Propagation Of Surface Elastic Waves Research Articles

Speed of Surface Elastic Wave Propagation over the Human Chest

Speeds of surface elastic wave propagation over the human chest along and across the ribs are found. Ten healthy male volunteers have participated in the experiment. Vibrations of a striker-vibrator and a light accelerometer in contact with the chest have been detected using a specially designed hardware and software complex. The transfer function phase for passage of elastic waves over the chest is calculated. Wave propagation speeds are found using the phase method (frequency dependence of the transfer function phase). Differences between the speeds along and across the ribs are found in the frequency ranges from 27 to 100 Hz and from 100 to 200 Hz with the maximal-to-minimal speed ratio of 1.8. It is shown that one of the causes for the differences between the speeds can be different local elasticity and viscosity of the chest tissues.

Electrical resistivity and elastic wave propagation anisotropy in glancing angle deposited tungsten and gold thin films

We report on experimental investigations of electrical resistivity and surface elastic wave propagation in W and Au thin films sputter-deposited by glancing angle deposition. For both metals, the angle of deposition α is systematically changed from 0 to 85°. Dense and compact films are produced with a normal incident angle α = 0°, whereas inclined and porous columnar architectures are clearly obtained for the highest angles. Group velocities and DC electrical resistivities of W and Au films are significantly changed in x and y directions as α increases from 0 to 85°. Isotropic behaviors are always observed for Au films, whereas anisotropic velocity and resistivity are clearly measured in W films prepared with incident angles higher than 60°. The anisotropic coefficient reaches 1.8 for velocity and 2.0 for resistivity in W films, while it remains in-between 1.0 and 1.2 in Au films whatever the incident angle. This directional dependence of electrical resistivity and elastic wave propagation is connected to the anisotropic structural characteristics of W inclined columns (fanning of their cross-section), while Au columns exhibit a more symmetric growth as a function of the incident angle.

Anisotropic propagation imaging of elastic waves in oriented columnar thin films

We report on the observation of strongly anisotropic surface acoustic wave propagation on nanostructured thin films. Two kinds of tungsten samples were prepared by sputtering on a silicon substrate: a conventional thin film with columns normal to the substrate surface, and an oriented columnar architecture using the glancing angle deposition (GLAD) process. Pseudo-Rayleigh waves (PRWs) were imaged as a function of time in x and y directions for both films thanks to a femtosecond heterodyne pump-probe setup. A strong anisotropic propagation as well as a high velocity reduction of the PRWs were exhibited for the GLAD sample. For the wavevector k/2π = 3 × 105 m−1 the measured group velocities vx and vy equal 2220 m s−1 for the sample prepared with conventional sputtering, whereas a strong anisotropy appears (vx = 1600 m s−1 and vy = 870 m s−1) for the sample prepared with the GLAD process. Using the finite element method, the anisotropy is related to the structural anisotropy of the thin film’s architecture. The drop of PRWs group velocities is mainly assigned to the porous microstructure, especially favored by atomic shadowing effects which appear during the growth of the inclined columns. Such GLAD thin films constitute a new tool for the control of the propagation of surface elastic waves and for the design of new devices with useful properties.

Guidance of surface elastic waves along a linear chain of pillars

The propagation of surface elastic waves, or surface phonons, is considered along a linear and periodic chain of cylindrical pillars sitting on a semi-infinite solid substrate. A variety of guided modes, some of them exhibiting a very low group velocity, are shown to exist at frequencies close to the resonance frequencies of the pillars. Although the pillar diameter is typically smaller than half the relevant wavelength, lateral radiation on the surface is found to be canceled. Surface guidance is explained by the hybridization of the resonating pillars with the continuum of elastic waves of the substrate.

New frontiers in elastic metamaterials for controlling surface waves

In this presentation, we show recent results obtained by our research group on two types of elastic metamaterial that are capable of controlling the propagation of surface elastic waves at various physical scales: from tens of meter in geophysics to millimeters in ultrasonic. We begin from the geophysical scale introducing a metamaterial that uses soft soil inclusions in the ground to create a lens for detouring seismic surface waves around an obstacle at frequency <10 Hz. We then move to the smaller scale presenting a metamaterial that exploits the local resonances in a subwavelength collection of resonators (vertical rods) attached to a finite (plate) or semi-infinite (halfspace) substrate to control either the A0 mode in the plate or Rayleigh waves in the halfspace. We focus on the halfspace case and we illustrate how Rayleigh waves can be (1) mode converted into S-waves or stopped and trapped by a graded array of resonators (seismic rainbow); (2) focused, or detoured using a resonant metalens (Luneburg, Maxwell, and Eaton type) made with the vertical rods. The metamaterial are presented using results from time domain numerical simulations, laboratory and geophysical experiments to highlight the broad applicability of these objects across the wavelength spectrum.

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.

