Polarization-spectral anomalies of surface waves in an almost layered elastic half space

The propagation of Love and Rayleigh waves in an isotropic elastic half space whose properties vary little in a horizontal direction is considered. Expressions are obtained for the admixed components of the displacements.Translated from Zapiski Naukchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 102–114.     

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.     

Modelling of thermoelastic Rayleigh waves in a solid underlying a fluid layer with varying temperature

The present paper is aimed at to study the propagation of surface waves in a homogeneous isotropic, thermally conducting and elastic solid underlying a layer of viscous liquid with finite thickness in the context of generalized theories of thermoelasticity. The secular equations for non-leaky Rayleigh waves, in compact form are derived after developing the mathematical model. The amplitude ratios of displacements and temperature change in both media at the surface (interface) are also obtained. The liquid layer has successfully been modeled as thermal load in addition to normal (hydrostatic pressure) one, which is the distinctive feature of the present study and missing in earlier researches. Finally, the numerical solution is carried out for aluminum-epoxy composite material solid (half-space) underlying a viscous liquid layer of finite thickness. The computer simulated results for dispersion curves, attenuation coefficient profiles, amplitude ratios of surface displacements and temperature change have been presented graphically, in order to illustrate and compare the theoretical results. The present analysis can be utilized in electronics and navigation applications in addition to surface acoustic wave (SAW) devices.     

Plane problem of interaction between an elastic longitudinal wave and a cylindrical shell with axial cut

We have proposed a procedure for investigating the stressed state of a thin-walled round cylindrical shell with a cut along its generatrix, which is placed into an elastic space. A longitudinal elastic wave is incident on the shell. The procedure is based on the use of the Rayleigh expansion in partial waves. We have obtained relations for determining the displacement jumps and angle of rotation at the lips of the shell cut, the radial component of the displacement vector and the normal force in the cylindrical shell, as well as the stresses and displacements in the elastic medium. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 131–137, January–March, 2008.     

Dispersion properties of nonstationary SV Rayleigh waves near the surface of an inhomogeneous elastic body

The physical characteristics of the surface of nonstationary SV Rayleigh waves are studied and formulas are obtained for the phase and group velocities (as functions of time and the observation point on the surface) of the Rayleigh waves. These formulas are in accord with the familiar formulas for the phase and group velocities in the stationary case.Translated from Zapiski Nauchnykh Seminarov Leningradzkogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 173, pp. 172–179, 1988.     

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.     

微极各向同性弹性板中的Rayleigh-Lamb波

研究了无应力作用条件下，均匀、各向同性、圆柱形微极结构弹性板中波的传播．导出了对称和斜对称模式下波传播的特征方程．对短波这一极端情况，无应力圆板中对称和斜对称模态波的特征方程退化为Pmyle曲表面波频率方程．并得到薄板的计算结果．给出了位移和微转动分量，并绘制了相应图形．给出了若干特殊情况的研究结果及对称和斜对称模态特征方程的图示．     

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.     

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.     

Experimental study on the non- specularly reflected ultrasonic beam on a liquid- solid interface

The reflected fields of a slightly divergent ultrasonic beam on a liquid-solid interface are recorded by a Schlieren system, and the lateral beam displacements on the interface are measured. The range of the incident angle_i is around the Rayleigh angle_c. The displacements are found to decrease as the incident angle increases. Theoretical calculation reveals that the displacements decrease with the increase in the incident angle for a divergent incident beam, but increase with that for a convergent one. The calculated curve of- _i are in agreement with the experimental results.     

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.     

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.     

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.     

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.     

