Two-dimensional wave propagation in a rotating elastic solid with voids

Two-dimensional wave propagation is studied in an isothermal linear isotropic elastic material with voids rotating with constant angular velocity based on a theory of elastic material with voids developed by Ie?an (1986) in the thermoelastic context. It is found that there exist three coupled plane waves propagating with distinct phase speeds. The presence of voids and the rotation of the medium are responsible for this coupling. In the absence of voids, the classical longitudinal and transverse waves are found to be coupled through the rotation of the medium. At very large frequency or when the angular rotation is very small relative to the wave frequency the waves are decoupled and propagate with distinct phase speeds. These are (i) a longitudinal wave, (ii) a transverse wave and (iii) a longitudinal wave corresponding to the change in void volume fraction. The first two correspond to the waves of classical elasticity, while the third is new and arises from the presence of the voids. The results are illustrated graphically.     

A slow wave with the structure of an electromagnetic wave in piezoelectric and magnetostrictive media

The propagation of elastic waves in piezoelectric and magnetostrictive materials is considered theoretically. It is shown that an elastic wave in a piezoelectric can create not only a longitudinal electric field parallel to the wave normal (longitudinal piezoactivity) but also a transverse field of electric induction (transverse piezoactivity). The presence of a transverse induction field leads to the appearance of a magnetic field perpendicular to the direction of the wave normal and to the induction vector; therefore, the transverse-piezoactive wave is accompanied by a transverse wave having the structure of an electromagnetic wave and propagating with the speed of sound. Transverse-magnetostrictive elastic waves in magnetostrictive dielectrics are accompanied by a similar wave.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 32–36, October, 1976.     

Evaluation of the vibrational modes of the human skull as it relates to bone-conducted sound

Analytic and numerical models are used to study bone-conducted sound and how it relates to the vibrational modes of the human skull. The analytic model is based on the solution to the acoustic and elastic wave equations and the constraining boundary conditions for a fluid-filled elastic sphere. Both models predict that most of the acoustic energy of bone-conducted sound exists in the form of surface wave vibrations at the interface between two acoustic media rather than in the bone or cranial chamber. These surface waves have phase speeds much slower than the bulk sound speed for bone. The analytic model, based on spherical elastic shells, predicts a phase speed of 775 m/s and the first resonance frequency at 1500 Hz while the numerical solution yields approximate phase speeds of 450 m/s and provides a visual display of the surface waves and diffraction effects.     

Effect of Particle Number Density on Wave Dispersion in a Two-Dimensional Yukawa System

Effect of the particle number density on the dispersion properties of longitudinal and transverse lattice waves in a two-dimensional Yukawa charged-dust system is investigated using molecular dynamics simulation. The dispersion relations for the waves are obtained. It is found that the frequencies of both the longitudinal and transverse dust waves increase with the density and when the density is sufficiently high a cutoff region appears at the short wavelength. With the increase of the particle number density, the common frequency tends to increase, and the sound speed of the longitudinal wave also increases, but that of the transverse wave remains low.     

Heat pulse propagation in a crystal: A molecular dynamical calculation

The propagation of a heat pulse into a perfect bcc crystal is studied by means of molecular dynamical calculations. We observe second sound waves associated with the heat pulse as well as with longitudinal and transverse elastic pulses. Our results explain a number of features observed in second sound experiments and suggest that second sound is a phenomenon of general occurrence.     

Effect of the number of defect particles on the structure and dispersion relation of a two-dimensional dust lattice system

The effect of the number of defect particles on the structure and dispersion relations of a two-dimensional (2D) dust lattice is studied by molecular dynamics (MD) simulation. The dust lattice structures are characterized by particle distribution, nearest neighbor configuration and pair correlation function. The current autocorrelation function, the dispersion relation and sound speed are used to represent the wave properties. The wave propagation of the dust lattice closely relates to the lattice structure. It shows that the number of defect particles can affect the dust lattice local structure and then affect the dispersion relations of waves propagating in it. The presence of defect particles has a greater effect on the transverse waves than on the longitudinal waves of the dust lattice. The appropriate number of defect particles can weaken the anisotropy property of the lattice.     

DISCRETE HUYGENS' MODELLING APPROACH TO WAVE PROPAGATIONS IN A HOMOGENEOUS ELASTIC FIELD

The application of the discrete Huygens' modelling has been discussed for acoustic wave propagation problems, in which the scalar wave field problems have been focused. The present paper extends the application of the modelling to the elastic wave propagation in a homogeneous elastic medium in which two types of waves, the longitudinal wave and the shear wave, are independent except at the boundary. Each wave can be treated like a scalar wave until the two waves reach the boundary where they couple so as to satisfy the displacement or stress boundary condition. We propose the approach confining ourselves to the two-dimensional field. Some examples are demonstrated, whose solutions are compared with the vectorial wave modelling and finite difference modelling solutions whenever they are available.     

