Quasi-longitudinal Waves Research Articles

Interfacial imperfection on reflection and transmission of plane waves in anisotropic micropolar media

This study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface between two orthotropic micropolar elastic half-spaces with different elastic and micropolar properties. There exist three types of coupled waves in xy-plane. The reflection and transmission coefficients of quasi-longitudinal (QLD) wave, quasi-coupled transverse microrotational (QCTM) wave and quasi-coupled transverse displacement (QCTD) wave have been derived for different incidence waves and deduced for normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding. The numerical values of modules of the reflection and transmission coefficients are presented graphically with the angle of incidence for orthotropic micropolar medium (MOS) and isotropic micrpolar medium (MIS). Some particular cases of interest have been deduced from the present investigation.

Effect of the interrelationship of thermal and mechanical fields on the propagation of wave motions in cubically anisotropic thermoelastic materials

A characteristic equation for a system of equations of motion of a cubically anisotropic medium with allowance for the relaxation time of thermal disturbances has been obtained, and expressions for the velocities of propagation of modified elastic and thermal waves have been found. The surfaces of inverse velocities have been constructed and the influence of the effect of interrelationship of thermal and mechanical fields on the change in the phase velocities of propagation of a quasilongitudinal elastic wave and a thermal wave in different planes of a cubically anisotropic material has been analyzed.

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave ( T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave ( T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.

Diffraction of stress waves by a free or reinforced hole in an orthotropic plate

Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate

Modeling of Elastic Waves in Dynamically Loaded NiAl Bicrystals

Two methods have been used to simulate 2D elastic wave scattering in nickel aluminide (NiAl) bicrystals to study effects of grain boundaries and material anisotropy on elastic wave propagation. Scattering angles and amplitude ratios of the reflected and refracted waves produced at the grain boundary were calculated via slowness curves for both grains, which were plotted in the plane of incidence containing the grain boundary normal. From these curves, scattering angles were measured graphically and amplitude ratios were calculated based on the continuity of tractions and displacements at the boundary. To support these calculations, finite element simulations were performed with ABAQUS/EXPLICIT to obtain time- and space-dependent stresses. The results of each method correlated well with each other for four bicrystals. It was found that for bicrystals where the transmitted quasi-longitudinal (TQL) wave amplitude decreased across the boundary, diminished stresses were found in the finite element models for the same bicrystal. Conversely, where an increase in amplitude of the TQL wave was found, the finite element simulations showed that stress under the boundary increased. In general, the amplitude of the TQL wave was found to have a strong connection to the ratio of incident and TQL sound speeds. However, other directions in each grain are believed to contribute strongly to the overall scattering process since the pairs of bicrystals in this investigation had somewhat similar sound speeds. These findings correlated well with free surface cracking observed in a previous paper (Loomis, E., Peralta, P., Swift, D., and McClellan, K., 2005, Mater. Sci. Eng., Ser. A., 404(1-2), pp. 291–300), where cracks nucleated and propagated due to the focusing of scattered waves at the boundary. Specifically, in bicrystals oriented for shielding, the grain boundary was protected forcing cracks to grow outside of the shielded region.

Reflection/transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half-spaces

The present study is concerned with the reflection and transmission of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic half-spaces with different elastic and thermal properties. The reflection and transmission coefficients of quasi longitudinal (QL-) wave, quasi thermal (T-mode) wave and quasi transverse (QT-) wave have been derived for different incident waves. The reflection and refraction coefficients of different reflected and transmitted waves have been compared for the two generalized theories, i.e. Lord–Shulman theory [H.W. Lord, Y. Shulman, J. Mech. Phys. Solids 15 (1967) 299–309] and Green–Lindsay theory [A.E. Green, K.A. Lindsay, J. Elasticity 2 (1) (1972) 1–7] with angle of incidence. Some special cases of boundaries, i.e. normal stiffness, transverse stiffness, thermal contact conductance, slip boundary and welded contact boundary have been deduced from an Imperfect one. It is observed that thermal properties and imperfect boundary have significant effect on the propagation of waves.