Rayleigh waves having generalised lateral dependence

It is shown that the surface-guided elastic waves found by Kiselevfor isotropic materials and having displacements depending linearlyupon the Cartesian coordinate orthogonal to the sagittal planemay be generalised in many ways. For surface waves on any anisotropichalf-space, a simple procedure applied to the displacementswithin the standard surface wave having dependence eⁱ, where k · x – t and k is the (surface) wave vector,yields displacements depending linearly upon the surface cartesiancoordinate orthogonal to the group velocity vector. Moreover,repeated application of this (differentiation) procedure yieldsa hierarchy of waves having algebraic dependence of successivelyincreasing degree. For isotropic materials, substantial simplificationand generalization are possible. Solutions of all algebraicdegrees have identical depth dependence. This allows the solutionsto be constructed iteratively and motivates a search for generalsolutions having depth dependence of the normal displacementthe same as in the standard surface wave. The procedure givesa new derivation of the solutions found by Achenbach havingamplitude of the normal displacement of the surface given byany solution to the two-dimensional Helmholtz equation. Furthermore,exploiting the scale invariance (a property of surface waveson any homogeneous half-space) shows that in every surface-guideddisturbance of an elastic half-space, the elevation of the freesurface is a solution of the wave equation in two dimensions(the membrane equation). Using the paraxial approximation tothe membrane equation, high-frequency Rayleigh waves propagatingas narrow beams are described in terms of a scalar Gaussianbeam.     

An energy approach to the proof of the existence of Rayleigh waves in an anisotropic elastic half-space

An approach based on investigating the energy functional is applied for the first time to the classical problem of Rayleigh waves in an anisotropic half-space with a free boundary. The main object of the investigation is an ordinary differential operator in a variable characterizing the depth. An investigation of the spectrum by variational methods enables a new proof to be given of the existence of a Rayleigh wave in a linear elastic half-space with arbitrary anisotropy, which does not rest on the Stroh formalism.     

Rayleigh waves from a point source on a boundary free of tensions

The solutions of equations of elasticity theory that have a discontinuity only on a boundary free of tensions (Rayleigh waves) are considered. Initial data for the complex intensity of the surface Rayleigh waves are found in two simple media. The first elastic medium fills a half-space with Lamé parameters and density dependent on depth. The second medium is bounded by a curve determined by a natural equation. The parameters of the second medium depend on the arc length along the curve. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 132–149.     

Radiation problem of normal stress loading of bore surface

The radiation of elastic waves at normal harmonic stress loading of a ring strip of the cylindrical bore-surface in the infinite elastic medium is considered. The wave field is represented by contour integrals. By using the saddle-point method stress and displacement of asymptotic expansions in the far field were obtained. It is shown that in the far field P-waves bring radial displacements and stresses, and perpendicular to these, displacements and stresses are caused by S-waves. In the paper orientation diagrams of radial and circular displacements and frequency dependencies of relative distribution of radiation power source on types of waves are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Scattering theory for the elastic wave equation in perturbed half-spaces

In this paper we consider the linear elastic wave equation with the free boundary condition (the Neumann condition), and formulate a scattering theory of the Lax and Phillips type and a representation of the scattering kernel. We are interested in surface waves (the Rayleigh wave, etc.) connected closely with situations of boundaries, and make the formulations intending to extract this connection.

The half-space is selected as the free space, and making dents on the boundary is considered as a perturbation from the flat one. Since the lacuna property for the solutions in the outgoing and incoming spaces does not hold because of the existence of the surface waves, instead of it, certain decay estimates for the free space solutions and a weak version of the Morawetz arguments are used to formulate the scattering theory.

We construct the representation of the scattering kernel with outgoing scattered plane waves. In this step, again because of the existence of the surface waves, we need to introduce new outgoing and incoming conditions for the time dependent solutions to ensure uniqueness of the solutions. This introduction is essential to show the representation by reasoning similar to the case of the reduced wave equation.

     

Rayleigh wave attenuation due to scattering by stationary defects

We obtain expressions for the energy spectrum widths of Rayleigh waves arising because of their scattering by point and distributed defects of the surface, as well as by the edge dislocations on the surface and by the grooves of a random lattice in the surface plane. The calculations are valid when the defect density is small. Under certain conditions, our results coincide with the results of other authors who studied the scattering of Rayleigh waves by point defects and by the grooves of a random lattice. The calculations are based on the Keldysh diagram technique modified for the case of semibounded media.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 143, No. 2, pp. 241–257, May, 2005.