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An integral-equation, successive- substitution solution for the propagation of strain waves in a linear elastic material, developed in an earlier paper, is here extended to non-linear materials without creep (time- independent materials). A PREVIOUSLY-PUBLISHED PROBLEM, BASED ON EXPERIMENTAL DATA FOR NYLON STRING IS SOLVED BY THE SUCCESSIVE-SUBSTITUTION METHOD AND COMPARED WITH THE EARLIER SOLUTION OBTAINED BY THE METHOD OF CHARACTERISTICS. The agreement of the two solutions is at first good, but in the region where the stress- strain curve of the nylon is concave upward a tendency to oscillation builds up and the solution eventually oscillates. This occurs in approximately the same region where shock waves can appear in a method-of- characteristics solution. Oscillations in the strained portion of a string are examined theoretically and it is shown that the energy of standing waves can be used to obtain energy conservation. Although the successive-substitution method generates oscillations when it has to deal with a discontinuity in strain, the possibility that oscillations also actually exist as a means of conserving energy cannot be ruled out., See also AD682714.

Edited trans. of mono. Fizicheskie Svoyatva Gornykh Porod pri Vysokikh Termodinamicheskikh Parametrakh, n.p., 1971 p7-10.

Decoupling explosive energy by detonating charges in cavities larger than the charge is an effective method for reducing ground shock magnitudes over those of fully contained bursts. The report presents an analysis of ground motions generated by decoupled explosions in rock cavities. A simplified elastic solution is used to calculate particle motion magnitudes and time histories produced by an explosion in rock as a function of the initial cavity radius and the loading density of the explosive. Loading density is defined as the total explosive weight divided by the initial cavity volume. (Modified author abstract)

This paper deals with the problem of propagation of shear (or compression) waves in a plane-parallel layer of finite thickness. The waves are excited by an instantaneous displacement of the points of the lower plane, allowing for multiple reflections of the fronts from both boundaries of the layer. The layer material obeys the laws of linear viscoelasticity (the Kelvin-Voigt and Maxwell models). Exact expressions for displacements of the particles of the medium are derived. The paper investigates stationary vibrations of the layer, allowing for changes in the physicomechanical properties in thickness (inhomogeneous medium), and determines the resonance frequencies., Edited trans. of Prikladnaya Matematika i Programmirovanie (USSR) n3 p70-78 1970.

This report contains three principal sections corresponding to Tasks I, II, and III outlined in Proposal No. 18-R72, 6 September 1972. Section 1 is addressed to the conceptual aspects of using bubble devices for data processing which includes logic and memory. During the reporting period a specific requirement, data processing for space satellite attitude control, was chosen as a model for defining the necessary attributes for a bubble data processor. These attributes appear to be consistent with our analysis of the potential capabilities of bubble devices in terms of size, weight, power and data rate. The model suggests some specific logic requirements which will be translated into device hardware in the remaining months of the contract. Section 11 treats the hybrid technologies, bubble/optical guided wave interactions and bubble/elastic wave interactions. This work is behind schedule with regard to experimentation, but the conceptual aspects are well advanced. Several device concepts are presented in the report. Key to the success of these hybrid technologies are the strengths of the interactions. These interactions will be studied during the next reporting period. The results will determine whether or not to proceed to develop either hybrid technology under Task 111. Section 111 of the report deals with progress on ion-implant devices and Permalloy circuits for submicrometer diameter bubbles (small-bubbles). The small-bubble work is behind schedule, but progress is being made. Progress on ion-implant circuits has not been as rapid as initial results on the early devices would have indicated.

A suitably stratified ocean bottom will propagate a Love wave. If an object lies on the bottom, or even is buried in it, Love waves incident upon it will be scattered. Some of these are coupled to the water. A hydrophone towed in the sea can thus localize the position of the object. A need exists for a method of making an accurate determination of the shear modulus of the sea bottom. A procedure is demonstrated with a two layer laboratory model.

Differential equations of the propagation of cylindrical waves are obtained taking into account the change of volume and form in a nonlinear elastic medium. The fundamental equations for compressible and incompressible materials are found, taking into account small physical nonlinearity. The fundamental equations of the propagation of spherical waves in a nonlinear elastic medium are determined for small physical nonlinearity, which is characterized by the square of deformation intensity., Edited machine trans. of Rasprostranenie Uprugikh i Uprugo-Plasticheskikh Voln (3rd), n.p., n.d. Trudy (Transactions of the All-Union Symposium (3rd), n.p., n.d. Proceedings), Moscow, 1969 p149-162, by James R. Moore.

