The Variational Boussinesq Model (VBM) for waves above a layer of ideal fluid conserves mass, momentum, energy, and has decreased dimensionality compared to the full problem. It is derived from the Hamiltonian formulation via an approximation of the kinetic energy, and can provide approximate dispersion characteristics. Having in mind a signalling problem, we search for optimal dispersive properties of the ...

Journal: Wave Motion, pp. 309-322, 2012]]>In Part 1 (van Groesen and Andonowati [1]), we derived models for the propagation of coastal waves from deep parts in the ocean to shallow parts near the coast. In this paper, we will describe hybrid spatial-spectral implementations of the models that retain the basic variational formulation of irrotational surface waves that underlays the derivation of the continuous models. ...

Journal: Wave Motion, pp. 198-211, 2012]]>An exact representation is presented for the field inside a sphere (the observation sphere) due to primary sources enclosed by a second sphere (the source sphere). The regions bounded by the two spheres have no common points. The field of the primary sources is expressed in terms of Gaussian beams whose branch-cut disks are all centered at the origin ...

Journal: Wave Motion, vol. 48, no. 3, pp. 243-258, 2011]]>In the context of wave propagation through a three-dimensional acoustic medium, an analytical approach to estimate the boundary effects in the high-frequency (single) diffraction by thin rigid obstacles is developed. Starting from the classical Kirchhoff (approximate) representation, explicit formulas regarding three sample cases are obtained. The improvement with respect to previous approaches, usually based on refinements of the ...

Journal: Wave Motion, vol. 48, no. 5, pp. 408-422, 2011]]>In this paper we formulate relatively simple models to describe the propagation of coastal waves from deep parts in the ocean to shallow parts near the coast. The models have good dispersive properties that are based on smooth quasi-homogeneous interpolation of the exact dispersion above flat bottom. This dispersive quality is then maintained in the second order nonlinear terms ...

Journal: Wave Motion, vol. 48, no. 7, pp. 657-666, 2011]]>This paper presents a mathematical study for the Bragg scattering of water waves propagating over a series of rectangular poro-elastic submerged breakwaters. Based on the linear wave theory and the improved Biot's theory of poro-elastic media with suitable matching conditions, an analytical solution was obtained as a function of elasticity, permeability and geometry of the submerged breakwaters. ...

Journal: Wave Motion, vol. 48, no. 1, pp. 1-12, 2011]]>In this paper, the off-axial acoustic scattering of a high-order Bessel vortex beam by a rigid immovable (fixed) sphere is investigated. It is shown here that shifting the sphere off the axis of wave propagation induces a dependence of the scattering on the azimuthal angle. Theoretical expressions for the incident and scattered field from a rigid immovable sphere ...

Journal: Wave Motion, vol. 48, no. 5, pp. 392-400, 2011]]>A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid–air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more ...

Journal: Wave Motion, vol. 48, no. 8, pp. 707-716, 2011]]>In-plane elastic wave propagation in the presence of a damaged interface is investigated. The damage is modeled as a distribution of small cracks and this is transformed into a spring boundary condition. First the scattering by a single interface crack is determined explicitly in the low frequency limit for the case of a plane wave normally incident to the ...

Journal: Wave Motion, vol. 48, no. 2, pp. 105-115, 2011]]>We present, a model to calculate sound transmission through plates perforated with periodically distributed subwavelength holes. Measurements performed using aluminium-perforated plates immersed in water are compared to predictions obtained with the calculation model. The calculated results agree well with experimental ones. It is also showed, both experimentally and numerically, that the number of the transmission peaks, related to the ...

Journal: Wave Motion, vol. 48, no. 3, pp. 235-242, 2011]]>We investigate theoretically the effects of viscosity and surface films on small-amplitude Gerstner waves in deep water. The analysis is performed by using a Lagrangian formulation of fluid motion. For inviscid fluids with a free surface Gerstner waves of arbitrary amplitude are exact solutions of the nonlinear Lagrangian equations. These waves have a trochoidal surface shape. They possess vorticity, ...

Journal: Wave Motion, vol. 48, no. 4, pp. 301-309, 2011]]>Flexural waves are scattered by inclusions in a thin plate. For a single inclusion of arbitrary shape, reciprocity relations are obtained connecting coefficients in circular multipole expansions. Then, a formula for the effective wavenumber in a random arrangement of identical circular inclusions is derived, using the Lax quasi-crystalline approximation.

Journal: Wave Motion, vol. 48, no. 2, pp. 161-175, 2011]]>In a recent paper Destrade [1] studied surface waves in an exponentially graded orthotropic elastic material. He showed that the quartic equation for the Stroh eigenvalue p is, after properly modified, a quadratic equation in p2 with real coefficients. He also showed that the displacement and the stress decay at different rates with the depth x2 of the half-space. ...

