On the Rayleigh wave on a curvilinear boundary between elastic and fluid media

Along the boundary between elastic and fluid media, the surface Rayleigh wave propagates. The velocity of this wave v _R0 in the case of a plane boundary is less than the velocity of the Rayleigh wave v _R on a free plane boundary of an elastic medium and less than the velocity v _P0 in a fluid medium. To investigate the velocity v _R0 in the case of curvilinear boundaries, the propagation of Rayleigh waves under consideration along cylindrical and spherical surfaces is studied. The velocity of the Rayleigh wave depends on the curvature of the wave trajectory and the curvature in the direction perpendicular to the trajectory. Furthermore this velocity depends on the presence or absence of a fluid medium. Bibliography: 5 titles.     

Propagation of Rayleigh waves of sv type in transversely isotropic elastic media

The asymptotics of high-frequency surface waves in elastic media is studied for a special case of anisotropy, namely, for transversely isotropic media (where the parameters of elasticity are invariant with respect to rotations about one of the coordinate axes). In the zeroth asymptotic approximation, the slow Rayleigh waves (of SV type) under study are polarized in the plane of the normal section of the surface. The principal term of the asymptotics (which has the form of a space-time (caustic) expansion) is found, and calculations related to the necessity of introducing two additional faster waves with complex eikonals are carried out. The conditions on the elasticity parameters of the medium that insure the origination of the surface waves in question are obtained. Due to the specific structure of the elasticity tensor under consideration, the boundary of the medium is necesarily plane. For appropriate values of elastic parameters, the resulting formulas coincide with the corresponding expressions in the isotropic case. Bibliography: 8 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 278–293. Translated by Z. A. Yanson     

Rayleigh wave scattering by a plane strip in a deep ocean

A theoretical formulation to study the problem of scattering of Rayleigh waves due to the presence of a rigid plane strip in a deep ocean is presented. A rigid plane strip (0 ≤z ≤ H, 0 ≤x ≤ l) is fixed in the surface of the ocean occupyingz ≥ 0. Fourier transformation and Wiener-Hopf technique are used to arrive at the solution. The scattered Rayleigh waves behave as cylindrical waves emerging out of the corner of the strip and its image in the free surface of the ocean. The scattered waves are obtained in terms of Bessel functions whose behaviour near and far from the strip is well-known. The numerical calculations for the scattered waves show that their amplitude increases rapidly for a small increase in the value of the wave number. Scattering of Rayleigh waves due to a thin plane vertical barrier and a thin barrier in the free surface of the ocean has been considered as the special cases.     

Dispersion Equations for Rayleigh Waves in a Piezoelectric Periodically Layered Structure

Dispersion equations are proposed for acoustoelectric Rayleigh waves in a periodically layered piezoelectric half space with various types of boundary conditions. The properties of the medium are specified by the determining relations for the 6mm crystallographic class. These equations are obtained using the mathematical formalism of periodic hamiltonian systems. This approach makes it possible to include the anisotropy and the piezoelectric interaction of the mechanical and electric fields and is valid for stratified media with arbitrary variations in the properties along the periodicity axis. Numerical results are presented for alternating layers of CdS and ZnO. The influence of the piezoelectric effect and type of boundary conditions on the dispersion spectra of surface waves is examined.     

Viscoelastic Rayleigh waves in a layered structure with a weak lateral inhomogeneity

Rayleigh waves in an almost layered viscoelastic medium are studied by using the “surface” ray method based on real rays. Viscoelasticity is described in terms of the Maxwell-Boltzmann-Volterra model and, for high frequencies, is treated as perturbed perfect elasticity. In addition to the leading term of the ray asymptotics, which corresponds to the balance of energy along rays, the correction term describing anomalous displacements of the Love type is discussed. Bibliography: 10 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 7–13.     

Reflection and transmission of the surface <Emphasis Type="Italic">P</Emphasis>-waves on the line of jump in elastic parameters

Problems of diffraction of elastic surface waves of horizontal polarization (P-waves) on a line of jump in elastic parameters are considered. The corresponding coefficients of reflection, refraction, and transmission are obtained by means of the parabolic equation method. A comparison of the Rayleigh waves, SV-waves, and P-waves is carried out. Numerical values of the transformation matrix are found in the case where the whispering gallery wave transforms to a sum of whispering gallery waves and a homogeneous wave transforms to the first five modes of whispering gallery waves. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 342, 2007, pp. 106–137.     

