Showing papers on "Lamb waves published in 1971"

Nonlinear waves in the pitaevskii--gross equation.

Abstract: Nonlinear waves, solitary and periodic, are studied exactly in the Pitaevskii-Gross equation for the wave function of the condensate of a superfluid. We also study the relationship between these two waves and Bogoliubov's phonon, and the energies associated with these waves. The creation energy of a solitary wave with amplitudeA is proportional toA3/2. Solitary waves show interesting behavior on their collision due to their localized character. The effect of collision on solitary waves can be described by the phase shift. We give a formula of the phase shift on a collision of two solitary waves. We further discuss the decay of an arbitrary initial disturbance into solitary waves.

Thermoelastic waves in solids with thermal relaxation

Abstract: Maxwell's modified heat conduction equation is used to study plane harmonic waves in unbounded media as well as Rayleigh's surface waves propagating along a half-space consisting of linearly elastic materials that conduct heat. Explicit expressions are obtained for various parameters that characterize these waves. Relevant results of previous investigations are deduced as special cases.

Transmission and Reflection of Plane Waves at an Elastic-Viscoelastic Interface

Abstract: Summary The reflected and transmitted waves due to an elastic plane sinusoidal P or SV wave impinging on the plane interface between an elastic and a linearly viscoelastic medium are found analytically for any type of viscoelastic behaviour. The properties of these waves depend both on the frequency of the incident wave and the angle of incidence of the impinging wave. Some general properties of the transmitted waves are that both the dilatational and equivoluminal waves in the viscoelastic media have refraction angles less than 90°, the displacement trajectories of material points in the viscoelastic media are ellipses, and the waves attenuate with increasing distance from the interface.

Propagation of Harmonic Waves in a Composite Elastic Cylinder

Abstract: In this paper, the propagation of harmonic waves with an arbitrary number of circumferential nodes in an infinitely long two‐layered composite circular elastic rod is investigated. The composite rod is made of a circular solid rod encased by a circular shell having different material properties. The frequency equation derived on the basis of the three‐dimensional linear isotropic elastic theory is presented. The reduction of this equation to the frequency equations for some special problems, such as longitudinal wave propagations, torsional wave propagations, flexural wave propagations, axial‐shear vibrations, and plane‐strain vibrations is discussed. Simplified equations for phase velocities of longitudinal and torsional waves at very long wavelength are obtained. Numerical results, in terms of frequency and real wavenumber, are given for a composite rod made of a soft core with a stiff casing.

A Technique for Precision Measurements of Elastic Surface Wave Properties on Arbitrary Materials

Abstract: A technique is described for determining both the elastic surfce wave velocity and its temperature coefficient. The technique can be used on very small samples and is not restricted to any particular class of materials, such as piezoelectrics. It employs an adaptation of the old method of acoustic wave generation with a dc pulse rather than an rf signal applied to a piezoelectric transducer. The generator and receiver transducers are very small chips, approximating point sources, and at the receiver the vertical component of particle velocity is measured as a function of time enabling one to distinguish clearly between various types of surface modes, e.g., Rayleigh wave, pseudosurface wave, Lamb wave, etc. The technique yields absolute surface wave velocities accurate to 0.2% and is readily adaptable to the use of the sing‐around technique for measuring relative changes in the sound velocity as small as 1 ppm.

Surface waves in magneto-elastic initially stressed conducting media

Abstract: The object of the present paper is to investigate the magneto-elastic surface waves in an initially stressed conducting medium. The theory of magneto-elastic surface waves in an initially stressed conducting medium has firstly been deduced and then it has been employed in investigating the particular cases of surface waves such as (i) Rayleigh waves (ii) Love waves and (iii) Stoneley waves. The wave-velocity equations obtained in different cases are in agreement with the corresponding classical results when the solid is initially unstressed and the magnetic field is absent or the material is non-magnetic.

Erratum: Signal Generation via Nonlinear Interaction of Oppositely Directed Sonic Waves in Piezoelectric Semiconductors

Abstract: When an ultrasonic wave propagates in a properly oriented piezoelectric semiconductor, it gives rise to both an electric field wave and a space‐charge wave. The rf signal developed across the crystal by the propagating wave is quite small. However, if one launches ultrasonic waves from the opposite ends of a properly oriented piezoelectric crystal so that the two waves travel toward each other, when the two waves meet, a rf signal of large amplitude, twice the frequency of the ultrasonic wave, will be developed across the crystal and the envelope (time function) of the double‐frequency rf signal represents the convolution integral between the two envelopes of the ultrasonic waves which were launched into the crystal from the opposite ends.

Wave propagation in two layered medium under initial stresses

Abstract: In this paper, the frequency equation for phase velocity of waves propagated in a laminated medium consisting of two eleastic layers of finite thickness under initial stresses, has been obtained. It has been shown that when wave length becomes very small compared to the thickness of each layer, the wave approaches two Rayleigh waves at the two outer surfaces with the possibility of Stoneley waves at the interface. The propagation ofSH-waves in the composite medium under initial stresses has also been discussed. A particular case has been taken to find the velocity of Love wave in the homogeneous half space under initial compressive stresses.Biot's incremental deformation theory has been used.

