Dispersion of laser generated surface waves in an epoxy-bonded layered medium

In this paper, the dispersion of laser generated surface wave in an epoxy bonded copper-aluminum layered specimen is studied. A laser ultrasonic experiment based on the point-source/point-receiver (PS/PR) technique was conducted to measure the surface wave signals in the layered specimen. The received wave signals were then processed in the frequency domain to obtain the dispersion relation of the fundamental surface wave mode. Theoretical calculations of the dispersion relations of the fundamental surface wave modes in two-layered and three-layered specimens were conducted to explore the influence of the bonding layer thickness on the dispersion relation. The experimental dispersion relation for the epoxy bonded copper-aluminum layered specimen is in good agreement with the calculated dispersion relation. The influence of the bonding layer thickness on the dispersion relation is studied and the potential application of the present results to the NDE of bonded layered media based on laser ultrasonics is also addressed.     

INHOMOGENEOUS WAVES IN ANISOTROPIC POROUS LAYER OVERLYING SOLID BEDROCK

The problem of propagation of inhomogeneous waves in anisotropic porous layered medium is studied using transfer matrix. Firstly, transfer matrix for an anisotropic porous layer is derived. Biot's poro-elastic theory is incorporated to model the acoustics of anisotropic porous layer. The interface between porous layer and elastic half-space is considered as imperfect and modified boundary conditions are applied for this more realistic situation. The theory of transfer matrix is used to derive the analytical expression for the surface impedance. Numerical computation of results is done for different degrees of bonding in the low as well as high-frequency range. In the first case, which is relevant to geophysical studies, the surface impedance is predicted for low-frequency range and surface impedance for second model is computed in high-frequency range. It is observed that loose bondedness is accompanied by the loss of energy at the interface. The technique of transfer matrix is utilized to compute the surface impedance in both cases. The role of surface impedance in seismological studies and in the study of composites is discussed.     

Two-dimensional analysis of the effect of an electrode layer on surface acoustic waves in a finite anisotropic plate

The effect of a metal layer over an elastic substrate on surface acoustic wave propagating in the structure can be evaluated precisely for semi-infinite solids and infinite plates, but there is no accurate analytical solution if the finite size of the plate has to be considered. By expanding displacements with eigensolutions of surface acoustic waves in a semi-inifite solid, a set of two-dimensional equations similar to the Mindlin plate theory are obtained. Then for a thin electrode layer, the effect is considered through the approximation of displacements in the metal layer with the ones in the substrate, and an integration over the thickness incorporated the properties of the metal layer into equations through the modification of material properties with the decaying indices of surface acoustic waves and the thickness of the metal layer. Using AT-cut quartz crystal as the substrate, we present the effect of silver electrode layers of finite thickness on the phase velocity of propagating surface acoustic waves.     

Circumferential waves in a composite circular cylinder

Circumferential waves propagating in a layered, circular cylinder are studied. The cylinder consists of an elastic circular core encased in a hollow, circular cylinder of distinctly different elastic properties. Both smooth and bonded contact are considered. The effect of curvature and layer thickness on the phase velocity of the lowest mode(s) is investigated for both an acoustically softer and an acoustically stiffer layer. When the outer radius of the composite cylinder is unbounded, Stoneley waves are a limiting case as the ratio of the radius of the core to the wavelength increases beyond bounds. When the outer radius is finite, waves in a layer and a half-space result for this limit. Some attention is also directed to the limiting case of small layer thickness to the wavelength ratio. In the limit as this ratio vanishes, the motion of the core reduces to that of Rayleigh waves on the curved surface. For smooth contact, the motion of the core becomes uncoupled from that of the layer for this limiting case, and two distinct modes are seen to exist.     

Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

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 microns 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.     

Effect of porous surface layer on wave propagation in elastic cylinder immersed in fluid

To study the damage to an elastic cylinder immersed in fluid, a model of an elastic cylinder wrapped with a porous medium immersed in fluid is designed. This structure can both identify the properties of guided waves in a more practical model and address the relationship between the cylinder damage degree and the surface and surrounding medium. The principal motivation is to perform a detailed quantitative analysis of the longitudinal mode and flexural mode in an elastic cylinder wrapped with a porous medium immersed in fluid. The frequency equations for the propagation of waves are derived each for a pervious surface and an impervious surface by employing Biot theory. The influences of the various parameters of the porous medium wrapping layer on the phase velocity and attenuation are discussed. The results show that the influences of porosity on the dispersion curves of guided waves are much more significant than those of thickness, whereas the phase velocity is independent of the static permeability. There is an apparent "mode switching" between the two low-order modes. The characteristics of attenuation are in good agreement with the results from the dispersion curves. This work can support future studies for optimizing the theory on detecting the damage to cylinder or pipeline.     

