrasound spectroscopy (RUS) takes advantage of the known relationship between the parameters. In particular, for a freely suspended object, with three of the four parameters (vibrational spectra, density, geometry, or elastic moduli) known the remaining one can be calculated. From a materials characterization standpoint it is straight-forward to measure density and geometry but less so to measure all the elastic moduli. It has recently become possible to quickly and accurately measure vibrational spectra, and using code written at Los Alamos, calculate all the elastic moduli simultaneously. This is done to an accuracy of better than one percent for compression and 0.1 percent for shear. RUS provides rapid acquisition of materials information here-to-fore obtainable only with difficulty. It will greatly facilitate the use of real materials properties in models and thus make possible more realistic modeling results. The technique is sensitive to phase changes and microstructure. This offers a change to input real data into microstructure and phase change models. It will also enable measurement of moduli at locations in and about a weld thus providing information for a validating coupled thermomechanical calculations.