The application of laboratory data on velocities of elastic waves in interpreting seismographic material imposes distinct requirements for experimental work. It is important to know not only the simultaneous effect of comprehensive pressure on elastic wave velocity, but also the effect of the extended interstitial area. Such investigations have been undertaken for low-porous crystalline rock. It was established that filling the interstitial areas with liquid greatly affected longitudinal wave velocity in this type of rock; the greater the length of the rimiform porosity, the greater the effect., Edited trans. of Fizicheskie Svoistva Gornykh Porod pri Vysokikh Termodinamicheskikh Parametrakh (3rd) n.p. 11-16 Oct 71. Material, Kiev, 1971 p48-51.

The is a comprehensive report on the theoretical and experimental performance of devices using elastic surface waves in layered structures. The following are the main achievements of this effort: (1) Space charge coupled convolvers and correlators using surface waves and layer waves; experimental demonstration of lowest insertion loss, a few orders of magnitude lower than the previous state-of-the-art devices; and development of a detailed theory. (2) A new technique for optical probing of surface waves and layer waves: experimental determination of the decay parameter of a surface wave in the direction normal to the propagation surface; and the complete elastic fields in the layer wave structure; demonstration of 25% diffraction efficiency for each first order with only 500 mw of electrical power driving the surface wave transducers. Other important contributions in this report are the theoretical analysis of the layer wave propagation including loss or gain, and the observation of streaming phenomena in a liquid layer due to layer waves. (Author)

The purpose of this grant was to investigate some of the effects of anisotropy and inhomogeneity on the propagation of seismic waves by theoretical analysis and comparison with seismograms from the Antarctic ice sheet. Four specific topics were considered: (1) reflection coefficients at an isotropic-anisotropic boundary, (2) surface wave propagation in the presence of a strong velocity gradient, (3) conversion between body wave types upon total internal reflection, that is at the turning point of a refracted arrival, and (4) the continuous bodily conversion of P waves into shear waves in the course of propagation through a strong velocity gradient.

Edited machine trans. of Vsesoyuznogo Simposiuma po Rasprostraneniyu Uprugo-Plasticheskikh Voln v Sploshnykh Sredakh, n.p., n.d. Paper, n.p., 1966 p332-346, by John A. Miller.

The paper discusses research on the applicability of nonclassical equations of the dynamics of a cylindrical shell, obtained by use of the exponential series method, to the study of short-wave processes in a shell. Shell theory equations are given. (Author), Trans. from Prikladnaya Mekhanika (USSR) v6 n10 1970.

The study was initiated to determine the influence of an underlying rock interface on the response of buried cylinders to blast loading. Static and dynamic tests were conducted on eight different 6-inch-diameter steel cylinders buried horizontally in a dense, dry sand. The major variables were the cylinder thickness and the location concrete bottom. Measurements were made of hoop strain, vertical diameter changes, and accelerations of the cylinder; free-field stress, strain, and acceleration of the soil; and surface overpressure. (Modified author abstract), Report on Support of Project Sanguine.

The similarities and differences between acoustic and magnetic surface waves as compared with light waves are discussed. This comparison suggests several advantages of surface wave ring interferometers over optical ring interferometers for rotation sensing. The primary advantages are increased sensitivity, ease of construction, and size reduction. Proposed designs for such sensors are given. In the appendixes the optical ring interferometer and ring laser are reviewed. (Author)

Edited trans. of Bulgarska Akademiya na Naukite, Sofia. Geofizichen Institut. Izvestiya, v12 n131-137 1968.

Nonlinear electroelastic equations, quadratic in the small field variables, are applied in the analysis of second harmonic generation of surface waves in piezoelectric solids. Preliminary to the treatment of the anisotropic piezoelectric case, the more tractable problems of the second harmonic generation and parametric excitation of surface waves in isotropic elastic solids are treated. In all instances the solutions asymptotically satisfy the nonlinear differential equations and boundary conditions on the surface of the semi-infinite solid to a specified order in a small parameter. Since the equations are quadratic, rather than cubic, in the small field variables, only the initial spatial rates of growth of the harmonically generated and parametrically excited waves are determined. Nevertheless, an extension of the analysis to enable the calculation of more than the aforementioned initial slopes is indicated. In the isotropic elastic case the solution for the second harmonic reveals, among other things, that the ratio of the dilatational to equivoluminal portions of the growing second harmonic is the same as in the input Rayleigh wave. (Author)