Two-dimensional diffraction of plasma, thermal, and elastic waves generated by an infrared laser pulse in semiconductors

When a $1064\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser pulse is focused at the surface of silicon, it has been observed that the material contracts whereas heating should produce expansion. In addition to the usual thermal acoustic source, a nonthermal sound generation results of photoexcitation of electron-hole pairs. To describe the optoacoustic effect in semiconductors, it is thus necessary to account for thermoelastic and other deformation sources simultaneously. The acoustic signal is then strongly dependent on the nature of the space-time evolution of both the photoexcited charge carriers and temperature. In this paper, assuming line focusing of the laser pulses, a model is implemented that accounts for the two-dimensional (2D) character of charge carrier motion and heat conduction. Relevant differential equations are coupled together and with the wave motion equation to describe acoustic diffraction. Three sets of equations are linearized in a 2D Fourier domain and solutions are found with an appeal to convenient boundary conditions. The conditions for 2D diffraction of plasma, thermal, and elastic waves are analyzed. Experiments are performed on a $5\phantom{\rule{0.3em}{0ex}}\mathrm{mm}$ thick silicon plate with a Nd:yttrium aluminum garnet laser that delivers $20\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$ pulses. Signals are measured for epicenter and off epicenter positions. Very good agreement is obtained with calculated signals for both positions demonstrating that both sound generation mechanism and anisotropy are accurately taken into account. In addition to the expected material contraction accompanying quasilongitudinal bulk acoustic waves, the other remarkable feature is the change in the shape of the signals observed for a same angle, but for two laser energies. The results emphasize the nonlinear photoacoustic response of the material, with respect to the laser energy. It is accurately represented by the calculations, assuming prevailing of Auger electron-hole recombination process and nonlinear dependency of charge carrier lifetime with respect to its density.

Determination of elastic coefficients of bone and composite materials by acoustic immersion technique

Elastic properties of single parts of a human skeleton are necessary to know for modelling bone tissue-implants interactions as well as for diagnostic purposes. This paper contributes to the methodology of the evaluation of elastic properties of bones by the ultrasonic wave inversion. The method was developed on composite structures such as plates and cylindrical shells. Final results are then demonstrated on the bovine cortical bone specimen. Properties are supposed to exhibit an orthotropic or a transversally isotropic symmetry. Quasi-longitudinal and quasi-transversal waves are generated from the wave diffraction on the liquid/specimen interface. Wave velocity fields obtained by the ultrasonic scanning technique are used as an input to the inversion procedure for all elastic constants determination. Experimental results are confronted with the numerical modelling of the wave propagation and the stability of resulting data is evaluated by the statistical method based on the Monte-Carlo simulation. The suggested approach has a potential for the qualify of such measurements performed on fresh bones and also for improvement in-situ ultrasonic techniques.

Experimental studies of quasi-longitudinal waves power flow in corrugated plates

The structural intensity technique using cross-spectral densities is used to estimate the quasi-longitudinal wave power in rectangular and trapezoidal corrugated plates in the frequency domain. The two-point transducer method for in-plane power in naturally orthotropic plate, whose thickness is uniform, is used for measuring in-plane vibration power transmission of these plates. The method of elastic equivalence is used to facilitate power flow estimation. It is also necessary to re-model the trapezoidal corrugated plate to rectangular corrugated plate so as to apply the method of elastic equivalence. An isotropic plate is also used for this measurement. Measured in-plane power flow from corrugated plates is compared to that from isotropic plate. The effects of in-plane stiffness on vibration power flow are also investigated. In-plane power flow is observed to reduce gradually as the frequency increases. The effects of in-plane stiffness of the plates on quasi-longitudinal wave power are insignificant in the frequency range of interest. Some negative values of power are also observed at some frequencies at lower range.

