Elastic Surface Waves Research Articles

Elastic surface waves in crystals – Part 2: Cross-check of two full-wave numerical modeling methods

We obtain the full-wave solution for the wave propagation at the surface of anisotropic media using two spectral numerical modeling algorithms. The simulations focus on media of cubic and hexagonal symmetries, for which the physics has been reviewed and clarified in a companion paper. Even in the case of homogeneous media, the solution requires the use of numerical methods because the analytical Green’s function cannot be obtained in the whole space. The algorithms proposed here allow for a general material variability and the description of arbitrary crystal symmetry at each grid point of the numerical mesh. They are based on high-order spectral approximations of the wave field for computing the spatial derivatives. We test the algorithms by comparison to the analytical solution and obtain the wave field at different faces (stress-free surfaces) of apatite, zinc and copper. Finally, we perform simulations in heterogeneous media, where no analytical solution exists in general, showing that the modeling algorithms can handle large impedance variations at the interface.

Experimental observation of locally-resonant and Bragg band gaps for surface guided waves in a phononic crystal of pillars

We report on the experimental study of the propagation of surface guided waves in a periodic arrangement of pillars on a semi-infinite medium. Samples composed of nickel pillars grown on a lithium niobate substrate were prepared and wide bandwidth transducers were used for the electrical generation of surface elastic waves. We identify a complete band gap for surface guided waves appearing at frequencies markedly lower than the Bragg band gap. Using optical measurements of the surface vibrations and by comparison with a finite element model, we argue that the low frequency band gap arises because of local resonances in the pillars. When resonance is reached, the acoustic energy is confined inside the pillars and transmission through the array is strongly reduced. At higher frequencies and inside the Bragg band gap, the incident surface elastic waves are almost completely reflected and the observed exponential decay of the transmission is similar to the case of phononic crystals made of holes in a substrate.

Measurement of the Rayleigh wave polarization using 1D Laser vibrometry

The paper presents measurement procedures for the evaluation of velocity/displacement components of surface elastic waves through a single beam Laser Vibrometer. The developed technique is applied for the estimation of Rayleigh wave polarization in aluminum specimens. The estimated polarization orbits are compared with the analytical ones to demonstrate the effectiveness of the measurement technique. The estimations rely on the preliminary analysis of the recorded signals in the frequency/wavenumber domain, as enabled by the fine spatial resolution provided by a scanning Laser vibrometer, which allows identification and separation of Rayleigh waves from the recorded wavefield. In addition, comparison of polarization measurements performed on untreated and shot-peened samples suggests the measurement technique as a tool for the estimation of the effect of residual stresses on the polarization properties of surface waves.

Technically Induced Surface Wave Fields, Part I: Measured Attenuation and Theoretical Amplitude-Distance Laws

Abstract The attenuation of the amplitudes with distance of technically induced surface wave fields is analyzed in theory and experiments. Experimental results of technically induced ground vibration are presented and collected from literature, which show a power-low attenuation A ∼ r - q of amplitudes A with distance r and exponents q >0.5 higher than for elastic surface waves. Additional attenuation effects are analyzed theoretically. The most important effect is due to the material or scattering damping. Each frequency component is attenuated exponentially as A ∼exp(- kr ), but for a broadband excitation, the sum of the exponential laws yields a power law with a higher exponent. Some more effects are discussed, for example the dispersion of the Rayleigh wave due to the layering of the soil, which yields a stronger attenuation A ∼ r - q - dq , including an additional exponent of dq =0.5 in case of an impulsive loading.

Elastic waves interacting with a thin, prestressed, fiber-reinforced surface film

Elastic surface waves propagating at the interface between an isotropic substrate and a thin, transversely isotropic film are analyzed. The transverse isotropy is conferred by fibers lying parallel to the interface. A rigorous leading-order model of the thin-film/substrate interface is derived from the equations of three-dimensional elasticity for prestressed, transversely isotropic films having non- uniform properties. This is used to study Love waves.

A long-wave model for the surface elastic wave in a coated half-space

The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional ‘quasi-static’ elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate.