It is evident that a detonation, in particular in compressible soils, casuses the formation both of straight, longitudinal (circumferential) and surface waves of various types (this article is concerned with surface waves of a topographical type). The experimental part investigated was performed at the experimental detonation base of the Academy of Sciences of the Ukrainian SSR in loamy soils with a volumetric charge of 1.9 g/sq cm and with natural moisture of 22-25% using a seismic apparatus (the detectors VBP-III, VIB-A, VEGIK, and the N-700 oscillographs)., Edited trans. of Akademiya Nauk URSR, Kiev. Dopovidi. Seriya B: Geologiya, Geofizyka, Khimiya ta Biologiya, n4 p344-347 1972.

Representations are derived that describe the interactions of the waves that are reflected from both perfectly rigid and perfectly free interfaces during the arrival of a centered wave with any wave traveling in the opposite direction. These are used to analyze the early stages of the deformation produced when the traction at the loaded boundary continues to vary after changing discontinuously. (Author-PL), See also AD-767 264.

14 Jun 72,FHolland,Melvin G. ;Willingham,Charles B. ;Matsinger,John H. ;S-1487F30602-72-C-0044RADCTR-72-291(*delay lines, piezoelectric crystals), (*piezoelectric transducers, design), semiconductor devices, substrates, silicon, ultrasonic radiation, attenuation, zinc compounds, oxideszinc oxides, *acoustic waves, *surface waves, piezoelectric materials, semiconductors, surface waves, elastic wavesThe program was to study and characterize an acoustic surface wave, multiple-tap, delay line structure using sputtered zinc oxide (ZnO) overlay piezoelectric films on metal interdigital arrays, on a silicon surface. The tasks included investigation of surface acoustic wave generation techniques as well as the study of surface wave propagation on the ZnO/Si surface. The structures were used to prepare a sequence generator and its reciprocal matched filter to experimentally demonstrate the generation and correlation of a biphase sequence.

The specific viscosity, and its dependence on velocity gradient, plays an important role in studies of the structure of macromolecules in dilute solution. A satisfactory theoretical interpretation of the non-Newtonian viscosity of solutions of ellipsoidal particles has been given by Kuhn and Kuhn, and also by Saito, who made use of Peterlin's distribution function for the orientation of particle axes in the streaming liquid and calculated the energy dissipation due to both the hydrodynamic orientation and the Brownian motion. Also, a theory for the non-Newtonian viscosity of solutions of rod-like particles has been developed by Kirkwood. These theories involve extensive computations which have been carried out here with the aid of a computing machine by expressing Saito's results in terms of Legendre coefficients previously evaluated in the related problem of double refraction of flow. As a result, data are available for the dependence of the viscosity factor nu on axial ratio and on the parameter alpha, where alpha = G/Theta, G being the velocity gradient in sec (exp -1). With these data it will be possible to determine the rotary diffusion constants of ellipsoidal particles from the non-Newtonian viscosity of their solutions, and also to correct viscosity measurements to zero velocity gradient in order to obtain the intrinsic viscosity. Data are also included for the evaluation of Theta from the dependence of nu at alpha = 0 on the frequency of periodic shear waves., Published in The Journal of Chemical Physics, v23 n8 p1526-1532, Aug 1955.

The interaction of plane elastic waves with a thin, hollow, cylindrical shell embedded in an elastic medium are investigated. The cylindrical shell is considered to be elastic, isotropic, homogeneous, and of infinite length. It is surrounded by an elastic, isotropic, and homogeneous medium whose motions conform to the ordinary theory of elasticity. A plane stress wave, either dilatational or shear, with a step variation in time, whose wave front travels in a direction perpendicular to the cylinder axis, envelops the shell. Later, a Duhamel integral is used to study other wave shapes for the incident stress.

A simplified theory, taking into account the effects of lateral or radial inertia, is described for the study of the propagation of elastic-plastic waves in a slender rod. This approximate theory, which is developed through an approach similar to that used by Hermann and Mindlin in their study of elastic- wave propagation, yielded results that show qualitative agreement with some preliminary BRL experimental observations and with other past theoretical and experimental results.

