Showing papers on "Longitudinal wave published in 2000"
TL;DR: In this article, the dynamical behavior of these giant waves is addressed as solutions of the nonlinear Schrodinger equation in both 1+1 and 2+1 dimensions, and analytical results for 1 + 1 dimensions are discussed and numerically demonstrated for certain sets of initial conditions.
349 citations
TL;DR: The singularities of complex scalar waves are their zeros; these are dislocation lines in space, or points in the plane as mentioned in this paper, and the singularities are their zero points.
Abstract: The singularities of complex scalar waves are their zeros; these are dislocation lines in space, or points in the plane. For waves in space, and waves in the plane (propagating in two dimensions, o...
307 citations
Book•
20 Jan 2000
TL;DR: In this article, the authors describe different types of cyclastic wave propagation, including non-linear ACOUSTIC SURFACE WAVES on CRYSTALS and non-linear wave swarms in MARTENSITIC STRUCTURES.
Abstract: 1. DIFFERENT TYPES OF CRYSTAL 2. DISCRETE AND CONTINUUM DESCRIPTIONS: GENERAL INTRODUCTION 3. ELASTICITY AND ANELASTICITY: CONTINUOUS VIEWPOINT 4. ELASTICITY AND ANELASTICITY: DISCRETE VIEWPOINT 5. COUPLED FIELDS IN ELASTICITY 6. NONLINEAR WAVES IN ELASTIC CHAINS 7. NONLINEAR WAVES IN ELASTIC CRYSTALS WITH A MICROSTRUCTURE 8. NONLINEAR WAVES IN MARTENSITIC STRUCTURES 9. NONLINEAR ACOUSTIC SURFACE WAVES ON CRYSTALS 10. SHOCK WAVES AND PHASE-TRANSITION FRONTS IN THERMOELASTIC CRYSTALS 11. MISCELLANI 12. POSTFACE BY WAY OF CONCLUSION
266 citations
TL;DR: In this article, the authors compare results from tomographic studies with results from diffracted shear waves (Sdiff) and compressional waves (Pdiff) in the lowermost mantle using different forward and inverse methods.
Abstract: Strong heterogeneity at a variety of scale lengths has been imaged in the lowermost mantle using different forward and inverse methods. Coherent patterns in differential travel times of waves that sample the base of the mantle—such as diffracted shear waves (Sdiff) and compressional waves (Pdiff)—are readily apparent, and are compared with results from tomographic studies. Travel time and waveform modeling studies have demonstrated the presence of intense lateral variations in a variety of mapped features, such as a regionally detected high velocity D″ layer, ultra-low velocity zones, D″ anisotropy, strong scattering and heterogeneity. Such short-wavelength variations currently preclude confident mapping of D″ structure at smaller scales. Issues of seismic resolution and uncertainties are emphasized here, as well as the limitations of one-dimensional modeling/averaging in highly heterogeneous environments.
236 citations
TL;DR: In this article, the authors generalize Biot's theory of poroelasticity to incorporate wave propagation effects and show how effects that are usually attributed to squirt flow under partially saturated conditions can be explained alternatively in terms of the double-porosity model.
222 citations
TL;DR: In this article, it was shown that the solitary wave of a model for nonlinear dispersive waves in cylindrical compressible hyperelastic rods is orbitally stable, and that the shape of the wave is stable.
194 citations
IBM1
TL;DR: Atomic simulations of crack propagation along a weak interface joining two harmonic crystals show that a mode II shear dominated crack can accelerate to the Rayleigh wave speed and then nucleate an intersonic daughter that travels at the longitudinal wave speed.
Abstract: We have performed atomic simulations of crack propagation along a weak interface joining two harmonic crystals. The simulations show that a mode II shear dominated crack can accelerate to the Rayleigh wave speed and then nucleate an intersonic daughter that travels at the longitudinal wave speed. This contradicts the general belief that a crack can travel no faster than the Rayleigh speed.
192 citations
TL;DR: In this article, a nonlinear dispersive equation was derived for a system of incompressible hyperelastic rods with a vertical singular line in the phase plane, which leads to the appearance of shock waves.