Journal: Wave Motion, vol. 48, no. 4, pp. 335-344, 2011]]>Ultrasonic testing for defects in anisotropic material is one of the difficult problems in non-destructive testing (NDT) with elastic waves. Even though a series of studies have been performed on the waves interacting with flaws, however, only a small portion was on anisotropic materials. In this paper, an analytical solution for the far-field scattering response of a side ...

Journal: Wave Motion, vol. 48, no. 3, pp. 275-289, 2011]]>We introduce a new conserved quantity, Normalized Energy Density (NED), alternative to the conventional definition of energy for a layered structure in a 2D SH problem. NED is defined by the average of power of a half transfer function multiplied by the impedance, and the conservation across the material interface is analytically proved for a two-layered case. For three, ...

Journal: Wave Motion, vol. 48, no. 7, pp. 602-612, 2011]]>Mild-slope (MS) type equations are depth-integrated models, which predict under appropriate conditions refraction and diffraction of linear time-harmonic water waves. By using a streamfunction formulation instead of a velocity potential one, the complementary mild-slope equation (CMSE) was shown to give better agreement with exact linear theory compared to other MS-type equations. The main goal of ...

Journal: Wave Motion, vol. 48, no. 3, pp. 223-234, 2011]]>Lamb waves using surface-bonded piezoelectric transducers (PZTs) have been widely used for nondestructive testing (NDT). However, the identification of individual Lamb wave modes and the subsequent data interpretation are often difficult due to the dispersive and multimodal natures of Lamb waves. To tackle the problem, a Lamb wave mode decomposition technique using concentric ring and circular PZTs is proposed. ...

Journal: Wave Motion, vol. 48, no. 4, pp. 358-370, 2011]]>Transformational acoustics offers the theoretical possibility of cloaking obstacles within fluids, provided metamaterials having continuously varying bulk moduli and densities can be found or constructed. Realistically, materials with the proper, continuously varying anisotropies do not presently exist. Discretely layered cloaks having constant material parameters within each layer are a viable alternative, but due to their discrete nature, may become ineffective ...

Journal: Wave Motion, vol. 48, no. 6, pp. 505-514, 2011]]>A mapped orthogonal functions technique is extended for solving three-dimensional acoustical wave problems with taking into account electrical sources. For validation and illustration purposes, it is applied to the determination of the frequency spectrum of a piezoelectric disc resonator. Formulation is given for the calculation of the electric input admittance along with specializations for open- and short-circuit boundary ...

Journal: Wave Motion, vol. 48, no. 1, pp. 93-104, 2011]]>In the last decade, Meshless Methods have found widespread application in different fields of engineering and science. Beyond novelty, their mathematical simplicity and numerical accuracy have been the key of their rapid dissemination. Among meshless techniques, RBF (Radial Basis Functions) based methods can be simple and general to solve the problems related to multiple areas of applied physics and engineering. ...

Journal: Wave Motion, vol. 48, no. 5, pp. 423-440, 2011]]>A one-dimensional weakly-nonlinear model equation based on a Lagrangian-averaged Euler-α model of compressible flow in lossless fluids is presented. Traveling wave solutions (TWS)s, in the form of a topological soliton (or kink), admitted by this fourth-order partial differential equation are derived and analyzed. An implicit finite-difference scheme with internal iterations is constructed in ...

Journal: Wave Motion, vol. 48, no. 8, pp. 782-790, 2011]]>Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the ...

Journal: Wave Motion, vol. 48, no. 1, pp. 83-92, 2011]]>The present work deals with the possibility of propagation of torsional surface wave in fluid saturated poroelastic layer lying over nonhomogeneous elastic half space. Both the media are assumed to be under compressive initial stress. The half space has two types of inhomogeneity, viz; hyperbolic and quadratic. The dispersion equation for torsional wave in porous layer has been derived and ...

Journal: Wave Motion, vol. 48, no. 2, pp. 184-195, 2011]]>We derive the so-called Generalized Impedance Boundary Conditions (GIBC) that model thin dielectric coatings with variable width located on a perfect electric or magnetic conducting surface. We treat the 2-D electromagnetic problem for both TM and TE polarizations. The expressions of the GIBCs are obtained up to the third order (with respect to the coating width). The order ...

Journal: Wave Motion, vol. 48, no. 7, pp. 680-699, 2011]]>This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-...