Dispersion of waves and characteristic wave surfaces in functionally graded piezoelectric plates

An inhomogeneous layer element method is presented to analyze the dispersion of waves and characteristic wave surfaces in plates of functionally graded piezoelectric material (FGPM). In this method, the FGPM plate is divided into a number of layered elements. The elemental elastic and electric properties are assumed as linear functions of the thickness to adopt the variety of the material property of FGPM. The Hamilton principle is applied to determine the governing equations. The phase velocity surface, phase slowness surface, phase wave surface, group velocity surface, group slowness surface, and group wave surface for FGPM plate are formulated using Rayleigh quotient and the orthogonality condition of the eigenvectors. These six surfaces are then used to illustrate the characteristics of waves in FGPM plates. Numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in FGPM plates.     

Excitation of seismoacoustic waves by a harmonic force source acting at the boundary of a liquid layer and an elastic halfspace

A problem on the excitation of seismoacoustic waves in a system of a homogeneous isotropic elastic halfspace covered with a liquid layer is solved in the case of action of a source of point harmonic force on the surface of an elastic medium. Integral expressions are obtained for the radiation powers averaged over a wave period for longitudinal and transverse waves in a solid. Mode excitation is analyzed in detail. Expressions describing parts of the mode powers radiated into a liquid layer and an elastic medium are obtained. Numerical analysis of radiation powers is conducted for spherical longitudinal and transverse waves as well as for the radiation powers of seismoacoustic modes in a solid halfspace and a liquid layer. It is determined that in the conditions characteristic of bottom rocks in the case, where the basin depth is several times and more larger than the sound’s wavelength, about 2/3 of the total power is radiated into a liquid.     

Instabilities in the sliding of continua with surface inertias: An initiation mechanism for brake noise

This paper presents a model for friction-induced vibration in brake systems, which takes a homogeneous tribological layer on the brake pad into account. The derived model consists of two flat elastic bodies sliding against each other with a constant coefficient of friction. In brake tribology, like in most tribological processes, a surface structure is observed, which can be modeled as an additional film of homogenized mass distribution bonded on the moving continua. The developed mechanical model and its analytical solution show an excitation mechanism that bases on the interaction of normal and frictional shear force and on the elastic coupling of spatial directions. The derived solution allows to study stability and eigenforms of the sliding process: on the frictional plane traveling surface waves are generated, with stability properties depending on parameters of the tribological layer. A parameter study analyzes the frictional couple of brake disk and pad and the related surface state. It is found that increasing inertias of surface structures on the pad strengthen instabilities of the sliding system. A comparison with experiments suggests a similar dependency between surface state and stability as observed by the model under discussion.     

Simple Solutions to the Wave Problem on the Surface of a Fluid with the Linear Hydroelastic Model

Doklady Physics - The problem of generation of waves on the surface of a water layer placed on an elastic base is considered. It is assumed that the generating source is located inside the elastic...     

Determination of elastic properties of Si/Ge superlattices and Si1-xGex films from surface acoustic modes by Brillouin scattering

Surface acoustic waves (SAW) have been measured by means of Brillouin scattering (BS) both as a function of k×h and the direction of k in the sample plane (k is the wavevector of the surface acoustic mode and h the thickness of the film). The velocity of the Rayleigh wave on sufficiently thick films (h > 4000 Å) has been experimentally found to ve uneffected by the elastic properties of the substrate material. Thus the directional dependence of the hypersonic surface wave is completely determined by the elastic properties of the layer material alone and reflects its crystallographic symmetry. The SL's can be treated as media with effective elastic constants because the wavelength of the thermally excited Rayleigh wave is much longer than the SL period. Furthermore, the angular dispersion of the SAW can be used to calculate the elastic constants of each film separately.     

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.     

Quasi elasto-electromagnetic surface waves on a piezo-plasma-like layer

Considering a piezo-plasma-like layer with finite thickness and hexagonal symmetry whose main symmetry axis is parallel to the z axis and approximating it by an isotropic medium, we study the coupling of the elastic wave with plasma properties of the medium with and without spatial dispersion and collisions. In this case we investigate the coupled surface quasi elasto-electromagnetic wave propagating on the interface of piezoelectric layer with vacuum. Furthermore, the coupling of elasticity and ion-acoustic waves is investigated.     