Abstract: In the literature, it has been conjectured that solitary shock waves can arise in incompressible hyperelastic rods. Recently, it has been shown that this conjecture is true. One might guess that when compressibility is taken into account, such a wave, which is both a solitary wave and a shock wave, can still arise. One of the aims of this paper is to show the existence of this interesting type of wave in general compressible hyperelastic rods and provide an analytical description. It is difficult to directly tackle the fully nonlinear rod equations. Here, by using a non–dimensionalization process and the reductive perturbation technique, we derive a new type of nonlinear dispersive equation as the model equation. We then focus on the travelling–wave solutions of this new equation. As a result, we obtain a system of ordinary differential equations. An important feature of this system is that there is a vertical singular line in the phase plane, which leads to the appearance of shock waves. By considering the equilibrium points and their relative positions to the singular line, we are able to determine all qualitatively different phase planes. Those paths in phase planes which represent physically acceptable solutions are discussed one by one. It turns out that there is a variety of travelling waves, including solitary shock waves, solitary waves, periodic shock waves, etc. Analytical expressions for all these waves are obtained. A new phenomenon is also found: a solitary wave can suddenly change into a periodic wave (with finite period). In dynamical systems, this represents a homoclinic orbit suddenly changing into a closed orbit. To the authors9 knowledge, such a bifurcation has not been found in any other dynamical systems.
175 citations
TL;DR: In this paper, the authors investigated the role of wave breaking in a stratified fluid and found that wave amplitude is defined as the maximal excursion of the stratified layer and the breaking introduces a broadening of the waves.
Abstract: Solitary waves propagating horizontally in a stratified fluid are investigated. The fluid has a shallow layer with linear stratification and a deep layer with constant density. The investigation is both experimental and theoretical. Detailed measurements of the velocities induced by the waves are facilitated by particle tracking velocimetry (PTV) and particle image velocimetry (PIV). Particular attention is paid to the role of wave breaking which is observed in the experiments. Incipient breaking is found to take place for moderately large waves in the form of the generation of vortices in the leading part of the waves. The maximal induced fluid velocity close to the free surface is then about 80% of the wave speed, and the wave amplitude is about half of the depth of the stratified layer. Wave amplitude is defined as the maximal excursion of the stratified layer. The breaking increases in power with increasing wave amplitude. The magnitude of the induced fluid velocity in the large waves is found to be approximately bounded by the wave speed. The breaking introduces a broadening of the waves. In the experiments a maximal amplitude and speed of the waves are obtained. A theoretical fully nonlinear two-layer model is developed in parallel with the experiments. In this model the fluid motion is assumed to be steady in a frame of reference moving with the wave. The Brunt-Vaisala frequency is constant in the layer with linear stratification and zero in the other. A mathematical solution is obtained by means of integral equations. Experiments and theory show good agreement up to breaking. An approximately linear relationship between the wave speed and amplitude is found both in the theory and the experiments and also when wave breaking is observed in the latter. The upper bound of the fluid velocity and the broadening of the waves, observed in the experiments, are not predicted by the theory, however. There was always found to be excursion of the solitary waves into the layer with constant density, irrespective of the ratio between the depths of the layers.
155 citations
TL;DR: In this article, the authors have made sets of independent compressional and shear wave velocity measurements, which with density, allow them to completely characterize the transverse isotropy of samples from five metamorphic belts: the Haast schist terrane (South Island, New Zealand), Poultney slate, Chugach phyllite, Coldfoot schist, and Pelona schist (United States).
Abstract: We have made sets of five independent compressional and shear wave velocity measurements, which with density, allow us to completely characterize the transverse isotropy of samples from five metamorphic belts: the Haast schist terrane (South Island, New Zealand), Poultney slate, Chugach phyllite, Coldfoot schist, and Pelona schist (United States). These velocity measurements include compressional wave velocities for propagation parallel, perpendicular, and at 45° to the symmetry axis, shear wave velocity for propagation and particle motion perpendicular to the symmetry axis, and shear wave velocity for propagation parallel to the symmetry axis. Velocity measurements were made up to pressures of 1 GPa (∼35-km depth) where microcracks are closed and anisotropy is due to preferred mineral orientation. Our samples exhibit compressional wave anisotropy of 9–20% as well as significant shear wave splitting. Metamorphic terranes that are anisotropic to ultrasonic waves may also be anisotropic at the scale of active and passive seismic experiments. Our data suggest that a significant thickness (10–20 km) of appropriately oriented (steeply dipping foliation) schist in the crust could contribute as much as 45% of observed shear wave splitting. Our data set can also be used to model the effects of crustal anisotropy for active source seismic experiments in order to determine if the anisotropy of the terrane is significant and needs to be taken into account during processing and modeling of the data.