Journal: Wave Motion, vol. 48, no. 3, pp. 197-213, 2011]]>The early short time transient response of an L-shaped plate is investigated by the method of reverberation ray matrix (MRRM) and the generalized ray method (GRM). The MRRM and GRM have been successfully used to study the transient elastic wave transmitting in the beams, planar trusses, space frames and infinite layered media. In the present paper, these two methods ...

Journal: Wave Motion, vol. 48, no. 5, pp. 371-391, 2011]]>Perhaps the simplest non-trivial problem in small deformation dynamic plasticity is expansion of a spherical cavity in an infinite elastic-perfectly-plastic medium. Here, example problems are considered with two boundary conditions at the cavity's surface: constant velocity and constant pressure. Attempts to obtain analytical solutions are complicated by the fact that, in general, the elastic–plastic boundary ...

Journal: Wave Motion, vol. 48, no. 5, pp. 441-452, 2011]]>Coherent backscattering enhancement (CBE) was introduced in disordered, random or chaotic media. In this study, our attention is focused on simple parallelepipedic cavities, as contrary to the widespread opinion, CBE can also be observed for a pure-tone source in a one-dimensional (1-D) cavity. This approach is of two-fold interest. First, analytical calculus predicts a dimensional dependence ...

Journal: Wave Motion, vol. 48, no. 3, pp. 214-222, 2011]]>In this paper we study two-dimensional flows of incompressible viscoelastic Maxwell media with Jaumann corotational derivative in the rheological constitutive law. In the general case, due to the incompressibility condition, the equations of motion have both real and complex characteristics. Group properties of this system are studied. On this basis, two submodels of the Maxwell model are selected, which ...

Journal: Wave Motion, vol. 48, no. 8, pp. 727-737, 2011]]>We discuss here nano-scale size localized wave excitations, which are intrinsic localized traveling modes in two-dimensional anharmonic crystal lattice systems. In particular, using different initial conditions of coordinates and momenta we search for the longest lasting excitations in triangular lattices. As most stable and longest lasting unaltered appear quasi-one-dimensional Toda-like solitons running in rectilinear chains ...

Journal: Wave Motion, vol. 48, no. 8, pp. 753-760, 2011]]>In this article we introduce a MAC protocol designed for underwater localization and time-synchronisation. The MAC protocol assumes a network of static reference nodes and allows blind nodes to be localized by listening-only to the beacon messages. Such a system is known to be very scalable. We show localization and time-synchronization algorithms can be designed for listen-...

Journal: Wave Motion, pp. 1-5, 2011]]>This study examines the error distribution of aggregated MPDUs in 802.11n networks and whether or not forward error correction like raptor coding at the link layer would be useful in these networks. Several experiments with Qualcomm 4x4 802.11n hardware were performed. Two devices were used in a data link, while a third device sniffed all transmitted packets. The ...

Journal: Wave Motion, 2011]]>Security weaknesses often stem from users trying to comply with social expectations rather than following security procedures. Such normative conflicts between security policies and social norms are therefore undesirable from a security perspective. It has been argued that system developers have a "meta-task responsibility", meaning that they have a moral obligation to enable the users of the system they ...

Journal: Wave Motion, pp. 11-24, 2011]]>We analyse an asymptotic low-dimensional model of anti-plane shear in a thin bi-material strip containing a periodic array of interfacial cracks. Both ideal and non-ideal interfaces are considered. We find that the previously derived asymptotic models display a degree of inaccuracy in predicting standing wave eigenfrequencies and suggest an improvement to the asymptotic model to address ...

Journal: Wave Motion, 2011]]>The system of Coupled Nonlinear Schrödinger's Equations (CNLSE) is solved numerically by means of a conservative difference scheme. Values of the cross-modulation parameter, α2, are chosen to induce repelling collisions. The resulting waveforms are fitted to soliton profiles and studied via internal parameters including phase velocity to gain insight into the dynamics of the repelling collisions. A decaying ...

Journal: Wave Motion, vol. 48, no. 8, pp. 805-813, 2011]]>This paper investigates the three-dimensional (3D) scattering of guided waves by a through-thickness cavity with irregular shape in an isotropic plate. The scattered field is decomposed on the basis of Lamb and SH waves (propagating and non-propagating), and the amplitude of the modes is calculated by writing the nullity of the total stress at the boundary of ...

Journal: Wave Motion, vol. 48, no. 7, pp. 585-601, 2011]]>An analytical solution of the mild-slope wave equation is derived to describe long wave propagating over the idealized dredge excavation pit. The pit is assumed to be axisymmetrical and composed of a flat bottom and a convex slope. The convex slope is expressed by a simple power function. The problem is solved in the polar coordination system by the ...

