Showing papers on "Longitudinal wave published in 1995"

Wave propagation in layered anisotropic media : with applications to composites

Abstract: Introduction - historical background. Part 1 Field equations and tensor analysis: the stiffness tensor material symmetry matrix forms of stiffness engineering constants transformed equations expanded field equations planes of symmetry. Part 2 Bulk waves: an overview the Christoffel equation material symmetry computer aided analysis group velocity energy flux. Part 3 Generalized Snell's law and interfaces: boundary conditions characterization of incident waves critical angles two fluid media two isotropic media. Part 4 Formal solutions: common form of solutions triclinic layer the monoclinic case higher symmetry materials formal solutions in fluid media the alpha-c relation and the Christoffel equation. Part 5 Scattered wave amplitudes: notation reflection from a free surface scattering from fluid-solid interfaces scattering from solid-solid interface. Part 6 Interface waves: surface waves pseudo-surface waves Scholte waves. Part 7 Free wave in plates: free waves in triclinic plates free waves in monoclinic plates higher symmetry material plates numerical computation strategy. Part 8 General layered media: geometric description of unit cell analysis properties of the transfer matrix free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 9 Propagation along axes of symmetry: geometry SH waves motion in the sagittal plane free waves on the layered cell waves in a periodic medium bottom bounding solid substrate. Part 10 Fluid-loaded solids: reflection from a substrate plates completely immersed in fluids higher symmetry cases leaky waves experimental technique. Part 11 Piezoelectric effects: basic relations of piezoelectric materials simplified field equations analysis formal solutions higher symmetric materials remarks on the monoclinic-m case reflection and transmission coefficients sample illustration remarks on layered piezoelectric media. Part 12 Transient waves: theoretical development source characterization integral transforms of formal solutions isotropic media anisotropic media Cagniard-de Hoop transformation semi-space media. Part 13 Scattering from layered cylinders: field equations formal solutions in isotropic cylinders characterization of incident waves formal solutions for a layer scattering amplitudes. Part 14 Elastic properties of composites: general description of fibrous composites the model the layered model the square fibrous case anisotropic fibre and matrix strain energy approach undulated fibre appendix.

Velocity and attenuation of elastic waves in finely layered porous rocks

Abstract: SUMMARY We perform a theoretical study of the effect of fine layering on the compressional-wave velocities and attenuation coefficients in fluid-saturated rocks. This effect in a permeable rock differs from that in a purely elastic solid because of the local flow of the pore fluid across the interfaces, which is caused by the passing wave. For analytical calculations. Biot theory is applied to non-homogeneous (randomly and periodically layered) porous media leading to Biot's equations with variable coefficients. By analysing these equations with the help of a statistical perturbation technique we obtain the velocity and normalized attenuation 1/Q of the fast compressional wave as a function of frequency f. Both attenuation and velocity dispersion are found to obtain their maximum values near some frequency f0, at which the Biot slow-wave attenuation length equals the mean inhomogeneity size (mean layer thickness or characteristic length). In the low-frequency limit, 1/Q is proportional to f1/2 for random and to f for periodic layering. At frequencies higher than f0, attenuation decreases with increasing frequency as f−1/2, regardless of the particular type of layering. The results for periodic layering are in a good agreement with recently published exact results. The results for the more realistic case of random layering with exponential correlation reveal more gradual changes of velocity and attenuation versus frequency than those for a periodically layered medium.

Wave propagation in heterogeneous, porous media: A velocity‐stress, finite‐difference method

Abstract: A particle velocity-stress, finite-difference method is developed for the simulation of wave propagation in 2-D heterogeneous poroelastic media. Instead of the prevailing second-order differential equations, we consider a first-order hyperbolic system that is equivalent to Biot's equations. The vector of unknowns in this system consists of the solid and fluid particle velocity components, the solid stress components, and the fluid pressure. A MacCormack finite-difference scheme that is fourth-order accurate in space and second-order accurate in time forms the basis of the numerical solutions for Biot's hyperbolic system. An original analytic solution for a P-wave line source in a uniform poroelastic medium is derived for the purposes of source implementation and algorithm testing. In simulations with a two-layer model, additional «slow» compressional incident, transmitted, and reflected phases are recorded when the damping coefficient is small. This «slow» compressional wave is highly attenuated in porous media saturated by a viscous fluid. From the simulation we also verified that the attenuation mechanism introduced in Biot's theory is of secondary importance for «fast» compressional and rotational waves. The existence of seismically observable differences caused by the presence of pores has been examined through synthetic experiments that indicate that amplitude variation with offset may be observed on receivers and could be diagnostic of the matrix and fluid parameters. This method was applied in simulating seismic wave propagation over an expanded steam-heated zone in Cold Lake, alberta in an area of enhanced oil recovery (EOR) processing. The results indicate that a seismic surface survey can be used to monitor thermal fronts

