Time-Dependent Wave-Structure Interaction Revisited: Thermo-piezoelectric Scatterers

In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided an appropriate scaling factor is employed. As usual, based on estimates for solutions in the Laplace-transformed domain, we may obtain properties of corresponding solutions in the time-domain without having to perform the inversion of the Laplace-domain solutions

Finite element modeling of ultrasonic wave propagation with application to acoustic microscopy

The development of NDE techniques and the accurate interpretation of measurement signals require a firm understanding of the physical process of energy/defect interactions. This in turn demands an accurate model for the propagation of ultrasonic waves in acoustic and elastic media. Analytical approaches are restricted due to the arbitrary geometries of the discontinuities involved. In this work, a comprehensive numerical model based on the finite element method is developed to simulate ultrasonic wave propagation in ultrasonic NDE systems with emphasis on application to acoustic microscopy;Starting from the governing equations of dynamic elasticity, semi-discretized finite element equations in the space domain are derived according to the variational principle. Direct time integration is carried out through the explicit central difference scheme. Both linear and quadratic elements are implemented with comparison and verifications. Material properties, including anisotrophy, inhomogeneity, viscous damping and arbitrary discontinuities are handled successfully by the model. For ultrasonic systems containing a fluid/solid interface, the governing equations for both the solid and fluid media have to be solved simultaneously with the interfacing boundary conditions properly satisfied. In this case the solid and fluid media are formulated by the displacement vector and pressure scalar respectively. The coefficient matrices are rendered symmetric by introducing a new potential variable for the fluid medium;The transient fields of pulsed transducers in solids and their interaction with flaws are treated in detail. The fields of spherically focused transducers and time-delay arrays are examined. The wave field profiles are compared with those obtained by the classical impulse response method and good agreement is achieved. As an integral part of acoustic microscopy, the visualization of propagation properties of transient leaky Rayleigh waves is also presented. Wave propagation in an acoustic lens and focused waves probing a fluid/solid and solid/solid interfaces as situations in acoustic microscopy are characterized. The finite element model proves to be an effective tool for acoustic device design and ultrasonic NDE

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas

Spectral elements for guided waves. Formulation, Dispersion Analysis and Simulation Results