150 citations
TL;DR: In this article, the authors concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form.
Abstract: ▪ Abstract We concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form. These effects are discussed in the context of standing gravity and gravity-capillary waves, Faraday waves, and parasitic capillary waves. Focus is primarily on post-1989 research. Regarding standing waves, new waveforms and the large effect that small capillarity can have are considered. Faraday waves are discussed principally with regard to viscous effects, hysteresis, and limit cycles; nonlinear waveforms of low mode numbers; contact-line effects and surfactants; breaking and subharmonics; and drop ejection. Pattern formation and chaotic and nonlinear dynamics of Faraday waves are mentioned only briefly. Gravity and gravity-capillary wave generation of parasitic capillaries and dissipation are considered at length. We conclude with our view on the direction of future research in these areas.
TL;DR: In this paper, the authors investigated the flow and surface structure in laminar wavy films over a Reynolds number range from Ref=ρūδf/η=27-200.
TL;DR: In this article, slow magnetosonic waves were identified in polar plumes, at heights up to about 1.2 R☉ using the Extreme Ultraviolet Imaging Telescope (EIT) observations of quasi-periodic EUV intensity fluctuations, and higher in the corona using the UVCS white-light channel.
Abstract: Recently, slow magnetosonic waves were identified in polar plumes, at heights up to about 1.2 R☉ using the Extreme Ultraviolet Imaging Telescope (EIT) observations of quasi-periodic EUV intensity fluctuations, and higher in the corona using the Ultraviolet Coronagraph Spectrometer (UVCS) white-light channel. First, we derive the linear dispersion relation for the slow waves in the viscous plasma. Next, we derive and solve an evolutionary equation of the Burgers type for the slow waves, incorporating the effects of radial stratification, quadratic nonlinearity, and viscosity. Finally, we model the propagation and dissipation of slow magnetosonic waves in polar plumes using one-dimensional and two-dimensional MHD codes in spherical geometry. The waves are launched at the base of the corona with a monochromatic source. We find that the slow waves nonlinearly steepen as they propagate away from the Sun into the solar wind. The nonlinear steepening of the waves leads to enhanced dissipation owing to compressive viscosity at the wave fronts. The efficient dissipation of the slow wave by compressive viscosity leads to damping of the waves within the first solar radii above the surface. We investigate the parametric dependence of the wave properties.
TL;DR: An effective medium theory for composite materials is used and shows that the presence of a volume fraction of 3 to 10% liquid in the form of oblate spheroidal inclusions aligned in the equatorial plane between iron crystals is sufficient to explain the aforementioned seismic phenomena.
Abstract: Seismological studies indicate that the inner core of Earth is anisotropic for compressional waves (P waves), and has low shear wave (S wave) velocity, and high seismic attenuation. Using an effective medium theory for composite materials, we show that the presence of a volume fraction of 3 to 10% liquid in the form of oblate spheroidal inclusions aligned in the equatorial plane between iron crystals is sufficient to explain the aforementioned seismic phenomena. Variation of S-wave velocity between the polar axis and equatorial plane is more sensitive to the addition of liquid than that of P waves. The liquid could arise from the presence of dendrites or a mixture of elements other than iron that exist in liquid form under inner-core conditions.
TL;DR: In this paper, the shape memory alloys are used to control the dynamics of wave propagation in rods and an analytical model is presented to study the attenuation capabilities of the composite rods and to determine the influence of the various design parameters of the inserts that can control the width of the pass and stop-bands.