A three dimensional analytical solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques

Abstract: This paper presents an original three dimensional (3D) analytical general solution of the longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar and its applications to some experimental methods of material behaviour testing to improve their accuracy. One application is to take into account the wave dispersion effects in the split Hopkinson pressure bar (SHPB) setup composed of viscoelastic bars. Another is to eliminate the geometrical effects in an impulse test in which the linear viscoelastic material properties can be deduced from the change in the wave shape due to the propagation between two points of measurement in a specimen bar.

Three‐dimensional instabilities of film flows

Abstract: Two‐dimensional (2‐D) interfacial waves on flowing films are unstable with respect to both two‐ and three‐dimensional instabilities. In this paper, several distinct three‐dimensional instabilities that occur in different regions of the parameter space defined by the Reynolds numberR and the frequency f of forced two‐dimensional waves are discussed in detail. (a) A synchronous 3‐D instability, in which spanwise deformations of adjacent wave fronts have the same transverse phase, appears over a wide range of frequency. These transverse modulations occur mainly along the troughs of the primary waves and eventually develop into sharp and nearly isolated depressions. The instability involves many higher harmonics of the fundamental 2‐D waves. (b) A 3‐D surbharmonic instability occurs for frequencies close to the neutral curve f c (R). In this case, the transverse modulations are out of phase for successive wave fronts, and herringbone patterns result. It is shown that this weakly nonlinear instability is due to the resonant excitation of a triad of waves consisting of the fundamental two‐dimensional wave and two oblique waves. The evolution of wavy films after the onset of either of these 3‐D instabilities is complex. However, sufficiently far downstream, large‐amplitude solitary waves absorb the smaller waves and become dominant.

Some aspects of the physics and numerical modeling of biot compressional waves

Abstract: We investigate the problem of wave propagation in a porous medium, in the framework of Biot's theory, computing the numerical solution of the differential equations by a grid method. The problems posed by the stiffness of the equations are circumvented by using a partition (or splitting) time integrator which allows for an efficient explicit solution as in the case of nonstiff differential equations. The resulting algorithm possesses fourth-order accuracy in time and "infinite" (spectral) accuracy in space. Alternatively, a second-order algorithm, based on a Crank–Nicolson method, provides similar stability properties, although lower accuracy. The simulations correctly reproduce the wave forms of the fast and slow compressional waves and their relative amplitudes. Moreover, we observe the static slow mode, particularly strong when the source is a bulk perturbation or a fluid volume injection. The numerical results are confirmed by the analytical solution.

Relativistic ponderomotive force, Uphill acceleration, and transition to chaos.

Abstract: Starting from a covariant cycle-averaged Lagrangian the relativistic oscillation center equation of motion of a point charge is deduced, and analytical formulas for the ponderomotive force in a traveling wave of arbitrary strength are presented. It is further shown that the pondermotive forces for transverse and longitudinal waves are different; in the latter, uphill acceleration can occur. In a standing wave there exists a threshold intensity above which, owing to transition to chaos, the secular motion can no longer be described by a regular ponderomotive force.

The Role of Longitudinal Waves in Quartz Crystal Microbalance Applications in Liquids