Résumé : La surveillance de l’intégrité des structures (Structural Health Monitoring - SHM) est une nouvelle technologie, et comme toute nouvelle avancée technologique, elle n’a pas encore réalisé son plein potentiel. Le SHM s’appuie sur des avancées dans plusieurs disciplines, dont l’évaluation non-desctructive, les matériaux intelligents, et les capteurs et actionneurs intégrés. Une des disciplines qui permet son déploiement est la simulation numérique. Le SHM englobe une variété de techniques basées sur la génération d’ondes vibratoires et d’ondes ultrasonores guidées. L’utilisation d’ondes guidées offre en particulier une vaste gamme d’avantages. Le défi majeur associé à la pleine utilisation de la simulation numérique dans la conception d’un système SHM basé sur l’utilisation d’ondes guidées réside dans les ressources de calcul requises pour une simulation précise. La principale raison pour ces exigences est la dispersion induite par la discrétisation numérique, tel qu’indiqué dans la littérature. La méthodes des éléments spectraux (SEM) est une variante de la p-version de la méthode des éléments finis (FEM) qui offre certains outils pour solutionner le problème des erreurs de dispersion, mais la littérature souffre toujours d’une lacune dans l’étude systématique des erreurs de dispersion numérique et de sa dépendance sur les paramètres de simulation. Le présent ouvrage tente de combler cette lacune pour les théories d’ingénierie en vibrations. Il présente d’abord le développement de la formulation des éléments spectraux pour différentes théories d’ingénierie pertinentes pour la propagation des ondes vibratoires dans différents types de structures, comme des tiges et des plaques. Puis, une nouvelle technique pour le calcul des erreurs de dispersion numériques est présentée et appliquée systématiquement dans le but d’évaluer la dispersion numérique induite en termes d’erreurs dans les vitesses de propagation. Cette technique est utilisable pour les différentes formes de propagation des ondes vibratoires dans les éléments structuraux visés dans la présente thèse afin d’évaluer quantitativement les exigences de précision en termes de paramètres de maillage. Les ondes de Lamb constituent un cas particulier de la déformation plane des ondes élastiques, en raison de la présence des doubles frontières à traction libre qui couplent les ondes longitudinales et de cisaillement et qui conduisent à une infinité de modes propagatifs qui sont dispersifs par nature. La simulation des ondes de Lamb n’a pas fait l’objet d’analyse systématique de la dispersion numérique dans la littérature autant pour la SEM que la FEM. Nous rapportons ici pour la première fois les résultats de l’analyse de dispersion numérique pour la propagation des ondes Lamb. Pour toutes les analyses de dispersion numérique présentées ici, l’analyse a été effectuée à˘ala fois dans le domaine fréquentiel et dans le domaine temporel. En se basant sur la nouvelle compréhension des effets de discrétisation numérique de la propagation des ondes guidées, nous étudions l’application de la SEM à la simulation numérique pour des applications de conception en SHM. Pour ce faire, l’excitation piézoélectrique est développée, et une nouvelle technique de condensation statique est développée et mise en œuvre pour les équations de la matrice semi-discrète, qui élimine le besoin de solution itérative, ainsi surnommée fortement couplée ou entièrement couplée. Cet élément piézoélectrique précis est ensuite utilisé pour étudier en détails les subtilités de la conception d’un système SHM en mettant l’accent sur la propagation des ondes de Lamb. Afin d’éviter la contamination des résultats par les réflexions sur les bords une nouvelle forme particulière d’élément absorbant a été développée et mise en œuvre. Les résultats de simulation dans le domaine fréquentiel jettent un éclairage nouveau sur les limites des modèles théoriques actuels pour l’excitation des ondes de Lamb par piézoélectriques. L’excitation par un élément piézoélectrique couplé est ensuite entièrement simulée dans le domaine temporel, et les résultats de simulation sont validés par deux cas de mesures expérimentales ainsi que par la simulation classique avec des éléments finis en utilisant le logiciel commercial ANSYS. // Abstract : Structural health monitoring (SHM) is a novel technology, and like any new technological advancement it has yet not realized its full potential. It builds on advancements in several disciplines including nondestructive evaluation, smart materials, and embedded sensors and actuators. One of the enabling disciplines is the numerical simulation. SHM encompasses a variety of techniques, vibration based, impedance and guided ultrasonic waves. Guided waves offers a wide repertoire of advantages. The major challenge facing the full utilization of the numerical simulation in designing a viable guided waves based SHM System is the formidable computational requirements for accurate simulation. The main reason for these requirements is the dispersion induced by numerical discretization as explained in the literature review. The spectral element (SEM) is a variant of the p-version finite element (FEM) that offers certain remedies to the numerical dispersion errors problem, yet it lacks a systematic study of the numerical dispersion errors and its dependence on the meshing parameters. The present work attempts to fill that gap for engineering theories. It starts by developing the formulation of the spectral element for different relevant engineering theories for guided waves propagation in various structural elements, like rods and plates. Then, extending the utility of a novel technique for computing the numerical dispersion errors, we systematically apply it in order to evaluate the numerically induced dispersion in terms of errors in the propagation speeds. This technique is employed for the various forms of guided waves propagation in structural elements covered in the present thesis in order to quantitatively assess the accuracy requirements in terms of the meshing parameters. The Lamb guided waves constitute a special case of the plane strain elastic waves, that is due to the presence of the double traction free boundaries, couple in the section plane and this coupling leads to an infinitude of propagating modes that are dispersive in nature. Lamb waves simulation have not been a subject of numerical dispersion analysis in the open literature neither for SEM nor FEM for that matter. We report here for the first time the numerical dispersion analysis results for Lamb waves propagation. For all the numerical dispersion analysis presented here, the analysis was done for both the frequency domain and time domain analysis. Based on the established understanding of the numerical discretization effects on the guided waves propagation, we utilize this knowledge to study the application of SEM to SHM simulations. In order to do so the piezoelectric excitation is developed, and a new static condensation technique is developed for the semidiscrete matrix equations, that eliminate the need for iterative solution, thus dubbed strongly coupled or fully coupled implementation. This accurate piezoelectric element are then used to study in details the intricacies of the design of an SHM system with specific emphasis on the Lamb waves propagation. In order to avoid the contamination of the results by the reflections from the edges a new special form of absorbing boundary was developed and implemented. The Simulation results in the frequency domain illuminated the limitations of the current theoretical models for piezoelectric excitation of Lamb waves. The piezoelectric excitation of a fully coupled element is then simulated in the time domain, and the results of simulation was verified against two cases of experimental measurements as well as conventional finite element simulation using the commercial software ANSYS

Wave Propagation

A wave is one of the basic physics phenomena observed by mankind since ancient time. The wave is also one of the most-studied physics phenomena that can be well described by mathematics. The study may be the best illustration of what is “science”, which approximates the laws of nature by using human defined symbols, operators, and languages. Having a good understanding of waves and wave propagation can help us to improve the quality of life and provide a pathway for future explorations of the nature and universe. This book introduces some exciting applications and theories to those who have general interests in waves and wave propagations, and provides insights and references to those who are specialized in the areas presented in the book