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 measurements of layered nanocomposite materials by Brillouin spectroscopy

Surface Brillouin spectroscopy makes it possible to measure surface elastic wave propagation parameters at frequencies up to 20 GHz or more. This enables us to measure the elastic properties of surface layers only a small fraction of a micrometre thick. The wavelength and incident angle of the light determine the wavenumber of surface elastic waves (SAW) that scatter the light inelastically, and their frequency can be found by measuring the change in wavelength of the scattered light. By analysing the elastic wave modes present in the surface, the elastic properties can be deduced. We have used this technique to measure the elastic properties of layered nanocomposite materials, which are widely used in the packaging industry. 12 μm polymer films (PET) were coated with glass oxide layers of thickness as little as 25 nm, to give transparent nanocomposite structures with excellent gas barrier properties. In order to understand and model the behaviour of these films under deformation, it is necessary to determine the elastic properties of the different layers. Evaluation of the elastic properties presents several challenges. First, the oxide layers are much thinner than the wavelengths of the surface phonons in surface Brillouin spectroscopy (and hence the depth probed), which usually lie in the range 250–500 nm. The anisotropic elastic properties of the PET substrate must therefore be measured accurately, and this can be done using bulk Brillouin spectroscopy. Second, a thin layer of metal (usually 10–20 nm) must be deposited on the glass surface so that the surface phonons scatter the light effectively. The elastic properties of the glass layer can then be deduced from surface Brillouin spectroscopy measurements, by simulating the surface wave modes of the metal/glass/polymer composite, and adjusting the parameters to give the best fit. In this way it is possible to observe how the properties of the glass vary as a function of thickness, and in turn to understand how to improve systematically the properties under deformation.

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.

Scattering of surface elastic waves at a vertical anisotropic layer

The propagation of surface elastic waves in an anisotropic inhomogeneous medium modelled by two vertically inhomogeneous anisotropic quarter-spaces and a thick vertically inhomogeneous anisotropic layer welded between the quarter-spaces is considered. The Green's function technique is applied to derive a set of equations for determination of scattering coefficients of the layer. Numerical results of Rayleigh-wave scattering by anisotropic versus isotropic layers are presented and discussed.

Surface elastic-wave propagation and amplification

Surface elastic-wave propagation, transduction, and amplification (in a piezoelectric semiconductor) are discussed with emphasis on characteristics useful in electronic devices. Computed curves show the dependence on distance from the surface of the elastic and the electric fields associated with surface elastic-wave propagation in cadmium sulfide. The interaction impedance, relating the external electric field to power flow, is computed for propagation on the basal plane of CdS and found to be low in comparison with values characteristic of electromagnetic slow-wave circuits. Amplification with a continuous drift field in cadmium sulfide is reported, and differences between surface- and bulk-wave amplifiers are discussed. Some operating characteristics and fabrication techniques for making electrode transducers on piezoelectric crystals are given, together with experimental results on several passive surface-wave devices.

The propagation of surface elastic waves in a cubic crystal

The paper discusses the possibility of the propagation of elastic waves, analogous to Rayleigh waves or Love waves, over a (0, 0, 1) surface of a cubic crystal. An examination of symmetrical cases in which the direction of propagation is parallel to the x -axis or makes an angle of 45° with it shows that waves with amplitude falling off exponentially with distance from the free face do not exist for every set of values of the three elastic constants chosen at random. For crystals of aluminium and copper these Rayleigh-type waves do not exist, but for rock salt their existence is demonstrated both for the symmetrical cases and for an asymmetrical case. In the latter the particles describe ellipses in a plane inclined to the direction of propagation. Waves of Love type can exist only in the two symmetrical cases cited; it is shown that then the general Rayleigh-type motion degenerates into a superposition of Rayleigh waves and Love waves. It is easily seen that for all types of crystals the general result will be the same, but that the algebraical and arithmetical work involved will be extremely heavy.

The continental layers of Europe‡

Summary The observed period and group velocities of Love waves propagated across Eurasia indicate that the thicknesses T1 and T2 of the granitic and intermediate layers of Eurasia satisfy the approximate equation 2T1 + T2 = 65.5 ± 6 km. If the equation obtained by Jeffreys from Japanese deep-focus earthquakes, T1 + 0.85 T2 = 30.3 ± 1.3 km., is accepted, we find T1 = 36.2 ± 7.4 km., T2 = −6.8 ± 9.4 km., implying that the thickness of the intermediate layer is not significantly different from zero. Taking T2 = 0 would then give T1 = 33 ± 3 km. This value does not seem compatible with the observed rate of outflow of heat; but the data concerning the rate of generation of heat through radioactive disintegration are very uncertain. Combined with the Love-wave equation, the isostatic equation indicates a thickness of about 30 km. for the floor of the Pacific Ocean; this is in general agreement with the work of Byerly and Vening Meinesz. The deep-focus earthquake equation then indicates that the base of the granitic continent, without any “intermediate layer,” should be at about the same level as the lower surface of the basalt layer under the Pacific Ocean, both continent and ocean floor resting on the horizontal surface of ultrabasic material. The need for further investigations into the propagation of surface elastic waves is manifest.