Abstract: The generation of shear waves in liquids by the quartz crystal microbalance (QCM) is evident from the influence of liquid properties on the QCM frequency and electrical characteristics. With the exception of a few reports, contributions from longitudonal waves that arise from nonuniform velocity profiles along the shear direction or nonideal contributions from crystal longtudinal and flexure modes have been largely ignored. The presence of these longitudinal components is demonstrated by the influence of a glass plate, fixed Gel to the QCM surface at a remote distance, on the QCM resonant frequency and electrical impedance characteristics. In agreement with a previous report, these effects can be observed even when the glass plate is positioned >1 cm away from the QCM, substantially longer than the shear wave decay length. Longitudinal standing waves are evident from the periodicity of the resonant frequency, inductance, capacitance, and resistance as the distance between the QCM and the glass plate. The wavelength of the standing waves agrees with that expected for the resonant frequency of the QCM and the fluid medium. The amplitude of the standing waves depends strongly upon the quartz crystal contour, as evident from extremely large frequency excursions observed for plano-convex crystals in witch energy trapping in the center of the resonator is greater than that for plano-plano crystals. Impedance analysis indicates that the frequency excursions are primarily a consequence of changes in the capacitance of the quartz crystals that result from a decrease in the compliance of the quartz resonator due to pressure exerted by the longitudinal waves. Standing waves resulting from reflection from the fluid-air interface are also observed, although the amplitude of the standing waves is smaller than the amplitude observed with the glass reflector plate owing to the larger reflection coefficient for the latter. However, the frequency excursions that result from small changes in the height of the fluid-air interface are substantial relative to frequency changes measured in typical QCM experiments. These results demonstrate that it is important to design QCM experiments to avoid contributions from longitudinal waves

Influence of compressional wave generation on thickness-shear mode resonator response in a fluid

Abstract: Acoustic interferometry was performed with thickness-shear mode (TSM) resonators to investigate the effect of compressional wave generation on the response (resonant frequency and damping). Resonator response was measured while the spacing between the resonator and adjacent solid was filled with fluid and the spacing was varied. A characteristic resonance response was observed whenever the spacing reached a multiple of λ c /2, where λ c is the compressional wavelength in the fluid. Compressional wave generation arises from a gradient in the inplane surface displacement. A model is proposed to predict the resonator response that arises from combined shear wave and compressional wave generation. Experimental data fit to this model determine device coupling to shear and compressional waves. The model also relates resonator response to the surface displacement profile. By measuring this displacement profile, compressional wave generation can be estimated. The effect of surface roughness and device geometry on shear and compressional wave coupling is examined. The results indicate that even in a semiinfinite fluid, compressional wave generation contributes significantly to device damping (motional resistance) but not to the frequency shift.

Applications of micromachined capacitance transducers in air-coupled ultrasonics and nondestructive evaluation

Abstract: Micromachined capacitance transducers have been investigated in practical situations where air-coupled ultrasound has current application. Their /spl sim/2 MHz bandwidths lead to good performance in pulse-echo and through transmission operation at solid surfaces. Applications in surface profiling and distance measurement have been investigated. For the transduction of waves within solid media, the devices are shown to be capable of detecting longitudinal and shear waves at solid surfaces, as well as Rayleigh and Lamb waves. Examples are also given of fully noncontact, through transmission of carbon fibre reinforced polymer plates. >

Nonlinear Waves in Elastic Media

Abstract: Mathematical Introduction Conservation Laws and Related Differential Equations. Hyperbolic Systems. Linear and Linearized Equations. Riemann Invariants. Boundary Conditions and Evolutionary Properties. Riemann Waves. Discontinuities and Relations on Them. Shock Adiabat. Evolutionary Conditions for Discontinuity. Low Intensity Discontinuities. Shock Adiabat Behavior in a Vicinity of the Jouget Point. Conservation Law in the Godunov Form. Entropy. Entropy Production and Entropy Density Change on a Discontinuity. Solutions with Discontinuities as a Limit of Continuous Solutions to Equations of a Complicated Model. Small Perturbations in Dissipative Media. Shock Wave Structure. On Plane Wave Problems in Elastic Media Elastic Medium Model. Governing Equations. Plane Wave Equations. Conditions on a Discontinuity. Shock Adiabat. Entropy Change Along the Shock Adiabat. Wave Isotropy and Anisotropy. Internal Energy of a Medium with Weak Wave Anisotropy. Elastic Potential for a Weakly Nonlinear Medium. Nonlinear Wave Propagation Through Media Interacting with Electromagnetic Fields. Riemann Waves Small Perturbations. Linear Waves. Equations for Riemann Waves. Quasilongitudinal Waves. Quasitransverse Riemann Wave. Parameter Variations in Quasitransverse Waves. Evolution of Quasitransverse Riemann Waves. Riemann Waves in the Case of Wave Isotropy. Shock Waves Relationships on a Weak Shock Wave. Quasilongitudinal Shock Waves. Quasitransverse Waves. Shock Adiabat. Entropy Nondecreasing Condition. Evolutionary Conditions on Shocks. Velocities in Quasitranverse Waves. The Number of Evolutionary Shock Waves and Their Types. Locations of Evolutionary Segments on the Shock Adiabat. Shock Transitions into a Given State. Special Forms of Initial Deformations. Quasitransverse Shock Waves for G/R2

