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We deduce the dispersion equations for Bleustein-Gulyaev-type waves propagating along a thin metal interlayer in a piezoelectric medium. The dynamic interaction of the matrix with the interlayer is modeled by the effective contact conditions of the composite components with regard for their electromechanical properties. The conditions required for the existence of these waves are analyzed. Keywords: piezoelectric medium, thin-walled metal interlayer, effective contact conditions, BleusteinGulyaev-type wave, dispersion equations., Introduction The problems of propagation of waves in piezoelectric bodies attract significant attention of the researchers caused, in particular, by the necessity of creation of new types of intellectual electromechanical [...]

Shear wave velocity, [V.sub.s], is an important mechanical-dynamic parameter allowing the characterization of a soil in the elastic range ([gamma] < [10.sup.-3]%). Thirty-five existing [G.sub.max] or [V.sub.s] laboratory correlations were examined in this study and are grouped into different general forms based on their geotechnical properties. A database of 11 eastern Canadian clay deposits was selected and used for the critical insights. The effect of the coefficient of earth pressure at rest, [K.sub.0], was also examined. A range of variation for each general form of correlation was determined to take the plasticity index and void ratio values of investigated sites into account. The analysis shows a significant scatter in [V.sub.s1] values predicted by existing correlations and raises questions on the applicability of these correlations, especially for eastern Canadian clays. New correlations are proposed for Champlain clays based on laboratory measurement of [V.sub.s] using the piezoelectric ring-actuator technique, P-RAT, incorporated in consolidation cells. An analysis of P-RAT results reveals the sample disturbance effect and suggests an approach to correct the effect of disturbance on laboratory [V.sub.s] measurements. The applicability of the proposed correlations, including the disturbance correction, is validated by comparison with in situ measurements using multi-modal analysis of surface waves (MMASW). Key words: shear wave velocity ([V.sub.s]), [K.sub.0] coefficient, correlations, eastern Canadian clays, Champlain clays, piezoelectric ring-actuator technique (P-RAT),multi-modal analysis of surface waves (MMASW). La vitesse des ondes de cisaillement, [V.sub.s], est un parametre mecanique-dynamique important pour caracteriser un sol dans le domaine elastique ([gamma] < [10.sup.-3]%). Parmi les correlations de laboratoire [G.sub.max] ou [V.sub.s] existantes, 35 ont ete examinees dans cette etude et sont regroupees sous differentes formes generales en fonction de leurs proprietes geotechniques. On a selectionne et utilise une base de donnees de 11 depots d'argile de l'est du Canada pour l'examen critique. L'influence de la pression des terres au repos, [K.sub.0], a ete egalement examinee. Une plage de variation pour chaque forme generale de correlation a ete determinee afin de prendre en compte la plasticite et les valeurs de l'indice de vide des sites etudies. Les resultats de l'analyse montrent la dispersion entre les valeurs de [V.sub.s1] predites par les correlations existantes et soulevent des questions sur l'applicabilite de ces correlations pour les argiles de l'est du Canada. De nouvelles correlations sont proposees pour les argiles de Champlain, basees sur la mesure en laboratoire de [V.sub.s] a l'aide de la technique des anneaux piezoelectriques, P-RAT, incorporee dans des cellules de consolidation. Une analyse des resultats du P-RAT revele l'effet du remaniement de l'echantillon et suggere une approche pour corriger l'effet du remaniement sur les mesures de [V.sub.s] en laboratoire. La possibilite d'appliquer les correlations proposees, y compris la correction du remaniement, est validee au moyen d'une comparaison des mesures in situ en utilisant l'analyse multimodale des ondes de surface (MMASW). Mots-cles : vitesse de l'onde de cisaillement ([V.sub.s]), coefficient [K.sub.0], correlations, argiles de l'est du Canada, argiles de Champlain, technique des anneaux piezoelectriques (P-RAT), analyse multimodale des ondes de surface (MMASW)., 1. Introduction Since the 1985 Mexico earthquake, a lot of effort has been invested by researchers into better assessing the dynamic response of soil deposits. The low strains shear modulus [...]