Wave propagation in an isolated porous Biot layer with closed pores on the boundaries

On the boundaries of such an isolated porous Biot layer, the total stresses and normal relative displacement are equal to zero. For this layer, the symmetric and antisymmetric dispersion equations are established and investigated. The wave field consists of normal waves. In this layer, one bending wave, two plate waves, and infinitely many normal waves propagate. For all these waves, we determine dispersion curves by analytical methods. The velocities of the bending wave and the second plate wave for the infinite frequency are equal to the Rayleigh velocity. Bibliography: 7 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 173–189.     

An Effective Model of a Fractured Medium

A homogeneous isotropic elastic medium intersected by three systems of fractures on which the jumps of stresses are proportional to displacements is considered. An effective model of this medium is described by equations differing from the respective equations of the elastic medium by additional terms. On the basis of the equations of the effective model, the wave field excited by a point source is established. An investigation of the integral representation of the wave field shows that the velocities of the longitudinal and transversal waves and of the Rayleigh wave are functions of the frequency and the wave numbers. Formulas for the phase and group velocities of these waves are derived. Bibliography: 3 titles.     

Propagation of surface electromagnetic waves similar to Rayleigh waves in the case of Leontovich boundary conditions

If on a surface Σ bounding an electromagnetic field, the Leontovich boundary conditions with a pure imaginary exponent are fulfilled, then surface electromagnetic waves propagating along Σ may exist. These waves have much in common with the Rayleigh waves in elasticity theory. In the paper, the ray theory of this electromagnetic analog of the Rayleigh waves is constructed. Bibliography: 6 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 5–19.     

Waves from a Deep Source of Longitudinal Waves in an Elastic Half Space with a Free Boundary

The nonstationary propagation of waves on the surface of an elastic half space from a deep expansion source (model of an explosion in a half space) is examined. Exact solutions are obtained in the form of integrals with finite limits and the general solution is calculated. Algebraic expressions are obtained for the Rayleigh wave. The transition of Rayleigh waves at the surface of the half space is studied. Calculations of Rayleigh waves from discontinuous pulsed sources are presented.     

Elastic wave propagation in a cylindrical bore situated in a micropolar elastic medium with stretch

Propagation of surface elastic waves in a cylindrical bore through a micropolar elastic medium with stretch is analysed in two cases. In the first case, the cylindrical bore is considered empty while in the second case, the bore is filled with homogeneous inviscid liquid. In both the problems, period equations are obtained in closed form. The problem of Banerji and Sengupta [2,3] has been reduced as a special case. Numerical calculations have been performed for a particular model and results obtained are presented graphically. It is noticed that the effect of micropolarity on dispersion curve is significant while the effect of micro-stretch on dispersion curve is not appreciable.     

The effect of thermal relaxation on rayleight surface waves in a thermoelastic medium

We study the problem of propagation of Rayleigh surface waves in thermoelastic media on the basis of the generalized coupled theory of thermoelasticity, which takes account of the phenomenon of thermal relaxation for sharply nonsteady thermal loads, thereby eliminating the paradox of infinite velocity of propagation of heat. It thus makes it possible to take account of the finite velocity of propagation of heat in the study of the process of propagation of Rayleigh surface waves. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 85–89.     

Rayleigh type wave dispersion in an incompressible functionally graded orthotropic half-space loaded by a thin fluid-saturated aeolotropic porous layer

This paper is concerned with the Rayleigh wave dispersion in an incompressible functionally graded orthotropic half-space loaded by a thin fluid-saturated aeolotropic porous layer under initial stress. Both the layer and half-space have subjected to the incompressible in nature. The particle motion of the Rayleigh type wave is elliptically polarized in the plane, which described by the normal to the surface and the focal point along with wave generation. The dispersion of waves refers typically to frequency dispersion, which means different wavelengths travel at a different velocity of phase. To deal with the analytical solution of displacement components of Rayleigh type waves in a layer over a half-space, we have taken the assistance of different methods like exponential, characteristic polynomial and undetermined coefficients. The dispersion relation has been derived based upon suitable boundary conditions. The finite difference scheme has been introduced to calculate the phase velocity and group velocity of the Rayleigh type waves. We also have derived the stability condition of the finite difference scheme (FDS) for the phase and group velocities. If a wave equation has to travel in the time domain, it is necessary to achieve both accuracy and stability requirements. In such cases, FDS is preferred because of its power, accuracy, reliability, rapidity, and flexibility. The effect of various parameters involved in the model like non-homogeneity, porosity, and internal pre-stress on the propagation of Rayleigh type waves have been studied in detail. Graphical representations for the effects of various parameters on the dispersion equation have been represented. Numerical results demonstrated the accuracy and versatility of the group and phase velocity depending on the stability ratio of the FDS.     