Journal: Wave Motion, vol. 48, no. 3, pp. 259-267, 2011]]>The intriguing concept of “anti-cloaking” has been recently introduced within the framework of transformation optics (TO), first as a “countermeasure” to invisibility-cloaking (i.e., to restore the scattering response of a cloaked target), and more recently in connection with “sensor invisibility” (i.e., to strongly reduce the scattering response while maintaining the field-sensing capabilities). In this paper, ...

Journal: Wave Motion, vol. 48, no. 6, pp. 455-467, 2011]]>We start by a review of the chronology of mathematical results on the Dirichlet-to-Neumann map which paved the way toward the physics of transformational acoustics. We then rederive the expression for the (anisotropic) density and bulk modulus appearing in the pressure wave equation written in the transformed coordinates. A spherical acoustic cloak consisting of an alternation of homogeneous ...

Journal: Wave Motion, vol. 48, no. 6, pp. 483-496, 2011]]>The interaction of the components of composite solitary waves governed by nonlinear coupled equations is studied numerically. It is shown how predictions of the known exact traveling wave solutions may help in understanding and explaining the process of reshaping seen as head-on and take-over collisions of individual solitary waves. The most interesting results concern the switch in the ...

Journal: Wave Motion, vol. 48, no. 8, pp. 773-781, 2011]]>One popular approach to cloaking objects from electromagnetic waves at moderately long wavelengths is the scattering cancelation technique. This mechanism is based on the use of a single homogeneous thin layer to cover an object of interest in order to provide scattering suppression in a given frequency band. This approach has also been recently extended to acoustic waves. This paper ...

Journal: Wave Motion, vol. 48, no. 6, pp. 468-482, 2011]]>We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the cloaked region, the scattered field is small and the scatterers are for all practical purposes undetectable. The devices are multipolar point ...

Journal: Wave Motion, vol. 48, no. 6, pp. 515-524, 2011]]>Formulas for the velocity of Stoneley waves propagating along the loosely bonded interface of two isotropic elastic half-spaces are derived using the complex function method. The derivation also shows that if a Stoneley wave exists, then it is unique. By using the obtained formulas, we can easily reproduce the numerical results previously obtained by Murty [G. S. Murty, Phys. ...

Journal: Wave Motion, vol. 48, no. 7, pp. 646-656, 2011]]>Several important examples of the N-wave equations are studied. These integrable equations can be linearized by formulation of the inverse scattering as a local Riemann–Hilbert problem (RHP). Several nontrivial reductions are presented. Such reductions can be applied to the generic N-wave equations but mainly the 3- and 4-wave interactions are presented as examples. Their one and ...

Journal: Wave Motion, vol. 48, no. 8, pp. 791-804, 2011]]>On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the deformation with the initial stress and in general, for a compressible material, it requires 10 invariants, reducing to 9 for an incompressible material. Expressions for the Cauchy ...

Journal: Wave Motion, vol. 48, no. 7, pp. 552-567, 2011]]>The Benjamin–Ono equation is especially challenging for numerical methods because (i) it contains the Hilbert transform, a nonlocal integral operator, and (ii) its solitary waves decay only as O(1/|x|2). We compare three different spectral methods for solving this one-space-dimensional equation. The Fourier pseudospectral method is very fast through use of the Fast Fourier Transform (...

Journal: Wave Motion, vol. 48, no. 8, pp. 702-706, 2011]]>The effect of viscosity on dispersion of capillary–gravity waves becomes significant when the attenuation coefficient is greater than about 2.5% of the wave number. For low viscosity fluids such as water this condition is met at frequencies greater than about 5kHz in which case direct measurement of wavelength is difficult. For higher viscosity fluids the effect appears at ...

Journal: Wave Motion, vol. 48, no. 2, pp. 176-183, 2011]]>Directional excitation and detection of sound in the periodic baffle system are analyzed using the method developed earlier in electrostatics. The phenomenon is exploited in phased array transducers applied in ultrasonography, nondestructive evaluation and testing. The nice feature of the applied method is that the matrices of the resulting system of the equations are relatively easy for computations and that ...

Journal: Wave Motion, vol. 48, no. 2, pp. 130-145, 2011]]>We derive high-order corrections to a modulation theory for the propagation of internal gravity waves in a density-stratified fluid with coupling to the mean flow. The methodology we use allows for strong modulations of wavenumber and mean flow, extending previous approaches developed for the quasi-monochromatic regime. The wave mean flow modulation equations consist of a system of ...

Journal: Wave Motion, vol. 48, no. 7, pp. 667-679, 2011]]>This paper studies nonlinear waves in a prestretched cylinder composed of a Blatz–Ko material. Starting from the three-dimensional field equations, two coupled PDEs for modeling weakly nonlinear long waves are derived by using the method of coupled series and asymptotic expansions. Comparing with some other existing models in literature, an important feature of these equations is that they ...