Reflection and Transmission of Rayleigh Waves in a Wedge—II

Abstract: Summary The problem of the reflection and transmission of Rayleigh waves in an elastic wedge discussed in an earlier paper for the case of incidence from infinity is now studied in more detail and for the more general case of an incidence from a finite distance from the corner. A detailed application is made of the effect of the critical regions of Rayleigh waves in Lamb's half-space problem when a series of interactions with the wedge faces are considered. These interactions are two-fold, viz. those due to the inwardly progressing waves and those due to the outwardly receding waves. Both lead to contributions given by certain integral equations. While in the latter case the integral equations behave like the Fredholm equations, in the case of the former the behaviour is like Volterra equations of second kind at lower range of wedge angles and like the Fredholm equations at higher range and there is a mixed character in the intermediate values. These approximations lead to dividing the range of the wedge angle, which we take to be from 0" to 180", into five parts at points depending on the critical angles of Lamb's problem. The solutions in these parts are piecewise continuous. A brief outline of the corner wave effects is also included. The numerical results show that the present theory can explain well some of the important experimental features of the problem that were only partially achieved by previous theories. 1. Introduction In a previous part of this work Viswanathan, Kuo & Lapwood (1971) showed that the problem of the reflection and transmission of Rayleigh waves in an elastic wedge is significantly influenced by the actual regions in which these waves can exist in the more fundamental problem of a half-space with a source usually known as the Lamb's problem. In the above work which we refer to as Part I henceforth, we treated the case when the incident field was from infinity. Moreover, the effects of the critical regions for the existence of Rayleigh waves defined in the context of the Lamb's problem were only partially incorporated while dealing with the interactions with the wedge boundaries. In particular such effects were not applied to the waves that travel towards the corner. The purpose of the present work is to study the more general case when the source of the initial Rayleigh field lies at a finite distance 1 from the corner. Further, we

Determination of the Unloading Boundary in Longitudinal Elastic-Plastic Stress Wave Propagation.

Abstract: : For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod. (Author)

Nonlinear Interaction Between Circularly Polarized Waves and Electron Plasma Waves

Abstract: This paper presents a general analysis of nonlinear three‐wave interaction in a hot magnetoplasma between circularly polarized waves propagating at small angles to the static magnetic field, and electron plasma (Langmuir) waves propagating parallel First, the coupled mode equations are derived by iterative solution of the Vlasov equation Simplified expressions for the coupling coefficients are then obtained for all of the wave combinations for which the frequency and wave number synchronism conditions can be satisfied, and the wave coupling coefficients are nonzero These comprise interactions among three right‐hand polarized waves, two circularly polarized waves and one Langmuir wave, and three Langmuir waves The paper concludes with a brief discussion of the specific cases most likely to be worth subjecting to detailed numerical analysis

Analysis of Ground Wave Propagation in Layered Media.

Abstract: : The propagation of elastic waves in a multilayered geological environment is analyzed based on the theory of generalized-rays and the method of Lamb-Cagniard-Pekeris. The waves are generated by an underground explosion which is approximated by a point source. Velocity responses at receivers at ranges about one to three times the thickness of the source layer are calculated with a new computer code. The results are exact within the framework of the theory of elastic waves. Comparisons of the calculated results with the observations made at the Nevada Test Site in 1966 show considerable discrepencies. (Author)

Surface elastic wave propagation studies in lunar rocks

Abstract: Elastic surface wave amplitude and propagation velocity in lunar rocks, calculating Poisson ratio

Wave Forces On Pile Sections Due To Irregular And Regular Waves

Abstract: Wave action on pile-sections and entire piles has been studied. Twenty-nine waves and ten spectra were generated and the corresponding forces were measured. The obstacle was a single verticle pile with three force-meters located at different levels. For regular waves, most of the results can be justified by use of added mass and drag coefficients values from the Keulegan and Carpenter relationship. For irregular waves, a good fit between measured data and computer values was obtained for spectral analysis (L.E.Borgman method). Orbital velocity measurements are necessary for interpreting full-scale studies.

Propagation and Amplification of Shear‐Horizontal Waves in Piezoelectric Plates

Abstract: Propagation of shear horizontal waves in class C6v piezoelectric plates with polar (or sixfold) axis in the transverse horizontal direction is analyzed for various boundary conditions: faces electrically free, shorted, or coupled to a thin homogeneous semiconductor plate. The case considered is that of identical physical conditions at the opposite faces, which permits the symmetric and antisymmetric waves to be treated independently. Of the above waves, the lowest modes behave as transverse surface waves at high frequencies, and the higher modes retain their oscillatory behavior in the thickness direction. Numerical solutions are obtained for amplification and phase velocity in PZT under different boundary conditions, and it is shown that the phase velocity can also be strongly dependent on the drift velocity of carriers in the semiconductor. The shapes of the dispersion and amplification‐frequency curves are also drift‐dependent, especially in the vicinity of cutoff.

A correspondence for acceleration waves in elastic non-conductors

Abstract: It is shown that Truesdell's theorem on the existence of waves in an inhomogeneous elastic material can be readily carried over to the case of an elastic non-conductor of heat, provided that the isentropic elasticity tensor is strongly elliptic. That is, there is at least one direction in which one longitudinal wave and two transverse waves with orthogonal amplitudes may exist and propagate. Further, if one considers a situation for which the waves are necessarily plane, then one finds that the amplitudes of these waves depend on the mechanical properties of the material alone, independent of its thermal properties. In other words, one would not be able to ascertain the effects of the thermal properties of the material on the behaviour of these waves.