Nonlinear sawtooth-shaped waves

Abstract: This survey is devoted to experimental and theoretical results on interaction and self-action processes of strongly distorted waves containing shock fronts. Such sawtooth-shaped disturbances can be formed during the propagation of the wave through media where the nonlinearity predominates over competitive factors like dispersion, diffraction, and absorption. The specificity of nonlinear processes for sawtooth-shaped waves is particularly emphasised. The recently observed phenomena such as self-action of beams, self-refraction of shock pulses and saturation of the signal in focus, as well as current applied problems, are described.

Axial propagation of helicon waves

Abstract: Traveling‐ and standing‐wave characteristics of the wave fields have been measured in a helicon discharge using a five‐turn, balanced magnetic probe movable along the discharge axis z. Helical and plane‐polarized antennas were used, and the magnitude and direction of the static magnetic field were varied, yielding three primary results. (1) As the density varies along z, the local wavelength agrees with the local dispersion relation. (2) Beats in the z variation of the wave intensity do not indicate standing waves, but instead are caused by the simultaneous excitation of two radial eigenmodes. Quantitative agreement with theory is obtained. (3) The damping rate of the helicon wave is consistent with theoretical predictions based on collisions alone.

Determination of near surface residual stresses on welded joints using ultrasonic methods

Abstract: Ultrasonic velocity measurements are used to determine residual stresses induced by welding processes. A welded stainless steel pipe and aluminium alloy plate are analysed in their near surface residual stress distribution by using subsurface longitudinal waves and Rayleigh waves. The experimental procedure is presented: measurement of time of flight, calibration of the acoustoelastic effect, methods for residual stress measurements. The effects of a slightly orthotropic symmetry on wave velocities are investigated in the case of the aluminium alloy plate, which exhibits a texture due to rolling processes. Special calibration, performed on two test specimens, allows the effect of this texture to be taken into account. The acoustic birefringence technique is also used in the case of the aluminium plate to verify the stress distribution in the thickness. The results of surface residual stress distribution are compared with those obtained with an X-ray diffraction technique.

Two-dimensional periodic waves in shallow water. Part 2. Asymmetric waves

Abstract: We demonstrate experimentally the existence of a family of gravity-induced finiteamplitude water waves that propagate practically without change of form in shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional, and periodic. The basic template of a wave is hexagonal, but it need not be symmetric about the direction of propagation, as required in our previous studies (e.g. Hammack et al. 1989). Like the symmetric waves in earlier studies, the asymmetric waves studied here are easy to generate, they seem to be stable to perturbations, and their amplitudes need not be small. The Kadomtsev–Petviashvili (KP) equation is known to describe approximately the evolution of waves in shallow water, and an eight-parameter family of exact solutions of this equation ought to describe almost all spatially periodic waves of permanent form. We present an algorithm to obtain the eight parameters from wave-gauge measurements. The resulting KP solutions are observed to describe the measured waves with reasonable accuracy, even outside the putative range of validity of the KP model.

Parasitic capillary waves: a direct calculation

Abstract: As in a previous theory (Longuet-Higgins 1963) parasitic capillary waves are considered as a perturbation due to the local action of surface tension forces on an otherwise pure progressive gravity wave. Here the theory is improved by: (i) making use of our more accurate knowledge of the profile of a steep Stokes wave; (ii) taking account of the influence of gravity on the capillary waves themselves, through the effective gravitational acceleration g* for short waves riding on longer waves.Nonlinearity in the capillary waves themselves is not included, and certain other approximations are made. Nevertheless, the theory is shown to be in essential agreement with experiments by Cox (1958), Ebuchi, Kawamura & Toba (1987) and Perlin, Lin & Ting (1993).A principal result is that for gravity waves of a given length L > 5 cm there is a critical steepness parameter (AK)c at which the surface velocity (in a frame of reference moving with the phase-speed) equals the minimum (local) speed of capillary-gravity waves. On subcritical gravity waves, with steepness AK (AK)c, capillary waves can only be generated in the wave troughs; they are trapped between two caustics near the crests. Generally, the amplitude of the parasitic capillaries is greatest on gravity waves of near critical (but not maximum) steepness.