Effect of shear-wave polarization on defect detection in stainless steel weld metal

Ultrasonic inspections of austenitic stainless steel weld metal are particularly difficult because of the dendritic structure and anisotropy of the material. The acoustic properties of stainless steel weld metal are discussed. Data on frequency spectra and variations in longitudinal and shear velocities with wave propagation direction are presented. Differences in shear velocities as great as 25% have been observed as the polarization direction is changed. The difference in detectability of artificial reflectors using shear waves of varying polarization is presented, and it is demonstrated in some cases that horizontally polarized shear waves can ‘detect’ a reflector in the weld metal where the traditional vertically polarized shear waves cannot.     

Sound velocity anomalies near the spin glass transition in an austenitic stainless steel alloy

A cusp in the magnetic susceptibility temperature dependence of a commercial manganese austenitic stainless steel alloy, attributable to spin-glass condensation, is accompanied by anomalies in the temperature dependences of both longitudinal and transverse ultrasonic wave velocities.     

Excitation of seismoacoustic waves by a harmonic force source acting at the boundary of a liquid layer and an elastic halfspace

A problem on the excitation of seismoacoustic waves in a system of a homogeneous isotropic elastic halfspace covered with a liquid layer is solved in the case of action of a source of point harmonic force on the surface of an elastic medium. Integral expressions are obtained for the radiation powers averaged over a wave period for longitudinal and transverse waves in a solid. Mode excitation is analyzed in detail. Expressions describing parts of the mode powers radiated into a liquid layer and an elastic medium are obtained. Numerical analysis of radiation powers is conducted for spherical longitudinal and transverse waves as well as for the radiation powers of seismoacoustic modes in a solid halfspace and a liquid layer. It is determined that in the conditions characteristic of bottom rocks in the case, where the basin depth is several times and more larger than the sound’s wavelength, about 2/3 of the total power is radiated into a liquid.     

Mechanical anisotropy and thermoacoustic properties of SnO2 under high pressures: an ab initio approach

The effects of hydrostatic pressures on the electronic, thermoacoustic and elastic anisotropies of SnO₂ in the rutile structure is analyzed up to 18 GPa. It is found that the polycrystalline bulk modulus B increases from 227 to 312 GPa between 0 and 18 GPa while the Young and shear moduli slightly decrease with pressures. The resulting polycrystalline ductility increases with pressures. The speed of the sound for longitudinal waves increases with pressure, while the transverse polarizations and the Debye temperature decrease. Large crystal anisotropy for the shear planes {001} between ? 110? and ? 010? directions under pressures, associated with the phase transition to the Cl₂Ca, is found.     

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.     

Elastic waves in suspensions

A model of heterogeneous medium taking into account the friction between the particles and liquid, as well as the relaxation of the small-size particles to the equilibrium on the stress, has been proposed to describe the propagation of the elastic waves in a suspension. A system of wave equations describing the propagation of a plane longitudinal wave has been formulated for the components of the medium. Analytical expressions for the sound velocity in a suspension has been obtained in the approximation in which the particles are completely carried away by liquid in the limiting cases in which the particles are in equilibrium under stress with the liquid or equilibrium is absent. The dependence of the sound velocity in the medium on the volumetric portion and the size of the inclusions has been studied. The obtained results agree with the experimental data and obtained analytical expressions for the sound velocity. The dynamics of the components of the medium at the propagation of the plane longitudinal monochromatic wave has been studied.     

A Helmholtz resonator buried in the ground as a source of seismic waves and low-frequency sound in the atmosphere

The procedure is given for calculating the total power of low-frequency sound and seismic waves produced by a Helmholtz resonator in the form of an air-filled spherical cavity buried in the ground and supplied with a hole through which it is connected with the atmosphere. The sound is generated by air oscillations in the resonator’s neck section that is open to the atmosphere, while the compression and shear elastic waves are generated in the bulk of the ground by cyclic pressure fluctuations that act on the spherical walls of the cavity. Calculations show that the coincidence of the resonance frequencies (within approximately ten to hundred hertz), at which both the sound radiation to the atmosphere and the elastic seismic radiation in the form of longitudinal and transverse bulk waves are maximum, can occur only when the resonator is placed in a loose ground characterized by reduced elastic characteristics. In these conditions, the power of transverse waves exceeds the sound power by a factor of two and the power of longitudinal waves is smaller than the sound power by a factor of several tens.     