Abstract: Longitudinal wave propagation is controlled using shape memory inserts placed periodically along rods. The inserts act as sources of impedance mismatch with tunable characteristics. Such characteristics are attributed to the unique behavior of the shape memory alloy whereby the elastic modulus of the inserts can be varied up to three times as the alloy undergoes a phase transformation from martensite to austenite, With such controllable capability, the inserts can introduce the proper impedance mismatch necessary to impede the wave propagation along the rods. An analytical model is presented to study the attenuation capabilities of the composite rods and to determine the influence of the various design parameters of the inserts that can control the width of the pass and stop-bands. The numerical results demonstrate the potential of shape memory alloys in controlling the dynamics of wave propagation in rods. Furthermore, the obtained results provide a guideline for designing inserts that are capable of filtering out selected excitation frequencies through proper adjustment of the geometry of the inserts as well as their activation strategies.
TL;DR: In this article, an analytical solution in the Laplace transform domain is obtained showing clearly two compressional waves and a second compressional wave known as the slow wave has been identified.
Abstract: Biot's theory of porous media governs the wave propagation in a porous, elastic solid infiltrated with fluid. In this theory, a second compressional wave, known as the slow wave, has been identified. In this paper, Biot's theory is applied to a one-dimensional continuum. Despite the simplicity of the geometry, an exact solution of the full model, and a detailed analysis of the phenomenon, so far have not been achieved. In the present approach, an analytical solution in the Laplace transform domain is obtained showing clearly two compressional waves. For the special case of an inviscid fluid, a closed form exact solution in time domain is obtained using an analytical inverse Laplace transform. For the general case of a viscous fluid, solution in time domain is evaluated using the Convolution Quadrature Method of Lubich. Of all the inverse methods previously investigated, it seems that only the method of Lubich is efficies and stable enough to handle the highly transient cases such as impact and step loadings. Using properties of three widely different real materials, the wave propagating behavior, in terms of stress, pore pressure, displacement, and flux, are examined. Of most interest is the identification of second compressional wave and its sensitivity of material parameters.
TL;DR: In this paper, a constructive method is given, for obtaining all small bounded travelling waves for generic potentials, near the first critical value of the velocity of the waves, which is given by solutions of a finite-dimensional reversible ordinary differential equation.
Abstract: We consider travelling wave solutions on a one-dimensional lattice, corresponding to mass particles interacting nonlinearly with their nearest neighbour (the Fermi-Pasta-Ulam model). A constructive method is given, for obtaining all small bounded travelling waves for generic potentials, near the first critical value of the velocity. They all are given by solutions of a finite-dimensional reversible ordinary differential equation . In particular, near (above) the first critical velocity of the waves, we construct the solitary waves (localized waves with the basic state at infinity) whose global existence was proved by Friesecke and Wattis, using a variational approach. In addition, we find other travelling waves such as (a) a superposition of a periodic oscillation with a non-zero uniform stretching or compression between particles, (b) mainly localized waves which tend towards a uniformly stretched or compressed lattice at infinity, (c) heteroclinic solutions connecting a stretched pattern with a compressed one.
TL;DR: A unified spectral and temporal representation is introduced for nondIFFracting waves that spans the commonly considered nondiffracting wave solutions and is extended to include singular Neumann and Hankel waves, or Y waves.
Abstract: A unified spectral and temporal representation is introduced for nondiffracting waves. We consider a set of elementary broadband X waves that spans the commonly considered nondiffracting wave solutions. These basis X waves have a simple spectral representation that leads to expressions in closed algebraic form or, alternatively, in terms of hypergeometric functions. The span of the X waves is also closed with respect to all spatial and temporal derivatives and, consequently, they can be used to compose different types of waves with complex spectral and spatial properties. The unified description of Bessel-based nondiffracting waves is further extended to include singular Neumann and Hankel waves, or Y waves. We also discuss connections between the different known nondiffracting wave solutions, and their relations to the present unified approach.
TL;DR: In this article, the Euler-Lagrange equation of a simple functional was used to describe the Stokes wave on the free surface of an infinitely deep irrotational flow under gravity without surface tension.
Abstract: Steady periodic water waves on the free surface of an infinitely deep irrotational flow under gravity without surface tension (Stokes waves) can be described in terms of solutions of a quasi-linear equation which involves the Hilbert transform and which is the Euler-Lagrange equation of a simple functional. The unknowns are a 2π-periodic function w which gives the wave profile and the Froude number, a dimensionless parameter reflecting the wavelength when the wave speed is fixed (and vice versa).