Journal: Wave Motion, vol. 48, no. 8, pp. 761-772, 2011]]>This work investigates the nonlinear longitudinal forced vibrations of a bar with hysteretic dynamics typical of rocks and man-made geomaterials. The material properties are described by a constitutive relation that includes energy dissipation effects consistently with hysteretic dynamics. The harmonic balance method and a perturbation technique that uses the material's modulus defect as perturbation parameter are employed to ...

Journal: Wave Motion, vol. 48, no. 4, pp. 345-357, 2011]]>Transformation theory is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by selection of the matrix relating displacements in the two descriptions. This gauge matrix can be chosen to make the transformed density isotropic for any transformation although the stress in the transformed ...

Journal: Wave Motion, vol. 48, no. 6, pp. 525-538, 2011]]>Across traveling autocatalytic fronts, density differences due to composition and temperature changes can lead to buoyancy-driven hydrodynamic instabilities deforming the front by convective motions. We study here the influence of heat losses through the walls of the reactor on the stability of such exothermic fronts in the gravity field. The stability domain is computed numerically in a parameter space ...

Journal: Wave Motion, vol. 48, no. 8, pp. 814-823, 2011]]>The emergence of soliton trains and interaction of solitons are analyzed by using a Boussinesq-type equation which describes the propagation of bi-directional deformation waves in microstructured solids. The governing equation in the one-dimensional setting is based on the Mindlin model. This model includes scale parameters which show explicitly the influence of the microstructure in wave motion. As ...

Journal: Wave Motion, vol. 48, no. 8, pp. 717-726, 2011]]>This paper reports a new numerical approach to simulate waves in elastic solids with cubic symmetry. The governing equation includes the equation of motion and the constitutive relation of the elastic medium. With velocity and stress components as the unknowns, the equations are a set of nine, first-order, hyperbolic partial differential equations. To aid numerical simulation, the characteristic form ...

Journal: Wave Motion, vol. 48, no. 1, pp. 39-61, 2011]]>This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed description of two variants of the Hardy space infinite element method which relies on the pole condition is given. The method can treat waveguide-type inhomogeneities ...

Journal: Wave Motion, vol. 48, no. 2, pp. 116-129, 2011]]>Gaussian beams are asymptotic solutions of linear wave-like equations in the high frequency regime. This paper is concerned with the beam formulations for the Schrödinger equation and the interface conditions while beams pass through a singular point of the potential function. The equations satisfied by Gaussian beams up to the fourth order are given explicitly. When a Gaussian beam ...

Journal: Wave Motion, vol. 48, no. 4, pp. 310-324, 2011]]>We study analytically and numerically primary pulse transmission in one dimensional systems of identical linearly elastic non-dispersive rods separated by identical homogeneous granular layers composed of n beads. The beads interact elastically through a strongly (essentially) nonlinear Hertzian contact law. The main challenge in studying pulse transmission in such strongly nonlinear media is to analyze the ‘basic problem’, namely, ...

Journal: Wave Motion, vol. 48, no. 7, pp. 567-584, 2011]]>The electromagnetic field scattered by an impedance plane is generally given by its plane wave expansion (Fourier representation). Here we derive an alternative expression which is more suitable for point source illumination. For this, we consider an original expression of the Hertz potentials for the incident field and express the scattered potentials in a novel form. A special function then ...

Journal: Wave Motion, vol. 48, no. 7, pp. 634-645, 2011]]>The effect of dust charge fluctuation on the existence and propagation of dust acoustic waves in unmagnetized dusty plasma is studied. Dispersion relation for the dust acoustic waves with temporal dust charge fluctuations is calculated based on the reductive perturbation technique. By considering two different limiting cases of the dust charging frequency, it is shown that the dusty plasma system ...

Journal: Wave Motion, vol. 48, no. 3, pp. 268-274, 2011]]>Imagining a medium composed of an arbitrary distribution of point-like heterogeneities, we study the reconstruction of scattered waves in Green's function derived from the cross-correlation function of waves excited by random noise sources of which the distribution is stationary and homogeneous. We show that the reconstruction process is intimately related to generalized forms of the optical theorem. ...

Journal: Wave Motion, vol. 48, no. 2, pp. 146-160, 2011]]>Despite many advances in the area of Underwater Wireless Sensor Networks (UWSN) during the last years, still many challenges need to be successfully tackled before large-scale deployment of underwater sensor networks becomes a reality. UWSNs usually employ acoustic channels for communications, which compared with radio-frequency channels, allow much lower bandwidths and have longer propagation delays. In the past, ...

