Semi-analytical analysis of the isolation to moving-load induced ground vibrations by trenches on a poroelastic half-space

A semi-analytical model is proposed to investigate the screening efficiency of trenches to moving-load induced ground vibrations. The ground is modeled as a fully saturated poroelastic half-space governed by Biot's dynamic poroelastic theory. The trenches are obtained by placing three rectangular elastic layers with appropriate width upon the poroelastic half-space. By Helmholtz decomposition, the displacement fields of the elastic layers are decomposed into three scalar potentials. Analytical solutions are obtained based on Fourier transform and Fourier series in the transformed domain. The time-domain results are obtained by the fast Fourier transform (FFT). The different performances of trenches on a saturated poroelastic half-space and a single-phase elastic half-space to the moving load-induced ground vibration are identified. It is found that the discrepancy of the screening efficiencies between the two models becomes significant when the load speed approaches the Rayleigh wave speed of the ground surface. Also, some parametric studies for the screening efficiency of the trench on the poroelastic half-space are presented.     

Contact mechanics analysis of oscillatory sliding of a rigid fractal surface against an elastic–plastic half-space

Oscillatory sliding contact between a rigid rough surface and an elastic–plastic half-space is examined in the context of numerical simulations. Stick-slip at asperity contacts is included in the analysis in the form of a modified Mindlin theory. Two friction force components are considered – adhesion (depending on the real area of contact, shear strength and interfacial adhesive strength) and plowing (accounting for the deformation resistance of the plastically deformed half-space). Multi-scale surface roughness is described by fractal geometry, whereas the interfacial adhesive strength is represented by a floating parameter that varies between zero (adhesionless surfaces) and one (perfectly adhered surfaces). The effects of surface roughness, apparent contact pressure, oscillation amplitude, elastic–plastic properties of the half-space and interfacial adhesion on contact deformation are interpreted in the light of numerical results of the energy dissipation, maximum tangential (friction) force and slip index. A non-monotonic trend of the energy dissipation and maximum tangential force is observed with increasing surface roughness, which is explained in terms of the evolution of the elastic and plastic fractions of truncated asperity contact areas. The decrease of energy dissipation with increasing apparent contact pressure is attributed to the increase of the elastic contact area fraction and the decrease of the slip index. For a half-space with fixed yield strength, a lower elastic modulus produces a higher tangential force, whereas a higher elastic modulus yields a higher slip index. These two competing effects lead to a non-monotonic dependence of the energy dissipation on the elastic modulus-to-yield strength ratio of the half-space. The effect of interfacial adhesion on the oscillatory contact behaviour is more pronounced for smoother surfaces because the majority of asperity contacts deform elastically and adhesion is the dominant friction mechanism. For rough surfaces, higher interfacial adhesion yields less energy dissipation because more asperity contacts exhibit partial slip.     

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).     

Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

Verzerrung anisotroper Körper durch Versetzungen mit Anwendung auf die Berechnung der Röntgenintensität

An elastic state in arbitrarily anisotropic cylinders is considered for the case in which the displacement does not vary in the direction of the axis. The first and second boundary-value problem are solved for the half-plane and the infinite plane with an elliptic hole as cross sections of the cylinders. With the aid of these solutions one can treat further domains by the method of successive approximation. For a general cross section the problem leads to a system of integral equations. The strain fields about straight dislocation lines parallel to the surface (which may be free from applied stress) are special cases of the treated state of deformation. The solution is given for 1) dislocations in a half-space, 2) dislocations in an infinite plate (through a recursion formula), 3) a dislocation in an infinite solid out of which an elliptic cylinder is cut containing the dislocation line. — From the strain one obtains a formula for the intensity distribution of X-rays reflected under certain conditions by a dislocation parallel to the surface of a half-space. Numerical results are given for two dislocations in Germanium.     