Bulk conical and surface helical acoustic waves in transversely isotropic cylinders; application to the stiffness tensor measurement

A point-source-point-receiver technique, based on laser generation and laser detection of acoustic waves, allows determination of mechanical properties of anisotropic cylinders. The anisotropic nature of the material and the geometry of the samples make the acoustic signature difficult to interpret. In addition to multiple surface waves, quasi-longitudinal and quasi-shear bulk waves are diffracted and acoustic rays are reflected with or without mode conversion at the cylinder surface. Moreover both bulk and surface diffracted waves have a dispersive behavior. To bypass the intricacies, wave fronts are synthesized with signals provided by scanning a straight line on the cylinder with the laser point source. Conical waves propagating in the volume and helical waves propagating along the surface are then numerically produced. The recovery of the stiffness-tensor components is based on the inversion of the bulk waves, phase velocities. The method is presented and applied to signals simulated or experimentally recorded for a composite material. The five independent stiffness coefficients of the hexagonal symmetry are thus measured with waveforms provided by a single scan along the cylinder surface. The method provides a unique mean for the noncontact measurement of elastic properties of cylindrical parts.

Effect of Substrate Thickness on Quasi-Longitudinal Leaky Surface Acoustic Wave Propagation on Quartz

Propagation properties of a quasi-longitudinal leaky surface acoustic wave (QLL-SAW) on rotated-Y cut quartz are described. It is found that by reducing the relative thickness of the quartz substrate, i.e., the ratio of the substrate thickness to the SAW wavelength, the Q-value of a QLL-SAW resonator can be improved. Its phase velocity is about 5704 m/s, which is close to the velocity of a longitudinal BAW (5750 m/s) and about 1.8 times that of a Rayleigh SAW. Propagation characteristics are simulated by a finite element method. The results obtained indicate that many guided wave modes exist near the velocity of the longitudinal BAW and strongly couple to QLL-SAW modes. Experimental results show that these guided wave modes affect QLL-SAW propagation and deteriorate resonator Q-values. By reducing the relative thickness of the quartz substrate, the frequency difference between the QLL-SAW and the guided wave modes is increased, which weakens the coupling. As a result, 700 MHz SAW resonators having a Q-value of more than 8000 are realized.

Influence of couple stresses on the propagation of elastic waves in a micropolar cubically anisotropic medium

Expressions for the phase and radial velocities of propagation of three-dimensional fronts of quasilongitudinal and quasitransverse elastic waves in a micropolar cubically anisotropic medium have been obtained. An analysis of the influence of the micropolar elastic constant on the dependence of the wave velocities on the angle of inclination of the normal to the wave surface has been made.

Nonlinear anisotropic description for the thermomechanical response of shocked single crystals: Inelastic deformation

A nonlinear anisotropic continuum framework for describing the thermoelastic-plastic response of single crystals shocked along arbitrary orientations has been developed. Our modeling approach incorporates nonlinear elasticity, crystal plasticity, and thermodynamic consistency within an incremental tensor formulation. Crystal plasticity was incorporated by considering dislocation motion along specified slip planes. The theoretical developments presented here are sufficiently general to also accommodate other types of inelastic deformation mechanisms. As representative applications of the theoretical developments, numerical simulations of shock wave propagation in lithium fluoride (LiF) and copper single crystals are presented and compared to wave profile data for several crystal orientations. Simulations of shock wave propagation along low-symmetry directions, where data are not available, are also presented to examine the propagation of quasilongitudinal and quasishear waves in crystals undergoing elastic-plastic deformation. Temperature calculations for the shocked single crystals are discussed.

Acoustic wave propagation through the boundary between a liquid and the Heusler ferromagnetic alloy

Incidence of an acoustic wave upon a plane boundary between a liquid and a ferromagnetic crystal is considered. The ferromagnet is the Ni2+x+yMn1−xGa1−y Heusler alloy with a shape memory, which is in the region of the premartensite or martensite phase transition in temperature. The directions of propagation and polarization and the amplitudes of the reflected and transmitted quasilongitudinal and quasitransverse waves in the (110) plane of the crystal are determined. Starting from a certain critical angle of incidence, a longitudinal wave in the crystal becomes inhomogeneous and gliding along the boundary with an accompanying surface oscillation. In the vicinity of the phase transition point, this wave may be radiated into the crystal bulk. Proceeding from the experimental data by Trivisonno for ultrasonic velocities and absorption in a Ni2MnGa crystal, numerical estimates are obtained for the aforementioned acoustic effects.