TL;DR: In this article, the authors measured the reduction of shear and longitudinal wave velocities caused by grain boundary melt, having nearly equilibrium textures, was measured accurately as functions of both melt fraction and dihedral angle.
Abstract: Borneol-diphenylamine, a binary eutectic system of the organic compounds, provides an appropriate analogue of melting in the Earth's mantle. Eutectic temperature is just above room temperature (43°C), and at this temperature the dihedral angle is about 40°. As the temperature increases, the dihedral angle gradually decreases at a rate of about 1.5° per 1°C, and becomes nearly zero at 70°C. Melt fraction change is small at this temperature range; this system is therefore appropriate in investigating a systematic effect of dihedral angle. Using this system, reduction of the shear and longitudinal wave velocities caused by grain boundary melt, having nearly equilibrium textures, was measured accurately as functions of both melt fraction and dihedral angle. The results demonstrate the significant effect of equilibrium melt geometry on shear wave velocities, while also showing that the effects of melting and dihedral angles are much smaller on the longitudinal waves. The quantitative effects of the melt fraction and dihedral angles on the acoustic wave velocities can be predicted theoretically using the elasticities of granular media derived as functions of grain-boundary contiguity [Takei, 1998]. The present experimental results described in this paper agree well with the theoretical predictions and demonstrate the validity of the theory. Clarifying the analogy and difference between the present organic system and the Earth's materials, the shear and longitudinal wave velocities of the partially molten rocks in the Earth were predicted as functions of melt fraction, dihedral angle, and the compressibility ratio between solid and melt.
TL;DR: In this paper, an ensemble of random-phase internal gravity waves is considered in the dynamical framework of the Euler-Boussinesq equations, and a kinetic equation for the mean spectral energy density of the waves is obtained under hypothesis of Gaussian statistics with zero correlation length.
Book•
01 Jan 2000
TL;DR: In this article, the authors present a survey of the history of guided wave propagation in crystal models and their representation by tensors, including elasticity and piezoelectricity properties.
Abstract: Historical Survey.- Waves, Fluid as a Scalar Model.- Crystal Properties and Their Representation by Tensors.- Elasticity and Piezoelectricity.- Plane Waves in Crystals.- Guided Waves.
TL;DR: In this paper, the small strain stiffness and anisotropic nature of two sands with different geological origin have been determined via laboratory seismic tests performed in a triaxial cell, where both shear and constrained compression waves were propagated in vertical, horizontal and oblique directions by means of five couples of piezoelectric transducers especially arranged in the specimens.
TL;DR: In this paper, the fabrication, evaluation and several applications of metallic buffer rods consisting of a core and a cladding are presented, where the core can have a taper shape and the cladding is fabricated by thermal spray techniques.
Abstract: The fabrication, evaluation and several applications of metallic buffer rods consisting of a core and a cladding are presented. The clad rods can have a taper shape and the cladding is fabricated by thermal spray techniques. Clad rods as long as 1 m have been fabricated. Experimental results show that the ultrasonic signals detected at 5 MHz with these buffer rods have very high signal to noise ratio (>35 dB) for both longitudinal and shear waves in a reflection mode. Applications to the measurement of the thickness of hot plates and molten metals up to 960°C and to the on-line monitoring of polymer extrusion are reported.
Patent•
TL;DR: In this paper, an imaging method for observing the propagation of a low-frequency shearing pulse wave simultaneously in multiple points of a diffusing viscoelastic medium was proposed.
Abstract: The invention concerns an imaging method for observing the propagation of a low-frequency shearing pulse wave simultaneously in multiple points of a diffusing viscoelastic medium (1). The method consists in transmitting at very high rate ultrasonic compression waves enabling to obtain a succession of images of the medium; then in delayed processing of the resulting images by intercorrelation to determine in each point of each image the movements of the medium while the shearing wave is being propagated.
TL;DR: In this article, a high-speed train entering a tunnel is studied theoretically and experimentally, and it is shown that the pressure rise across the wavefront is given approximately byformula here, where ρo, U, M, [Ascr ]o and [Ag] respectively denote the mean air density, train speed, train Mach number, and the cross-sectional areas of the train and the uniform section of the tunnel.