Journal: Wave Motion, pp. 1-8, 2011]]>The problem of TE-polarized surface wave scattering from a rectangular impedance groove located on an infinite reactive plane which is filled with dielectric material is considered for a rather general case where the impedances of the horizontal and vertical sides of the groove have different values. The multiple interactions up to the second order between the edges of the ...

Journal: Wave Motion, vol. 48, no. 1, pp. 24-38, 2011]]>Conditions for the existence of acoustic waveguide modes with the direction of the group velocity opposite to that of the phase velocity in supported layers are investigated. We begin with a study of a clamped-free layer and show that the occurrence of the negative slope in the dispersion of the second and higher order modes leading to backward propagation ...

Journal: Wave Motion, vol. 48, no. 5, pp. 401-407, 2011]]>We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating sufficiently rapidly decaying right- and left-propagating waves. We study the dynamics of weakly nonlinear waves, and using asymptotic multiple-scale expansions and averaging with respect to the fast time, we obtain a hierarchy ...

Journal: Wave Motion, vol. 48, no. 8, pp. 738-752, 2011]]>Journal: Wave Motion, vol. 48, no. 6, pp. 453-454, 2011]]>

One of the big issues in finite element solutions of wave propagation problems is the presence of spurious high-frequency oscillations that may lead to divergent results at mesh refinement. The paper deals with the extension of the new two-stage time-integration technique developed in our previous papers to the solution of wave propagation problems with explicit time-integration ...

Journal: Wave Motion, vol. 48, no. 7, pp. 625-633, 2011]]>We present an analysis of acoustic cloaks based on the homogenization of two fluidlike materials, with an emphasis on periodically layered imperfect cloaks, by removing the singularities of the acoustic parameters required for ideal cloaks. The conditions that material layers should satisfy are systematically analyzed and critically discussed according to their feasibility.

Journal: Wave Motion, vol. 48, no. 6, pp. 497-504, 2011]]>The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The ...

Journal: Wave Motion, vol. 48, no. 1, pp. 62-82, 2011]]>Journal: Wave Motion, vol. 48, no. 8, pp. 701-701, 2011]]>

The nonlinear processes of supratransmission and infratransmission are employed here in order to show numerically that binary information may be transmitted into (2+1)-dimensional, continuous Frenkel–Kontorova media spatially defined on a square, by perturbing harmonically two adjacent boundaries by means of Neumann conditions. The presence of these nonlinear phenomena is established numerically through a computational method that preserves the ...

Journal: Wave Motion, vol. 48, no. 1, pp. 13-23, 2011]]>In this paper, formulas for the velocity of Rayleigh waves in compressible isotropic solids subject to uniform initial deformations are derived using the theory of cubic equation. They are explicit, have simple algebraic forms, and hold for a general strain energy function. Unlike the previous investigations where the derived formulas for Rayleigh wave velocity are approximate and valid for only ...

Journal: Wave Motion, vol. 48, no. 7, pp. 613-624, 2011]]>Recently, some explicit results were obtained regarding non-uniqueness for the traction to displacement maps of bounded elastic bodies in 2D and 3D, under the assumption of an internal kinematic constraint. The approach utilized is that of transformation optics. As the approach could, under the usual continuum assumptions, handle all frequencies without resorting to active materials, it could potentially be ...

Journal: Wave Motion, vol. 48, no. 6, pp. 539-549, 2011]]>A transition matrix formulism for the scattering problems of elastic waves using a surface scatterer of three-dimensional half-space is derived by applying Betti's third identity and orthogonality conditions. The basis functions and their corresponding regular parts are derived from Lamb's singular solutions. The new orthogonal functions are constructed based on the linear transform. The intrinsic properties ...

Journal: Wave Motion, vol. 48, no. 4, pp. 325-334, 2011]]>Seismic scattering attenuation due to random lithospheric heterogeneity has been theoretically modeled using two approaches. One approach is the Born approximation theory (BAT), which is primarily used to treat weak continuous heterogeneity, and the other approach is the Foldy approximation theory (FAT), which deals with sparsely distributed discrete inclusions. We apply the BAT to elastic wave scattering due to inclusions ...

Journal: Wave Motion, vol. 48, no. 3, pp. 290-300, 2011]]>The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error estimates related to the discretization of the superposition integral and the Taylor expansion of the phase and amplitude off the center of the beam. ...

Journal: Wave Motion, vol. 47, no. 7, pp. 421-439, 2010]]>This paper considers the propagation of anti-plane shear waves in a half-space whose shear modulus and mass density have an arbitrary dependence on the distance from the free surface. An appropriate reformulation of the anti-plane displacement produces a governing equation for the reformulated displacement that is amenable to a solution in the high-frequency range. The boundary ...