Discontinuous wave interaction with interfaces between anisotropic elastic media

The problem about dynamic interaction of discontinuous waves with interfaces between anisotropic elastic media is considered. To investigate this phenomenon accompanied by formation of reflected and refracted quasi-longitudinal and quasi-shear discontinuous waves, a technique based on joint usage of the zero approximation of the ray theory and method of stereomechanical impact is proposed. It is used for the analysis of the wave front transformation, scattering and focusing. The setup problem solutions can be applied to discovering the most seismically hazardous zones in the earth’s crust, interpretation of geophysical data about geological rock structures and the analysis of the causes of dynamic delamination of layered composite and nanomaterials.

New type of an acoustic plate mode: quasi-longitudinal normal wave

A new type of an acoustic wave belonging to the family of the normal plate modes is discovered numerically and verified experimentally in ST, x-quartz plates with free surfaces. It exists within restricted bands of the normalized plate thickness H/ λ, where H is the thickness, λ is the wavelength, separated by forbidden H/ λ-bands attributed to the common plate modes. Polarization of the wave over the whole plate thickness is almost longitudinal. Velocity of the wave is close to or equal to the velocity of the longitudinal bulk wave, propagating in the same direction. The proximity or/and equality of the velocities is a necessary, but not sufficient condition of the existence of the new wave.

Isolation of Buildings from Ground-Borne Noise Using a Sand Stratum

The effect of an elastic stratum in reducing ground-borne sound transmission in buildings to be built above railway tunnels is investigated, by considering a sand layer between the bedrock and load bearing elements of the building. It is assumed that the initial vibrational energy that propagates from the foundation is in the form of quasi-longitudinal waves. The complete model as presented by the author in a previous paper is considered. Calculated results are compared with previous results for a typical building and it is shown that a sand layer can considerably reduce upward sound transmission in the building. The results of a parametric study to investigate the influence of the type of load-bearing elements and the thickness of the layer, on transmission of structure-borne sound in the building, are presented.

Surface acoustic waves in germanium single crystals

Impulsive stimulated light scattering has been used to measure surface wave power spectra of germanium single crystals. In addition to the familiar Rayleigh and pseudosurface acoustic waves, the spectra contain a feature with the directional dependence of the quasilongitudinal bulk wave. Comparisons are presented between measured and calculated spectra. The observed power spectra are found to contain sufficient information to determine all the elements of the elastic tensor.

Super high-velocity leaky waves guided by a layer inserted into piezoelectric crystals

A study is made of the existence of leaky waves that propagate along a layer inserted into a homogeneous medium faster than the quasi longitudinal bulk wave in this medium. It has been shown that a sufficient condition for such super high-velocity leaky solutions to originate is the presence of concavity on the slowness surface of the quasi longitudinal waves; the concavity required can exist in piezoelectric crystals. As an example, computations for KNbO 3 crystal containing a thin diamond film have been performed. In addition, we have discussed the occurrence of localized leaky solutions at the interface between two media that differ only by the sign of piezomoduli and at an infinitesimal thin metallic layer inserted into a homogeneous medium.

Elastic wave propagation and scattering in solids with uniaxially aligned cracks.

In this article, elastic wave propagation and scattering in a solid medium permeated by uniaxially aligned penny-shaped microcracks are studied. The crack alignment refers to the case in which the unit normals of all cracks are randomly oriented within a plane of isotropy. The analysis is restricted to the limit of the noninteraction approximation among individual cracks. Explicit expressions for attenuations and wave speeds of the shear horizontal, quasilongitudinal, and quasishear vertical waves are obtained using stochastic wave theory in a generalized dyadic approach. The ensemble average elastic wave response is governed by the Dyson equation, which is solved in terms of the anisotropic elastic Green's dyadic. The analysis of expressions is limited to frequencies below the geometric optics limit. The resulting attenuations are investigated in terms of the directional, frequency, and damage dependence. In particular, the attenuations are simplified considerably within the low frequency Rayleigh regime. Finally, numerical results are presented and discussed in terms of the relevant dependent parameters.