Isolated True Surface Wave in a Radiative Band on a Surface of a Stressed Auxetic

We demonstrate that a surface resonance (pseudosurface wave) may transform into a true surface wave, i.e., acquire an infinite lifetime, at a single isolated point within a bulk band (radiative region) in a model of a stressed auxetic material. In contrast with the secluded supersonic elastic surface waves, the one found here does not belong to a dispersion line of true surface waves. Therefore we propose to call it an isolated true surface wave (ITSW). The ITSW manifests itself by a deltalike peak in the local density of states and by anomalies in reflection coefficients. The phenomenon may be useful in redirecting energy and/or information from the bulk to the surface in devices supporting guided acoustic waves.

ULTRASOUND AS A PROBE OF PLASTICITY? THE INTERACTION OF ELASTIC WAVES WITH DISLOCATIONS

An overview of recent work on the interaction of elastic waves with dislocations is given. The perspective is provided by the wish to develop nonintrusive tools to probe plastic behavior in materials. For simplicity, ideas and methods are first worked out in two dimensions, and the results in three dimensions are then described. These results explain a number of recent, hitherto unexplained, experimental findings. The latter include the frequency dependence of ultrasound attenuation in copper, the visualization of the scattering of surface elastic waves by isolated dislocations in LiNbO3, and the ratio of longitudinal to transverse wave attenuation in a number of materials.Specific results reviewed include the scattering amplitude for the scattering of an elastic wave by a screw, as well as an edge, dislocation in two dimensions, the scattering amplitudes for an elastic wave by a pinned dislocation segment in an infinite elastic medium, and the wave scattering by a sub-surface dislocation in a semi-infinite medium. Also, using a multiple scattering formalism, expressions are given for the attenuation coefficient and the effective speed for coherent wave propagation in the cases of anti-plane waves propagating in a medium filled with many, randomly placed screw dislocations; in-plane waves in a medium similarly filled with randomly placed edge dislocations with randomly oriented Burgers vectors; elastic waves in a three-dimensional medium filled with randomly placed and oriented dislocation line segments, also with randomly oriented Burgers vectors; and elastic waves in a model three-dimensional polycrystal, with only low angle grain boundaries modeled as arrays of dislocation line segments.

Propagation of low-frequency waves in biological tissues and vessels

Elastic surface waves in biotissue are considered taking into account its structure, and dispersion dependences are presented. Effects of contact of vibroacoustic action on the soft tissue of a human’s arm are studied, and the biotissue activity manifests itself as a vibroreaction with different characteristic times. A thermodynamic approach to the construction of rheological relations of active mechanochemical media is described. Dispersion characteristics of acoustic processes in passive and active blood vessels are given.

Waves in Linear Elastic Media with Microrotations, Part 1: Isotropic Full Cosserat Model

In this article, we consider a problem of the surface elastic wave propagation within the framework of the isotropic Cosserat continuum. The medium deformation in this model is described not only by the displacement vector but also by a kinematically independent rotation vector. We discuss the general solution of equations of motion. This solution describes the following wave types: longitudinal and transverse bulk waves, Rayleigh wave, surface transverse wave in a half-space as well as Lamb wave and transverse wave in a thin layer. Within the framework of Cosserat continuum, both the Rayleigh and surface transverse waves in a half-space are dispersive. The transverse wave in a thin layer and the surface transverse wave in a half-space do not have any analogies in the classical elasticity theory.

Transformation of seismoacoustic energy into hydroacoustic

The experimental results and theoretical estimations of studies on mechanisms of transformation of elastic wave energy into hydroacoustic wave energy are presented in this paper. Elastic waves in the Earth’s crust were generated using a low frequency radiator, operating in the frequency range from 2 to 20 Hz. At the shore elastic waves were recorded by a 52.2-m horizontal laser strainmeter. Elastic surface waves spread at the bottom‐water interface and were partly transformed into hydroacoustic waves at the frequency of the radiated signals. Based on the experimental data obtained, the portion of elastic energy transformed into hydroacoustic energy was estimated.

Green's function model for time-reversal focusing of elastic surface waves.

Time-reversal focusing applied to an object buried in soil improves the ability to focus energy on the object, suggesting a promising method for mine and IED detection. As a rule, these devices are buried close to the ground surface at a depth smaller than an elastic surface wave penetration depth. A Green’s function approach is used to evaluate the field scattered by the object. Both the Green’s function and the source function representing the scattering site are expanded in eigenfunctions of the homogeneous wave equation. When the object is acoustically compact, the scattered wave amplitude on the surface is described in the frequency domain by a Hankel function of order zero. Below the surface, the scattered wave amplitude is described by a Bessel function of order zero multiplied by exponentials that decay with depth, plus its Hilbert transform. The Green’s function in the time domain is zero for negative time, and for positive time it is the Fourier transform of the Bessel function of order zero multiplied by the exponential depth dependence. The Green’s function is used twice to calculate scattering from the object, first by the probe wave and next by the time-reversed wave. [Work supported by ONR.]