Resonant oscillations of an elastic membrane on the bottom of a tank containing a heavy liquid

A study is made of the resonant oscillation modes in a three-dimensional channel filled by a heavy incompressible liquid, with a free surface at the top and an elastic membrane on the bottom. It is shown that for definite relations between the parameters of the channel and the inclusion there is a discrete spectrum, which extends only up to the waveguide cutoff frequency, in addition to the continuous spectrum of oscillation frequencies. The oscillation modes of the liquid have a localized character in the region of the inclusion. Zh. Tekh. Fiz. 69, 37–42 (August 1999)     

Elastic response of a free half-space to random force excitations applied on the boundary

A response of an elastic half-space to random forces applied normally to the free boundary is studied. This paper is the second part of the study we presented in [I.A. Shalimova, K.K. Sabelfeld, The response of an elastic three-dimensional half-space to random correlated displacement perturbations on the boundary, Physica A 389 (21) (2010) 4436–4449] where the case of random displacements on the boundary was considered. We analyze the white noise excitations in detail, and derive explicitly the mean of the elastic energy, the strain and displacement correlation tensors. Simulation algorithms are constructed both for displacement and strain random fields, which enables us to calculate any desired statistical characteristics.     

Effect of the surface free energy on the behaviour of surface and guided waves

The aim of this paper is to evaluate the influence of the surface free energy upon the propagation of the eigenmodes of structures, by studying successively (a) the Rayleigh wave for an elastic half-space, (b) the Lamb waves for an elastic layer, and (c) the guided modes for a tri-layer structure (e.g., metal/adhesive/metal). The surface free energy is a parameter which appears in the jump conditions of stresses and displacements at each interface, and which consequently modifies the eigenmodes, solutions of the boundary conditions system. As expected, the Rayleigh wave is dispersive and its velocity increases when the surface free energy increases. In the same way, the velocity of Lamb waves also increases except at normal angle of propagation where the surface free energy does not arise. Moreover, near the Rayleigh angle, the behaviour of the A₀ and S₀ Lamb modes varies strongly according to the surface free energy. Similar results are observed for the tri-layer structure.     

The effect of a surface impedance load on the properties of quasi-Rayleigh waves

The propagation of quasi-Rayleigh waves along an impedance-loaded plane boundary of an isotropic elastic half-space is studied theoretically. The dispersion equation of these waves is derived with allowance for the fact that an impedance load has both normal and tangential components. The conditions for the existence of such waves are analyzed depending on the magnitude and nature of each of these components. Specific examples of calculating the quasi-Rayleigh wave velocities are considered: for the models of surface and bulk cracked media, for a fluid layer in an elastic medium, and for a resonant load.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Dispersion dependences of elastic waves in an ice-covered shallow sea

The dispersion dependences of acoustic waves propagating under conditions close to an ice-covered shallow sea are investigated. A dispersion equation is derived for a layered medium consisting of an elastic layer (the ice cover), a liquid layer (the water column), and a homogeneous elastic half-space (the bottom). The possibilities of estimating certain parameters of the studied layered structure from an analysis of the dispersion curves are discussed. The results of numerical calculations are compared with the data of a full-scale experiment on detecting seismoacoustic signals in an ice-covered sea region.     

Forced oscillations of an axisymmetric structure in contact with an elastic half-space by a version of global local finite elements

A version of the global local finite element method (GLFEM) is presented for determining the steady state forced response of an axisymmetric structure in contact with an elastic, homogeneous, isotropic half-space. In this GLFEM version, conventional finite elements are used to model the structure and some portion of the sorrounding medium, and global functions in the form of a complete set of outgoing spherical harmonic waves for the entire space are used to capture the behavior in the half-space region beyond the finite element mesh. An arbitrary distribution of steady state normal loads may be applied to the structure. Full traction and displacement continuity are enforced at the finite element mesh interface with the outer region. On the half-space surface of the outer region, traction-free surface conditions are met by requiring a sequence of weighted-average integrals of the tractions to vanish. Comparison of the present results for the problem of a rigid plate in frictionless contact with the half-space with those obtained by krenk and Schmidt [1] show excellent agreement over a wide frequency range. Other examples on circular plates under various contact conditions with the half-space are presented as illustrations of the forced response.     