The low-strain dynamic behavior of Leda clays is investigated using resonant column (RC) and bender element (BE) tests. Four undisturbed, lightly overconsolidated Leda clay samples, collected from two sites near the St. Lawrence River valley, are tested at different strains, confining stresses, and frequencies. To evaluate the effect of excitation frequency, simultaneous measurements of shear wave velocity using RC and BE tests are performed. The results show that the samples from the different sites behave differently. The high sensitivity of the Leda clays does not have a significant effect on the modulus degradation curves. However, the measured degradation curves are similar to those of soft clays with high plasticity, which is contrary to the expected behavior of these low plasticity ([I.sub.p] = 6.2-20) specimens. Likewise, the measured damping ratios are on the lower end of the typical values reported for soils of high plasticity. Low values of damping ratio make the amplification of small seismic events more likely in Leda clay deposits. The difference in the shear wave velocity measurements from RC and BE tests ranges from 17% to 26% depending on the confinement, likely because of the strong influence of P-waves observed in the BE tests for these soils. Key words: shear modulus, damping ratio, shear wave velocity, seismic characterization, dynamic properties, soil testing. Le comportement dynamique a faible deformation des argiles Leda est etudie a l'aide d'essais de colonne resonante (RC) et d'elements plies (BE). Quatre echantillons d'argile Leda non perturbes et legerement surconsolides, preleves sur deux sites pres de la vallee du fleuve Saint-Laurent, sont testes a differentes contraintes, contraintes de confinement et frequences. Pour evaluer l'effet de la frequence d'excitation, des mesures simultanees de la vitesse de l'onde de cisaillement sont effectuees au moyen d'essais RC et BE. Les resultats montrent que les echantillons provenant des differents sites se comportent differemment. La sensibilite elevee des argiles Leda n'a pas d'effet significatif sur les courbes de degradation du module. Cependant, les courbes de degradation mesurees sont similaires a celles des argiles molles a plasticite elevee, ce qui est contraire au comportement attendu de ces eprouvettes a faible plasticite ([I.sub.p] = 6,2-20). De meme, les rapports d'amortissement mesures se situent dans la partie inferieure des valeurs typiques rapportees pour les sols ayant une plasticite elevee. Les faibles valeurs du rapport d'amortissement rendent l'amplification des petits evenements sismiques plus probable dans les depots d'argile a Leda. La difference entre les mesures de vitesse des ondes de cisaillement des essais RC et BE varie de 17 a 26 % selon le confinement, probablement en raison de la forte influence des ondes P observee dans les essais BE pour ces sols. [Traduit par la Redaction] Mots-cles : module de cisaillement, rapport d'amortissement, vitesse des ondes de cisaillement, caracterisation sismique, proprietes dynamiques, essais de sol., Introduction The Canadian Highway Bridge Design Code (CSA Group 2019) and National Building Code of Canada (NRCC 2015) have recently standardized the provisions of seismic design of infrastructures in which [...]