Propagation of Rayleigh waves in generalized magneto-thermoelastic orthotropic material under initial stress and gravity field

In this paper the influence of the gravity field, relaxation times and initial stress on propagation of Rayleigh waves in an orthotropic magneto-thermoelastic solid medium has been investigated. The solution of the more general equations are obtained for thermoelastic coupling by Helmoltz’s theorem. The frequency equation which determines Rayleigh wave velocity have been obtained. Many special cases are investigated from the present problem. Numerical results analyzing the frequency equation are obtained and presented graphically. Relevant results of previous investigations are deduced as special cases from these results. The results indicate that the effect of initial stress, magnetic field and gravity field are very pronounced.     

Energy Spectrum Width and Nonequilibrium Energy of Rayleigh Waves Scattered on a Two-Dimensional Near-Surface Electron Layer

We obtain expressions for the energy spectrum widths of Rayleigh waves corresponding to their deformational coupling to Fermi and Boltzmann electrons in a two-dimensional layer near the surface of a semibounded solid. We evaluate the nonequilibrium energy of Rayleigh waves that depends on these widths and is caused by the same coupling to the corresponding hot electrons. We show that this energy is independent of the degeneracy degree of the electrons and is given by the mean energy of free Rayleigh waves heated up to temperature of the electrons. We find conditions under which the thermodynamics is determined by this nonequilibrium energy of Rayleigh waves in films of a certain thickness with Fermi electrons near the surface and by the equilibrium energy of bulk phonons in thicker samples. All the results are obtained using the Keldysh diagram technique applied to the case of semibounded media.     

Attenuating Resonance Modes in a Cylindrical Waveguide Placed in an Elastic Medium

Interference attenuating waves traveling in a cylindrical elastic waveguide, placed in an elastic medium, are considered. The group velocity of these waves is intermediate between that of the P wave and that of the S wave; the phase velocity equals that of the P wave. The frequency of the waves is almost constant and is determined by the requirement of constructive interference. The dispersion and attenuation of these waves are described. Bibliography: 3 titles.     

Explicit secular equations of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity

The problem of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity was studied recently by Abd-Alla and Ahmed [A.M. Abd-Alla, S.M. Ahmed, Stoneley waves and Rayleigh waves in a non-homogeneous orthotropic elastic medium under the influence of gravity, Appl. Math. Comput. 135 (2003) 187–200], who derived the secular equation of the wave in the implicit form. In this paper, by using an appropriate representation of the solution, we obtain the secular equation of the wave in the explicit form. Moreover, considering its special cases, we derive explicit secular equations for a number of investigations of Stoneley waves under the influence of gravity, for which only the implicit dispersion equations were previously obtained.     

Effect of dust particles on a layer of micropolar ferromagnetic fluid heated from below saturating a porous medium

The problem of the effect of dust particles on the thermal convection in micropolar ferromagnetic fluid saturating a porous medium subject to a transverse uniform magnetic field has been investigated theoretically. Linear stability analysis and normal mode analysis methods are used to find an exact solution for a flat micropolar ferromagnetic fluid layer contained between two free boundaries. In case of stationary convection, the effect of various parameters like medium permeability, dust particles, non-buoyancy magnetization, coupling parameter, spin-diffusion parameter and micropolar heat conduction parameter are analyzed. For sufficiently large values of magnetic parameter M₁, the critical magnetic thermal Rayleigh number for the onset of instability is determined numerically and results are depicted graphically. It is also observed that the critical magnetic thermal Rayleigh number is reduced solely because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia and dust particles.     

表面效应对偏场下介电高弹体表面波传播的影响

采用表面薄层模型考察偏场下介电高弹体的表面效应,针对不同边界情形,建立一阶等效边界条件.基于有限变形电弹性体的线性增量理论,利用Stroh公式和Ting方法,给出等效边界条件的严格推导过程.进一步利用Stroh公式,获得了偏场下具有表面效应的介电高弹体中表面波的频散方程.以可压缩Neo-Hookean介电高弹体为例,分析了表面效应对预变形和电学偏场作用下的介电高弹体表面波传播特性的影响.结果表明,通过施加适当的偏场,可以调控和优化纳米声表器件的性能.