A theoretical and experimental study is described for the optical birefringence associated with the propagation of a plane shear wave in a viscoelastic medium. The shear wave propagation is characterized by a complex propagation constant from which the complex coefficient of shear viscosity of the medium may be derived. The optical bire fringence is related to the mechanical action of the shear wave by a complex mechano-optic coefficient. In the experiment the birefringence due to the shear wave is analyzed by transmitting circularly polarized light through the material at right angles to the direction of shear wave propagation and to the direction of particle displacement. The modified circularly polarized light is then analyzed by a plane analyzer and a photomultiplier detector. The mechanical and mechano-optic constants for the medium are determined for an aqueous milling yellow solution and for a polystyrene solution and are compared with independent determinations of these same factors from other experiments.

The report discusses the relationships between shock waves in plastic and elastic media with a barrier made from a non-deformable material., Edited trans. of Vsesoyuznogo Simpoziuma po Rasprostraneniyu Uprugo-Plasticheskikh Voln v Sploshnykh Sredakh, n.d., n.p. Materialy (All-Union Symposium on the Propagation of Elastic-Plastic Waves in Continuous Media, n.c., n.p. Materials), Baku, 1966 p245-257, by John Sechovicz.

The objective of the present study is to establish thermodynamically valid, non-isothermal stress strain relations for the elastic-plastic range, and to obtain solutions of typical one-dimensional problems involving unsteady temperatures. In the entropy balance equation and the expression for production of internal entropy are consider the limitations imposed by the second law of thermo dynamics upon plastic flow rules are investigated, and subsequently a set of non-isothermal plastic stress strain relations is introduced. It is then shown that these relations are in accord with thermodynamic irreversibility whenever the yield criteria of Tresca and von Mises are used. More over, it is found that the stress strain relations of von Mises are a special case of the non-isothermal stress relations proposed here. An additional problem concerns the specification of elastic tic unloading from a plastic state, and in the presence of a temperature dependent yield stress. Precise criteria for elastic loading and repeated plastic flow are presented. Part II of the report is concerned with an application of the general theory to a problem for the infinite half-space constrained against lateral motion, and subjected to a heat pulse uniformly applied over its boundary. In the analysis of this problem the yield criterion of Tresca is used; the transient and steady state solutions for both strain-hardening and perfectly plastic media, having either a constant or a temperature dependent yield stress, are presented. The appearance of elastic and plastic regions of loading and unloading is studied in some detail.

The asymptotic approximation method was applied to the calculation of normal modes of elastic waves in a solid medium. The approximations were based on the assumption that the properties of the medium are slowly varying functions of one coordinate in the sense of a small relative variation within a wave length. A comparison of dispersion curves computed by the approximate theory with those computed by the exact theory for a medium of 2 or 3 homogeneous layers indicated that the approximate theory is fairly accurate for normal modes of higher order than the fifth or sixth. The approximation for the lower modes is considered of some value for rough estimations, provided the approximations are used in conjunction with the limiting forms of the exact theory.

See also Volume 5, Number 18, AD-A040 411.

Formal progressing wave expansions are applied to problems involving one-dimensional wave propagation through inhomogenous elastic media. Expansions for the stress and particle velocity are obtained in addition to the expansion for the particle displacement which is a special case of previous results. Although one-dimensional problems could be solved with the previously reported asymptotic methods, it is more convenient to use the expansion in terms of the stresses to evaluate the expansion coefficients. The procedure is illustrated by solving several problems in layered and nonlayered inhomogeneous media where the compressional wave speed is subject to power and exponential variations with distance. (Author)

The pulse technique is the most frequently used laboratory method for measuring the speed of compressional (and shear) elastic waves in rock, sediment, and other samples. The method became easily possible during and after World War II because of developments in electronics, especially in pulse circuitry and oscilloscopes.

An interesting application of surface waves is in the field of underwater acoustic wave launchers and receivers. Present day acoustic antennas depend upon (excepting linear arrays) their cross sectional dimension to control the beam pattern. To obtain a narrow pattern a large cross section (in terms of wavelength) is necessary. In a surface wave antenna the length of the radiator rather than the cross section is of primary importance in the production of a large directivity index. But before any worthwhile radiator can be designed, information concerning the transmission of surface wave energy between media must be available. This paper deals with this question of surface wave transmission specializing in the field of launching underwater acoustic energy. Included will be a discussion of the mathematics of surface waves associated with boundaries between a solid and a vacuum, and a solid and a liquid. A description is given of the experimental setup and the resulting beam patterns obtained from surface waves launched from metallic rectangular bars will be shown.