Abstract: The compression wave generated by a high-speed train entering a tunnel is studied theoretically and experimentally. It is shown that the pressure rise across the wavefront is given approximately byformula herewhere ρo, U, M, [Ascr ]o and [Ascr ] respectively denote the mean air density, train speed, train Mach number, and the cross-sectional areas of the train and the uniform section of the tunnel. A monopole source representing the displacement of air by the train is responsible for the main pressure rise across the wave, but second-order dipole sources must also be invoked to render theoretical predictions compatible with experiment. The principal dipole is produced by the compression wave drag acting on the nose of the train. A second dipole of comparable strength, but probably less significant in practice, is attributed to ‘vortex sound’ sources in the shear layers of the back-flow out of the tunnel of the air displaced by the train.Experiments are performed that confirm the efficacy of an ‘optimally flared’ portal whose cross-sectional area S(x) varies according to the formulaformula herewhere x is distance increasing negatively into the tunnel, [lscr ] is the prescribed length of the flared section, and [Ascr ]E is the tunnel entrance cross-sectional area, given byformula hereThis portal is predicted theoretically to cause the pressure to increase linearly with distance across a compression wavefront of thickness ∼ [lscr ]/M, which is very much larger than in the absence of flaring. The increased wave thickness and linear pressure variation counteract the effect of nonlinear steepening of the wave in a long tunnel, and tend to suppress the environmentally harmful ‘micro-pressure wave’ radiated from the far end of the tunnel when the compression wave arrives. Our experiments are conducted at model scale using axisymmetric ‘trains’ projected at U ∼ 300 k.p.h. (M ≈ 0.25) along the axis of a cylindrical tunnel fitted with a flared portal. The blockage [Ascr ]o/[Ascr ] = 0.2, which is comparable to the larger values encountered in high-speed rail operations.
TL;DR: The main advantages of this new method are that imaging can be done near the focal plane, therefore an optimal signal to noise ratio is achieved, no interference with Rayleigh waves occurs, and the method requires only an approximate estimate of the material properties of the solid substratum where the cells are growing on.
TL;DR: In this paper, the wave behavior and flow characteristics of falling liquid films on a vertical wall and an inclined wall have been studied by means of a numerical simulation, in which the algorithm is based on MAC method.
TL;DR: It was found that the leading tensile pulse of the reflected longitudinal wave is responsible for the initiation of microcracks in regions inside the phantom where high tensile stresses are produced.
Abstract: Photoelastic and shadowgraph imaging techniques were used to visualize the propagation and evolution of stress waves, and the resultant transient stress fields in solids during shock wave lithotripsy. In parallel, theoretical analysis of the wavefront evolution inside the solids was performed using a ray-tracing method. Excellent agreement between the theoretical prediction and experimental results was observed. Both the sample size and geometry were found to have a significant influence on the wave evolution and associated stress field produced inside the solid. In particular, characteristic patterns of spalling damage (i.e., transverse and longitudinal crack formation) were observed using plaster-of-Paris cylindrical phantoms of rectangular and circular cross sections. It was found that the leading tensile pulse of the reflected longitudinal wave is responsible for the initiation of microcracks in regions inside the phantom where high tensile stresses are produced. In addition, the transmitted shear wave was found to play a critical role in facilitating the extension and propagation of the microcrack.
TL;DR: In this article, the generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermovisco- elastic plane waves of assigned frequency in an infinite viscoelastic solid of Kelvin-Voigt type.
Abstract: The generalized dynamical theory of thermo-elasticity proposed by Green and Lindsay is applied to study the propagation of harmonically time-dependent thermo-visco- elastic plane waves of assigned frequency in an infinite visco-elastic solid of Kelvin-Voigt type, when the entire medium rotates with a uniform angular velocity A more general dispersion equation is deduced to determine the effects of rotation, visco-elasticity, and relaxation time on the phase-velocity of the coupled waves The solutions for the phase velocity and attenuation coefficient are obtained for small thermo-elastic couplings by the perturbation technique Taking an appropriate material, the numerical values of the phase velocity of the waves are computed and the results are shown graphically to illustrate the