Journal: Wave Motion, vol. 47, no. 1, pp. 59-65, 2010]]>An inverse problem is formulated for (indirectly) measuring the sudden movement of the sea-floor by using a time-history record of the resulting water-wave elevation. The measurement problem is shown to have a unique solution, which can correspond to the real physical wave-source of the sudden movement of the sea-floor. However, the problem formulated herein is ...

Journal: Wave Motion, vol. 47, no. 3, pp. 146-155, 2010]]>The three-dimensional wave propagation in cubic materials like silicon AFM tips is investigated numerically. The used VS-FDTD (Velocity Stress Finite-Difference Time-Domain) code is explained starting with the fundamental equations for the wave propagation in cubic materials. The discretisation, the boundary conditions, and the stability conditions are considered. As a validation of the numerical code, first the ...

Journal: Wave Motion, vol. 47, no. 1, pp. 33-44, 2010]]>Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for scalar waves. The characteristic equation, the solution of which yields the effective wave numbers of coherent elastic waves, is obtained in ...

Journal: Wave Motion, vol. 47, no. 3, pp. 183-197, 2010]]>A spectral element (SE) implementation of the Givoli–Neta non-reflecting boundary condition (NRBC) is considered for the solution of the Klein–Gordon equation. The infinite domain is truncated via an artificial boundary B, and a high-order NRBC is applied on B. Numerical examples, in various configurations, concerning the propagation of a pressure pulse are used to demonstrate the ...

Journal: Wave Motion, vol. 47, no. 5, pp. 289-298, 2010]]>The far-field diffraction behaviour for canonical scattering problems involving corners or by sectors, in three-dimensions, is considered. The far-field results are obtained using ideas based upon embedding formulae and therefore complement and extend existing results. Specific geometries such as the flat cone (a sector) and a corner formed by a solid octant are considered in detail. The ...

Journal: Wave Motion, vol. 47, no. 5, pp. 299-317, 2010]]>In this paper, we present a comprehensive model for the numerical simulation of linear and nonlinear elastic waves in slender rods. The mathematical model, based on conservation of mass, conservation of linear momentum, and a hypoelastic constitutive equation, consists of a set of three first-order, fully-coupled, nonlinear, hyperbolic partial differential equations. Three forms of the model equations are ...

Journal: Wave Motion, vol. 47, no. 3, pp. 168-182, 2010]]>Many wave phenomena in physics are described by weakly nonlinear nearly monochromatic solutions in the form of modulated wave packets. The examples include ocean waves as well as waves in optics and in plasmas. There are a number of approaches to deriving the envelope equations for these theories of amplitude modulation. In this paper, we give a unified approach, based ...

Journal: Wave Motion, vol. 47, no. 8, pp. 552-563, 2010]]>Cancellous bone at the macroscopic level is known as being a two-phase anisotropic material composed of a solid rod-like or plate-like skeleton filled with viscous fluid. Quantifying the mechanical properties of cancellous bones by using ultrasound techniques should take into account these complexities. This paper proposes a model to investigate the transient ultrasonic wave propagation in a ...

Journal: Wave Motion, vol. 47, no. 2, pp. 117-129, 2010]]>Stress-wave propagation in solids can be controlled through imposing a gradual change of anisotropy in the material elasticity tensor. In this study, a transversely isotropic material is incorporated with a smoothly varying axis of anisotropy. It is shown that if this axis initially coincides with the stress-wave vector, then the energy of the plane waves would closely follow ...

Journal: Wave Motion, vol. 47, no. 8, pp. 519-536, 2010]]>Based on the eigenfunction expansion technique, an analytical study on wave generation by a piston wave maker in a deep wave flume in step-type is carried out. By matching ‘wavemaker’ solutions for the two regions at the cut above the step, the corresponding theoretical velocity potential and wave elevation in the flume are developed. The analytical solution is verified ...

Journal: Wave Motion, vol. 47, no. 1, pp. 1-11, 2010]]>The goal of this article is to provide different frameworks to the study of the wave propagation in complex elastic solids, namely, the singular surfaces method, the asymptotic analysis and the hierarchy of waves. A new point of view for the model of vectorial microstructures is given, and one-dimensional models (widely studied in the literature) are briefly presented. In ...

Journal: Wave Motion, vol. 47, no. 6, pp. 358-369, 2010]]>In this paper, we consider an initial–boundary value problem for the Korteweg–de Vries equation on the negative quarter-plane. The normalized Korteweg–de Vries equation considered is given byuτ+uux+uxxx=0,x0,τ>0,where x and τ represent dimensionless distance and time, respectively. In particular, we consider the case when the initial and boundary conditions are given ...