Surface dynamics of a nongyrotropic multiferroic with quadratic magnetoelectric interaction

The effect of quadratic magnetoelectric interaction on the conditions of propagation and localization of one-partial polariton and elastic surface waves has been studied by the example of a bounded centrosymmetric easy-axis ferroelectric antiferromagnet.

Functionally graded piezoelectric materials for modal transducers for exciting bulk and surface acoustic waves

We show that functionally graded piezoelectric materials can be used to make modal actuators through theoretical analyses of the excitation of extensional motion in an elastic rod and Rayleigh surface waves over an elastic half-plane. The results suggest alternatives with certain advantages for the excitation of bulk and surface acoustic waves.

POSSIBLE ZERO-FLUX TRANSPORT INDUCED BY DENSITY WAVES IN A SUPERSOLID TUBE

Macroscopic derivation of the entrainment in a supersolid cylinder induced by a surface elastic wave (of small amplitude) propagating along the flexible interface is conducted by considering the nonlinear coupling between the interface and the rarefaction effect. We obtain the critical bounds for zero-volume-flow-rate states corresponding to specific rarefaction measure and wave number which is relevant to the rather small critical velocity or disappearance of supersolid flows reported by Kim and Chan or Rittner and Reppy.

Surface elastic waves in granular media under gravity and their relation to booming avalanches

Due to the nonlinearity of Hertzian contacts, the speed of sound c in granular matter is expected to increase with pressure as P1/6. A static layer of grains under gravity is thus stratified so that the bulk waves are refracted toward the surface. The reflection at the surface being total, there is a discrete number of modes (both sagittal plane and transverse ones) localized close to the free surface. The shape of these modes and the corresponding dispersion relation are investigated in the framework of an elastic description taking into account the main features of granular matter: the nonlinearity between stress and strain and the existence of a yield transition. We show in this context that the surface modes localized at the free surface exhibit a waveguide effect related to the nonlinear Hertz contact. Sound propagation measurements in a laboratory scale channel as well as in the field (slip face of a singing dune), will be presented and compared to the theoretical predictions. Finally, these results will be used to constrain the possible dynamical mechanisms at the origin of booming avalanches.

Reflection and transmission of the surface P-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.

Diffraction of surface SV-waves on the line of jump in elastic parameters

A set of problems on the diffraction of elastic surface waves of vertical polarization (SV-waves) on the line of jump of elastic parameters is under consideration. Expressions for reflected and transmitted wave fields are obtained by means of the parabolic equation method. The corresponding transformation coefficients are found for the reflection and transmission. Bibliography: 7 titles.

Time-reversal focusing of elastic surface waves with an asymmetric surface layer

The effectiveness of time-reversal focusing is evaluated in the presence of an asymmetric surface layer that changes the direction of the propagating waves, but does not continually scatter or block the propagating wave front. Interactions between the wave front and the surface layer are dependent on the depth and material properties of the asymmetric surface layer and its orientation in the medium with respect to the incident wave. Time-reversal focusing is shown to perform significantly better than other excitation methods for the purpose of delivering energy to the location of a buried land mine.

Holographic and conventional bistatic synthetic aperture sonar imaging of cylinders: Comparison and ray interpretation

When synthetic aperture sonar is used to image elastic targets, subtle features can be present in the images associated with the dynamical response of the target being viewed. In an effort to improve the understanding of such responses as well as to explore alternative image processing methods, a laboratory-based system was developed in which targets were illuminated by a transient acoustic source and bistatic responses were recorded by scanning a hydrophone along a horizontal line. Images were constructed using a relatively conventional bistatic SAS algorithm and were compared with images based on supersonic holography. The holographic method is a simplification of one previously used to view the time evolution of a target’s response [B. T. Hefner and P. L. Marston, ‘‘Acoustics Research Letters Online’’ 2, 55–60 (2001)]. In the holographic method, the time evolution of the cross-range image was used to construct a two-dimensional image with an effective range coordinate. Various features for cylindrical targets were interpreted using quantitative ray theory. This includes contributions from guided surface elastic waves as well as transmitted-wave features. [Work supported by the Office of Naval Research.]