We study the spectrum of a thin (with the relative width h << 1) rectangular lattice of elastic isotropic (with the Lame constants [lambda] [greater than or equal to] 0 and [mu] > 0) plane waveguides simulating joining seams of a doubly periodic system of identical absolutely rigid tiles. We establish that the low-frequency range of the essential spectrum contains two spectral bands (passing ones for waves) of length O([e.sup.-[delta]/(2h)], [delta] > 0. Above these bands there is a gap of width O([h.sup.-2]) (stopping zones for waves) and then, in the mid-frequency range, above the cut-off value [mu][[pi].sup.2][h.sup.-2] of the continuous spectrum of the infinite cross-shaped waveguide, there is a family of spectral bands of length O(h); moreover, between some of these bands there are opened up gaps of width O(1). The character of the wave propagation depends on whether the frequencies are below or above the cut-off value. In the first case, the oscillations are strictly concentrated near the lattice nodes and the edges are practically immovable. In the second case, the oscillations are localized on the lattice edges, i.e., the nodes are left at relative rest. We show that single perturbations of nodes or edges can cause the appearance of points of the discrete spectrum under the essential spectrum or inside the gaps; moreover, an infinite collection of identical perturbations of nodes can also change the essential spectrum. Bibliography: 78 titles. Illustrations: 5 figures. Dedicated to Nina Nikolaevna Uraltseva who taught the author a lot in mathematics, UDC 517.956.227:517.956.8:517.958:539.3(2) 1 Introduction 1.1. Statement of the problem. On a rectangular elastic lattice (Figure 1 (a)), i.e., the union [[[OMEGA].sup.h] of thin (h << 1) strips [mathematical expression not [...]

For the quality control of cement mixing in clays, small-strain shear stiffness [G.sub.max] is now increasingly being used due to enhanced repeatability in shear wave velocity ([V.sub.s]) measurements. These stiff cemented clays have higher resonant frequencies that require the use of higher input frequencies in bender element testing for reliable [V.sub.s] measurements. However, the practical requirements for suitable signals (with minimal near-field effects and wave reflections) can often be difficult to implement. To facilitate such [V.sub.s] measurements, the current study proposes a methodology that can correct [V.sub.s] values corresponding to lower wave propagation distance to wavelength ratios ([L.sub.tt]/[lambda]) to more reliable values of [V.sub.s] at reference [L.sub.tt]/[lambda] criterion suggested in previous studies (e.g., 2, 3.33, and 4). Two clay types are mixed with ordinary Portland cement and various mix ratios are utilized to cover a wider range of soil stiffnesses. Based on the collected database, it is found that the resulting fitting functions enable the reasonable estimation of the stabilized [V.sub.s] values corresponding to the suggested [L.sub.tt]/[lambda] criterion regardless of the nature of the input sine signal. Key words: bender elements, shear waves, cemented clay, near-field effects. Pour le controle de la qualite du melange du ciment dans les argiles, on utilise de plus en plus une faible rigidite au cisaillement en contrainte [G.sub.max] en raison de la repetabilite accrue des mesures de la vitesse des ondes de cisaillement ([V.sub.s]). Ces argiles cimentees rigides ont des frequences de resonance plus elevees qui necessitent l'utilisation de frequences d'entree plus elevees dans le test des elements piezoceramiques (<>) pour des mesures [V.sub.s] fiables. Cependant, les exigences pratiques pour des signaux appropries (avec des effets de champ proche et des reflexions d'ondes minimes) peuvent souvent etre difficiles a mettre en reuvre. Pour faciliter de telles mesures [V.sub.s], la presente etude propose une methodologie permettant de corriger les valeurs de [V.sub.s] correspondant a des rapports de distance de propagation des ondes a la longueur d'onde ([L.sub.tt]/[lambda]) moins eleves a des valeurs plus fiables de [V.sub.s] au critere de reference [L.sub.tt]/[lambda] suggere dans des etudes anterieures (2, 3,33 et 4). Deux types d'argile sont melanges au ciment Portland ordinaire et divers rapports de melange sont utilises afin de couvrir une plus grande gamme de rigidite du sol. En se fondant sur de la base de donnees recueillies, on constate que les fonctions d'ajustement resultantes nous permettent d'estimer raisonnablement les valeurs [V.sub.s] stabilisees correspondant au critere [L.sub.tt]/[lambda] suggere, quelle que soit la nature du signal sinusoidal d'entree. [Traduit par la Redaction] Mots-cles: elements piezoceramiques (<< bender elements>>), vagues de cisaillement, argile cimentee, effets de champ proche., Introduction It is well established that small-strain shear stiffness ([G.sub.max]) is a fundamental parameter for static and dynamic analyses of soil (Burland 1989; Clayton 2011; Ku et al. 2013; Richart [...]