Surface acoustic oscillations in a periodically layered medium

The existence of surface acoustic waves at the interface between a periodically layered and a homogeneous half-space is predicted. The reason for the arisal of such waves is the violation of the transnational symmetry pertinent to the periodic structure. The properties of the surface waves at a free boundary and a boundary with an elastic half-space are considered.     

Instability of the flat surface of a magnetic fluid in a cylindrical cavity in the presence of a vertical magnetic field

The problem of a magnetic liquid which completely fills a vertical cylindrical cavity in an undeformable horizontal layer of a magnet having the same magnetic properties as the liquid is considered. The entire system is immersed in a uniform vertical magnetic field. in a linear formulation of the problem an approximate solution in the form of series is obtained for the evolution of an initial small deviation of the free surface of the liquid from its flat equilibrium shape. An experiment is performed which shows that the initially flat free surface takes on a stable domed shape as the field strength is increased (from zero) and that a further increase in the field in a certain restricted range leads to the formation of an annular corrugation. The structures observed, which are the result of the nonlinear stage in the development of the initial perturbation, are qualitatively similar to the first two modes of the solution obtained. Zh. Tekh. Fiz. 68, 23–30 (January 1998)     

Propagation of surface elastic waves in the Cosserat medium

The problem of surface elastic wave propagation in the Cosserat medium (half-space) is considered. The strained state is characterized by two independent vectors: displacement and rotation. Solutions to the equations of motion are sought in the form of wave packets specified by an arbitrary Fourier spectrum. It is shown that, if the solution is sought in the form of a three-component displacement vector and a three-component rotation vector dependent on time, depth, and longitudinal coordinate, the initial system splits into two systems, one of which describes the Rayleigh wave and the other corresponds to a transverse wave decaying with depth. For both waves, analytical solutions in terms of displacements are obtained. It should be particularly noted that, unlike the Rayleigh wave, the solution for the transverse surface wave has no analogues in the classical elasticity theory. The transverse wave solution is numerically compared with the Rayleigh wave solution.     

Elastic properties of magnetic materials

This review discusses the theoretical aspects of magnetoelastic coupling with emphasis on the magnetic perturbation of elastic properties. The basic theory of magnetostriction is set out with application to ferromagnets, ferrimagnets and antiferromagnets, and is followed by a discussion of the physical origin of the magnetoelastic coupling coefficients in both localized and itinerant magnetic systems. Magnetic contributions to elastic compliance are then discussed and sound velocity anomalies near magnetic phase transitions investigated, including the cooperative Jahn-Teller limit for which the acoustic mode itself drives a structural transition even when magnetic ordering does not occur. The review concludes with discussion of magnetoelastic (or mixed magnon-phonon) waves in low temperature magnetically ordered phases and with a study of local striction phenomena in magnetically dilute materials. The latter leads to a recognition of internal rearrangement modes which may also be present in concentrated magnetic systems, and which may or may not couple significantly to bulk homogenous strain.     

Lidar observation of the bubble trace in the sea surface layer

The evolutions of the signals of the elastic (Mie) and Raman backscattering of the Nd:YAG laser second-harmonic radiation in the upper layer of the sea under cavitational perturbation induced by the passage of a high-speed boat are compared under the conditions of the outdoor experiment. It is shown that the signal of the elastic scattering on bubbles returns to the background level within the time of ∼10 min. The relaxation time of the spontaneous Raman scattering signal can be an order of magnitude larger than this value (the evaluated value under the particular conditions of this experiment is ∼120 min). Interpretation is given to this difference in attenuation time of the elastic and inelastic scattering signals at the cavitational perturbation of the sea.     

Low-frequency sound transmission through a gas-liquid interface

Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.     

Generation of elastic waves in a laminated solid by a moving photothermal source

The steady state response of an elastic layered plate (laminate) which is subjected to a moving laser source illumination is studied. The response of the laminate is obtained using the transfer matrix approach. The application of the photo-thermal source (laser) to the upper surface of the laminate is formulated as equivalent stresses applied at the illuminated boundary. The equivalent stresses are derived with the use of the causality principle. It is shown that the generated displacement field is sensitive to the variations of the laminate inner structure and also to the variations of the elastic properties of a bonded elastic half-space.