A model for the propagation of nonlinear dispersive strain waves in a solid with defect clusters

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is developed with taking into account the interaction with atomic defect clusters. The governing nonlinear dispersive-dissipative equation describing the evolution of longitudinal strain waves is derived. An approximate solution of the model equation was derived which describes asymmetrical distortion of geometry of the solitary strain wave due to the interaction between the strain field and the field of clusters. The contributions of the finiteness of the relaxation times of cluster-induced atomic defects to the linear elastic modulus and the lattice dissipation and dispersion parameters are determined. The amplitudes and width of the nonlinear waves depend on the elastic constants and on the properties of the defect subsystem (atomic defects, clusters) in the medium. The explicit expression is received for the sound velocity dependence upon the fractional cluster volume, which is in good agreement with experiment. The critical value of cluster volume fraction for the influence on the strain wave propagation is determined.     

On the propagation of acceleration waves in incompressible hyperelastic solids

The conditions for the propagation of acceleration waves (sound waves) in incompressible elastic media undergoing finite deformation are investigated. The incompressible hyperelastic solid media is considered in accordance with the general constitutive theory of materials subject to internal mechanical constraints. The equation of motion of acceleration waves is obtained using the theory of singular surfaces. A general comparison is made between the magnitudes of the propagation speeds of waves in incompressible and unconstrained solid media by the use of Mandel's inequalities. The magnitudes of the speeds of propagation of acceleration waves in the incompressible hyperelastic material classes of neo-Hookean, Mooney-Rivlin, and St. Venant-Kirchhoff solids are determined. Comparisons are made of the specific results concerning the magnitudes of wave propagation speeds making use of the corresponding material parameters.     

Temperature dependent physical effects of ultrasonic wave in beryllium chalcogenides

Temperature dependent physical effects of ultrasonic wave viz. ultrasonic attenuation due to interaction of sound wave and thermal phonons, thermoelastic loss and dislocation damping have been studied in beryllium chalcogenides (BeX, X = S, Se and Te) in the temperature range 50-500 K, along three crystallographic directions of propagation viz. [1 0 0], [1 1 0] and [1 1 1] for longitudinal and shear modes of propagation. Second and third order elastic moduli have been obtained using electrostatic and Born repulsive potentials and taking hardness parameter and nearest neighbour distance as input data. Gruneisen numbers, acoustic coupling constants and drag coefficients have been evaluated for longitudinal and shear waves along different directions of propagation and polarization. The results have been discussed and compared with the available data. It has been found that the temperature dependence of ultrasonic attenuation follows the temperature variation of diffusion coefficient and is mainly dominated by phonon-phonon interaction.     

Use of Pulse-Echo Ultrasound Imaging in Transcranial Diagnostics of Brain Structures

The results are presented from computer simulations of acoustic pulse propagation in heterogenous media mimicking the human head in two-dimensional and three-dimensional geometries. In the three-dimensional experiment, the cranial bone is presented as a liquid layer with a speed of sound corresponding to that of longitudinal waves in the bone. In the two-dimensional experiment, both longitudinal and transverse waves are considered. Based on data obtained in the numerical experiments, the possibility of obtaining ultrasound images of point scatterers by compensating for aberrations introduced by cranial bones is studied. It is shown that even a simple time delay correction along straight rays greatly improves the quality of an ultrasound image obtained through a nonuniform-thickness solid layer.     

Elastic properties of NaxK1-xBr and Naxk1-xCl solid solutions

A pulsed ultrasonic method has been used to measure the speeds of longitudinal and transverse elastic waves along [100] and [110] in single crystals of Na_xK_1-xBr and Na_xK_1–xCl solid solutions in the range 20–180°C; the elastic constants c_ik have been determined. These values have been extrapolated to 0°K, while the bulk modulus and shear modulus have been calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 76–81, January, 1973.     

Acoustic studies of metal-ceramic composites with meso- and nanosize particles

The elasticity moduli and absorption coefficients of longitudinal ultrasonic waves with a frequency of 2–50 MHz depending on the steel concentration and sintering temperature of 1400–1700°C in vacuum were studied in samples of cermet-type composites on the basis of corundum and stainless steel. The results were discussed from the point of view of the elastic waves propagating in the fine-disperse two-phase medium at the presence of the intergrain and interphase boundaries, noticeably affecting the physical properties of the composite.