Properties of surface waves in an elastic cylinder filled with a liquid

The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide.     

Anomalous absorption of bulk shear sagittal acoustic waves in a layered structure with viscous fluid

It is demonstrated theoretically that the absorptivity of bulk shear sagittal waves by an ultra-thin layer of viscous fluid between two different elastic media has a strong maximum (in some cases as good as 100%) at an optimal layer thickness. This thickness is usually much smaller than the penetration depths and lengths of transverse and longitudinal waves in the fluid. The angular dependencies of the absorptivity are demonstrated to have significant and unusual structure near critical angles of incidence. The effect of non-Newtonian properties and non-uniformities of the fluid layer on the absorptivity is also investigated. In particular, it is shown that the absorption in a thin layer of viscous fluid is much more sensitive to non-zero relaxation time(s) in the fluid layer than the absorption at an isolated solid-fluid interface.     

Influence of adhesive layer properties on laser-generated ultrasonic waves in thin bonded plates

This paper studies quantitatively the generation of Lamb waves in thin bonded plates subjected to laser illumination, after considering the viscoelasticity of the adhesive layer. The displacements of such plates have been calculated in the frequency domain by using the finite element method, and the time domain response has been reconstructed by applying an inverse fast Fourier transform. Numerical results are presented showing the normal surface displacement for several configurations: a single aluminum plate, a three-layer bonded plate, and a two-layer plate. The characteristics of the laser-generated Lamb waves for each particular case have been investigated. In addition, the sensitivity of the transient responses to variations of material properties (elastic modulus, viscoelastic modulus, and thickness) of the adhesive layer has been studied in detail.     

Influence of the pinning of Abrikosov vortices on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure

The influence of surface-layer vortex pinning in a type-II superconductor on the propagation of surface magnetostatic waves in a ferromagnet-superconductor structure is analyzed. The pinning is assumed to be strong enough to prevent vortex displacement under the influence of the Lorentz force generated by the surface magnetostatic waves, so that the ground state of the superconductor is determined by the elastic properties of the vortex lattice and by pinning. In the given model the problem reduces to the analysis of the wave spectrum in the scattered field created by the disordered vortex surface layer. A calculation shows that the influence of this field on the surface magnetostatic-wave spectrum is slight and, hence, degradation of the shielding properties of the superconductor does not take place in the presence of strong vortex pinning (as opposed to the ferromagnet-ideal superconductor structure). Fiz. Tverd. Tela (St. Petersburg) 40, 32–35 (January 1998)     

Single-layer model of the hexagonal boron nitride nanomesh on the Rh(111) surface

An alternative model of the hexagonal boron nitride (h-BN) on nanomesh on the Rh(111) surface is presented. It explains the observed ultraviolet photoelectron spectroscopy spectra and reproduces experimental STM images introducing, instead of two, only one strongly corrugated layer of h-BN covering the whole Rh surface. In order to optimize the geometry of the BN layer we calculate the forces by density functional theory and analyze the interactions in the system. The final geometry is a result of a competition between BN-metal attraction or repulsion and elastic properties of the isolated h-BN layer. The calculated bonding energy is around 0.33 eV per BN molecule with a corrugation close to 0.55 A.     

Active fiber composites for the generation of Lamb waves

Active fiber composites (AFC) are thin and conformable transducer elements with orthotropic material properties, since they are made of one layer of piezoelectric ceramic fibers. They are suitable for applications in structural health monitoring systems (SHM) with acoustic non-destructive testing methods (NDT). In the presented work the transfer behavior of an AFC as an emitter of transient elastic waves in plate-like structures is investigated. The wave field emitted by an AFC surface bonded on an isotropic plate was simulated with the finite-difference method. The model includes the piezoelectric element and the plate and allows the simulation of the elastic wave propagation. For comparison with the model experiments using a laser interferometer for non-contact measurements of particle velocities at different points around the AFC on the surface of the plate were performed. Transfer functions defined as the ratio of the electric voltage excitation signal and the resulting surface velocity at a specific point are separately determined for the two fundamental Lamb wave modes. In order to take the orthotropic behavior of the AFC into account the transfer functions are determined for several points around the AFC. Results show that the AFC is capable to excite the fundamental symmetric and antisymmetric Lamb wave mode. The antisymmetric mode is mainly radiated in the direction of the piezoelectric fibers, while the symmetric mode is spread over a larger angle. The amplitudes of the emitted waves depend on the frequency of the excitation as well as on the geometric dimensions of the transducer.