Simple magnetohydrodynamic waves

Abstract: Large-amplitude magnetic field fluctuations often accompanied by density variations are frequently observed in front of the earth's bow shock and in the vicinity of comets by extraterrestrial in situ measurements. They are identified as a manifestation of magnetohydrodynainic (MHD) waves in space plasmas. Because of their large amplitudes (i.e. because the magnetic field amplitude is of the order of the ambient magnetic field, for instance), these fluctuations cannot be satisfactorily described by linear wave theory. In this paper the properties of one-dimensional MHD waves of arbitrary amplitude, i.e. so-called simple MHD waves, are investigated, and a relationship is derived between the enhancement of the magnetic field and the density as well as the propagation velocity. Fast large-amplitude magnetosonic waves exhibit wave steepening. Here the dependence of the steepening time on the wave amplitude is derived and illustrated numerically.

Observations of mirror waves and plasma depletion layer upstream of Saturn's magnetopause

Abstract: The two inbound traversals of the Saturn's magnetosheath by Voyagers 1 and 2 have been studied using plasma and magnetic field data. In a great portion of the subsolar magnetosheath, large-amplitude compressional waves are observed at low frequency (approximately 0.1 f(sub p)) in a high-beta plasma regime. The fluctuations of the magnetic field magnitude and ion density are anticorrelated, as are those of the magnetic and thermal pressures. The normals to the structures are almost orthogonal to the background field, and the Doppler ratio is on the average small. Even though the data do not allow the determination of the ion thermal anisotropy, the observations are consistent with values of T(sub perpendicular)/T(sub parallel) greater than 1, producing the onset of the mirror instability. All the above features indicate that the waves should be most probably identified with mirror modes. One of the two magnetopause crossings is of the high-shear type and the above described waves are seen until the magnetopause. The other crossing is of the low-shear type and, similarly to what has been observed at Earth, a plasma depletion occurs close to the magnetopause. In this layer, waves with smaller amplitude, presumably of the mirror mode, are present together with higher-frequency waves showing a transverse component.

Theory and simulation of low-frequency plasma waves and comparison to Freja satellite observations

Abstract: One-dimensional models of obliquely propagating nonlinear plasma waves were formulated and solved both analytically and numerically to interpret recent Freja satellite observations of low-frequency plasma waves detected in the low-Mtitude auroral magnetosphere. Analytic calculations revealed four types of steady state waves solutions. Time dependent initial value numerical calculations were compared to the steady state solutions and to Freja observations. One type of steady state wave solution emerged in the long time limit from the initial sinusoidal waves; however, the initial value simulations agreed best with the observations during the nonlinear steepening phase of the initial waveform at a time well before a steady state ws reached. From this result we concluded that many of the low altitudeuroral waves Freja has detected were oblique inertial Alfv6n waves that had nonlinearly steepened due to propagation into a region of lower Alfv6n speed. The nonlinear steepening was found to produce very large parallel currents. The current is sufficiently high to excite prallel electron drift instabilities, which may lead to electronnd ion energiztion and enhanced dissipation of auroral arc energy. 1.1. Scope of Work In this paper we theoretically explore the relationship of a class of low-frequency nonlinear oblique plasma waves to recent Freja satellite observations of solitary kinetic Alfv6n waves, hereafter called SKAW (Wahtund el at., 1994a; Louarn el at., 1994). We investigated low-frequency w < fi and small-scale L_  c/w e one- dimensional plane waves having a phase front oriented at a small angle aV/rolM to the geomagnetic field. These waves are commonly called inertial Alfvdn waves (Lysak and Dum, 1983; $eyter, 1990; Lysak, 1990; Hui and Seyler, 1992) and are widely believed to be a fun- damental aspect of small-scale auroral arcs. We formulated a one-dimensional fluid theory of iner- tial Alfvdn waves which included thermal electron and ion effects. We found analytic steady state solutions and compared the results to numerically determined time dependent initial value solutions. These solutions were then compared to se!ected Freja observations. The excellent agreement we found led us to important con-

Deep-water internal solitaty waves

Abstract: An experimental investigation of mode-2 (’lump-Like’) Solitary waves propagaling on a thin interface between two deep layers of different densities is presented. Small-and large-amplitude waves behaved differently: small waves carried energy and momentum, whereas sufficiently large waves also carried mass. Weakly nonlinear theory anticipated the result for amplitudes a/h [les ] 0.5 but did not provide even a qualitative description of the large-amplitude waves. In particular, the prediction that for waves to maintain permanent form their wavelength must decrease with increasing amplitude failed; instead the wavelength of large waves was observed to increase with increasing amplitude. Furthermore, whilst the waves were expected to emerge from interactions along their precollision trajectories, the large waves actually suffered a backward shift.