Journal: Wave Motion, vol. 47, no. 2, pp. 85-102, 2010]]>An elastic body with periodic teeth of finite height (a comb), insonified by incident ultrasonic wave and applied, with sliding contact, to the surface of another elastic body (a substrate), constitutes a typical arrangement of ultrasonic nondestructive testing system exploiting comb transducers. The arising scattering problem of incident wave on periodic voids between the teeth and the sliding teeth-substrate ...

Journal: Wave Motion, vol. 47, no. 8, pp. 508-518, 2010]]>For describing the longitudinal deformation waves in microstructured solids a Mindlin-type model is used. The embedding of a microstructure in an elastic material is reflected in an inherent length scale causing dispersion of propagating waves. Nonlinear effects, if taken into account, will counteract dispersion. A suitable balance between nonlinearity and dispersion may permit the propagation of solitary waves.Following ...

Journal: Wave Motion, vol. 47, no. 4, pp. 217-230, 2010]]>The three dimensional elastodynamic problem of diffraction of waves by a semi-infinite crack is reexamined. The application of Fourier transforms leads to a Wiener–Hopf matrix equation for its solution. An improved product factorization of this matrix due to Abrahams [1] is used to obtain relatively simple expressions for the various diffraction coefficients for incidence of plane and Rayleigh ...

Journal: Wave Motion, vol. 47, no. 5, pp. 327-332, 2010]]>In this paper we present inhomogeneous plane wave solutions within the context of linear theory of poroelastic materials. We consider the class of strongly elliptic homogeneous poroelastic materials with a center of symmetry. To construct the solutions in concern, we use the “directional-ellipse” method, which reduces the propagation problem to a secular equation for wave speeds and gives further ...

Journal: Wave Motion, vol. 47, no. 6, pp. 333-342, 2010]]>It is known that an anti-plane shear surface wave does not exist in anisotropic elastic half-space x2⩾0 when the material is homogeneous. For a functionally graded material for which the elastic stiffness C44, C45, C55 and the mass density ρ depend on the depth x2 of the half-space, an anti-plane shear surface wave may exist. Exact ...

Journal: Wave Motion, vol. 47, no. 6, pp. 350-357, 2010]]>A first-order ordinary differential system with a matrix of periodic coefficients Q(y)=Q(y+T) is studied in the context of time-harmonic elastic waves travelling with frequency ω in a unidirectionally periodic medium, for which case the monodromy matrix M(ω) implies a propagator of the wave field over a period. The main interest to the matrix logarithm ...

Journal: Wave Motion, vol. 47, no. 6, pp. 370-382, 2010]]>The existence of traveling waves in strongly inhomogeneous media is reviewed in the framework of the one-dimensional linear wave equation with a variable speed. Such solutions are found by using a homogenization, in which the variable-coefficient wave equation is transformed to a constant-coefficient Klein–Gordon equation. This transformation exists if and only if the spatial variations of ...

Journal: Wave Motion, vol. 47, no. 8, pp. 496-507, 2010]]>We present calculations of acoustic scattering from an aluminum cylinder near a rough interface computed using the elastodynamic finite integration technique (EFIT): a time-domain numerical method useful for pulse propagation in inhomogeneous fluid–elastic environments. These calculations are relevant to the modeling of underwater acoustic scattering by objects near the ocean seafloor in the low-frequency structural-acoustics regime ...

Journal: Wave Motion, vol. 47, no. 8, pp. 616-634, 2010]]>The work deals with the scattering of an incident surface wave propagating to the vertex of a circular impedance cone. Diffraction of the incident surface wave by the vertex gives rise to the reflected surface wave as well to the spherical wave from the vertex of the cone in the far-field approximation. The study is based on the Sommerfeld ...

Journal: Wave Motion, vol. 47, no. 4, pp. 241-252, 2010]]>Modulation theories, as used to describe the propagation of wavetrains, often possess a natural limitation in their tendency to finite-time breakdown via a wavenumber shock that occurs with the crossing of characteristics. For the geophysical example of linear wave propagation in an inviscid, density-stratified fluid, we demonstrate that the asymptotic corrections to modulation theory are sufficient for short-...

Journal: Wave Motion, vol. 47, no. 7, pp. 395-408, 2010]]>This paper describes the use of a boundary element formulation in the frequency domain to investigate the 2.5D acoustic wave propagation in an underwater configuration with a bottom irregularity, simulating the effect of a possible slippage between two flat parts of a waveguide. Each part is delimited by a free surface and a flat bottom, which may be built ...

Journal: Wave Motion, vol. 47, no. 8, pp. 676-692, 2010]]>