The wave equation in a thin laminated beam with contrasting stiffness and density of layers is considered. The problem contains two parameters: [epsilon] is a geometric small parameter (the ratio of the diameter and its characteristic longitudinal size) and w is a physical large parameter (the ratio of stiffness and densities of alternating layers). The asymptotic behavior of the solution depends on the combination of parameters [[epsilon].sup.2]w. If this value is small, then the limit model is the standard homogenized one- dimensional wave equation. On the contrary, if [[epsilon].sup.2]w is not small, then the limit model is presented by the so-called multicontinuum model, i.e., multiple one-dimensional wave equations, coupled or noncoupled and 'co-existing' at every point. The proof of these results uses the milticomponent homogenization method. Bibliography: 21 titles., The present article is dedicated to the memory of the outstanding mathematician V. V. Zhikov. He contributed to different fields of mathematics, in particular, one can mention his fundamental results [...]

Inner atomic interactions at the micro scale produce new effects that cannot be accounted for by the classical theory of elasticity. To study the impact of the microstructures of the material, generalized continuum theories involving additional microstructural material parameters are preferred. One such microcontinuum theory involving an additional material parameter called internal characteristic length (l) is a consistent couple stress theory. The study of leaky Rayleigh waves generated at the interface of solid half-space with liquid layer is of great importance for quick scanning and imaging of large civil engineering structures. The problem of leaky Rayleigh waves propagating in elastic half-space under liquid loading has been studied in the context of this consistent couple stress theory. Dispersion equations are obtained by developing the mathematical model of the problem. Phase velocity of leaky Rayleigh waves is studied for three different values of characteristic length parameter (l), which is of the order of internal cell size of the material. Effects of thickness of liquid layer are also studied on the phase velocity profiles. Key words: couple stress, characteristic length, leaky Rayleigh waves, liquid loading, dispersion. Les interactions atomiques a micro-echelle produisent des effets qui ne peuvent pas etre expliques par la theorie classique de l'elasticite. Afin d'etudier l'impact des microstructures des materiaux, des theories du continuum generalisees impliquant des parametres additionnels des microstructure du materiau sont generalement preferees. Une de ces theories du micro-continuum impliquant le parametre additionnel de materiau appele longueur caracteristique (l) est coherente avec la theorie du second gradient. L'etude des ondes de Rayleigh fuyantes generees a une interface d'un demi-espace solide avec une couche de liquide (type Scholte) est tres importante pour rapidement balayer et imager de grandes structures de genie civil. Le probleme d'ondes de Rayleigh fuyantes se propageant dans le demi-espace elastique sous une charge liquide est etudie ici dans le cadre de la theorie du second gradient. Nous obtenons les equations de dispersion en developpant le modele mathematique du probleme. La vitesse de phase des ondes de Rayleigh fuyantes est etudiee pour trois differentes valeurs du parametre de longueur caracteristique (l), qui est de l'ordre de grandeur de la cellule interne du materiau. Nous etudions aussi les effets de l'epaisseur de la couche liquide sur les profils de vitesse de phase. [Traduit par la Redaction] Mots-cles: theorie du second gradient, longueur caracteristique, ondes de Rayleigh fuyantes, charge liquide, dispersion., 1. Introduction In classical elasticity, microstructure of the material was neglected and its points were assumed to be the material particles. It was also assumed that matter is continuously distributed [...]

It is shown that Lorentz Invariance is a wave phenomenon. The relativistic mass, length contraction and time dilation all follow from the assumption that energy-momentum is constrained to propagate at the speed of light, c, in all contexts, matter as well as radiation. Lorentz Transformations, and both of the usual postulates, then follow upon adopting Einstein clock synchronisation. The wave interpretation proposed here is paradox free and it is compatible with quantum nonlocality., 1 Introduction 'But the division into matter and field is, after the recognition of the equivalence of mass and energy, something artificial and not clearly defined. Could we not reject [...]