A high‐speed photographic study of cavitation damage

Abstract: Cylindrical cavities, viewed through the side as they collapsed onto solid surfaces, were studied using high‐speed streak and framing photography. The cavities were collapsed asymmetrically using shock waves of varying amplitude so that the rear surface formed a high‐speed jet which crossed the cavity and interacted with the target surface. Schlieren optics were used to visualise waves in the fluid and in the target. Two features of the collapsing bubble affected the damage to the target surface. The first was the impact of the high‐speed liquid jet on either the rear wall of the cavity or the target itself. The second was the production of a strong compression wave on the rebound of the bubble after it reached minimum volume. Damage to the targets related to their material properties. Metals, with low compressive but higher tensile strengths, plastically deformed beneath the penetrating jet to form a pit. Brittle materials, with high compressive but low tensile strengths, deformed by cracking. The position of the cavity relative to the surface had a major effect upon the geometry of the damage. With the cavity close to the target, the penetrating jet dominated the damage leaving single pits. With the cavity at some distance, the rebound wave was more important than the jet giving rise to a circular damage mark. This mechanism can be used to re‐interpret previous experimental observations [Y. Tomita and A. Shima, J. Fluid Mech. 119, 535 (1986)].

Theory and observation of auroral substorms: A magnetohydrodynamic approach

Abstract: A theory of auroral substorm dynamics is constructed on the basis of MHD wave processes in the ionosphere-magnetosphere system. The basic view is that the substorm commences in the nightside near-Earth magnetosphere through a collapse of plasma equilibrium. The collapse releases a significant amount of free energy embedded initially in a collection of compressional waves. It is suggested that substorm dynamics after the collapse are determined by the evolution of these waves. We first investigate the quantitative ramifications of the waves in a two-dimensional box in the GSM yz cross section of the magnetotail. The model is constructed to allow the study of radiation of substorm wave energy into the solar wind and also encompasses the essential elements of resonant interaction in the plasma sheet boundary layer. The natural boundary condition leading to radiative loss is introduced. It is found that wave radiation into the solar wind can relax the magnetospheric system in less than a hour. The resonant Alfven modes driven by the normal compressional modes in the box are studied through the construction of proper dispersion equation. By studying the field-aligned current generated by resonances, we establish the auroral pattern expected to result from the coupling. Following the theoretical study, we examine an auroral substorm observed by the CANOPUS photometer array on February 20, 1990. It is found that, among the testable theoretical predictions, there exists a general agreement with the observations. We did find, however, that electron- and proton-induced aurora oscillate essentially in phase, thus implying a more complicated precipitation process.

Nonlinear Alfvén waves

Abstract: Some important nonlinear effects involving Alfven waves in plasmas are presented For illustrative purposes, we start with small amplitude Alfven waves and their relation with other low-frequency plasma modes We then show that Alfven and magnetosonic waves can be nonlinearly excited by a high-frequency external pump wave Finite-amplitude Alfven waves can either interact with the background plasma or with themselves, giving rise to a number of nonlinear phenomena such as wave- amplitude modulation or filamentation, density profile modification, as well as self-organization in vortical structures The nonlinear effects that are described here are of relevance to the large-amplitude disturbances which are frequently observed in laboratory and space plasmas

Reflection and refraction of longitudinal wave at an interface between two micropolar elastic solids in welded contact

Abstract: The problem of reflection and refraction of a longitudinal wave at an interface between two micropolar elastic solids is discussed. Amplitude ratios and energy ratios for various reflected and refracted waves have been obtained for a longitudinal wave impinging obliquely at a plane discontinuity of two linear micropolar elastic solids in welded contact. Numerical values of the amplitude ratios and energy ratios have been computed as a function of angle of emergence of the wave, for a specific model, and these have also been plotted graphically. Amplitude ratios as a function of frequency have also been computed and exhibited graphically. The results of Parfitt and Eringen [J. Acoust. Soc. Am. 45, 1258–1272 (1969)] have been derived as a special case. Some other special cases are discussed.