Trans. of Skhodyashohayasya Volna v Plasticheskoy Srede (Convergent Wave in a Plastic Medium), and Doklady Akademii Nauk SSSR (Proc. Academic Science USSR),(Russia), v131 n4 p769-772, 1965.

To date a number of works have been devoted to the dynamics of two-component media; for example, Ya. I. Frenkel' I), Kh. A. Rakhmatulin 2, Biot 3,4, and Zwicker and Gostain.5, However, the basic problem regarding the construction of equations of motion of two-component media has still-not ultimately been solved but requires additional study and experimental checking. Below we shall examine the simplest case of movement propagation of elastic waves in a homogeneous isotropic medium, consisting of solid and liquid components. The problems of the reflection of plastic waves and of surface waves on the free boundary of a semi-space were solved. It was shown that the relationship between stresses and deformations established by Ya. I. Frenkel' is equivalent to a similar relationship established by M. A. Biot, while the equations of motion of the latter are the more common., Trans. of Prikladnaya matematika i mekhanika (Applied Mathematics and Mechanics) v23 n6 p1115-1123, 1959.

Measurements of the propagation velocity of elastic waves in loose sea deposits is discussed., Trans. of Izvestiya Akademii Nauk SSSR (News of the Academy of Sciences USSR), Geophysical Series, n11 p1699-1701, 1959.

Supersedes AD-A120 199.

Supersedes AD-145 005.

Supersedes AD-16 319.

The properties of elastic wave propagation in thin truncated conical shells were studied. Theoretical results were compared with experimental data obtained by impacting a truncated shell with a steel ball. The method of solving the equations yielded continuous waveforms which could be compared directly with strain gage data. The general simultaneous equations for the conical shell were obtained and reduced to a single equation with longitudinal displacement as the unknown. Singularities were analyzed for physical meaning and simplifications were made by considering the low and high frequency ranges separately. Dependence on the conical angle and Poisson's ratio was not lost. The simplified equations were identified as special cases of the multidimensional wave equation, which has been studied previously in other branches of physics. Recognition of the general wave equation led to an investigation of wave propagation in multidimensional (abstract) space. Of the two unique types of solutions known to be available, the solution for radiating waves was found to be applicable and compared favorably with the experimental data. (Author)

The report supplements the previous phase report covering response energy summation analysis for a rigidly-connected coulomb damped elastic structure model, when subjected to all controlled patterns of sinusoidal vibration. Specimen curve evaluations for extended parameter ranges are facilitated by the use of computer plotting programs. (Author), Supplement to Rept. no. NADC-72185-AD dated 2 Feb 73.

Using a linear formulation, the author solves the non-stationary problem of transmission of a planar unidimensional longitudinal wave of stresses through a plane-parallel visco-elastic layer of finite thickness separating two linearly elastic half-spaces with different properties. The plane wave propagating in one of the elastic half-spaces strikes the layer boundary at right angles (unidimensional problem). The field in the other elastic half-space, excited as a result of multiple reflection of the fronts from the boundaries of the layer, is studied. Graphs of small displacements at a given point of elastic half-space are given., Trans. of Mekhanika Polimerov (USSR) n7 p151-156 Jan/Feb 71.

Contents: Linear problems of wave dynamics of isotropic deformable bodies; Representation of the solution of a wave equation in certain coordinate systems; Diffraction of waves in bodies limited by circular cylindrical surfaces; Wave diffraction in bodies with spherical cavities; Solution to problems of the diffraction of elastic waves on cylindrical surfaces; Wave diffraction in semi-bounded bodies with cavities; Principles of the theory of wave propagation in fibrous and granular media., Edited machine trans. of mono. Difraktsiya Uprugikh Voln v Mnogosvyaznykh Telakh, n.p., 1972 p1-256, by Robert D. Hill.

The paper continues the investigation of large amplitude waves in bounded media started by H. M. Cekirge and E. Varley (1973). It describes the early stages of the deformation produced in an elastic slab contained between two parallel, plane interfaces when the normal traction at one of them changes discontinuously. During the subsequent deformation energy is radiated across these interfaces to adjacent elastic materials. The disturbance in the slab could be caused by the arrival of a constant strength shock wave traveling through an adjacent material or when the slab, which forms part of a composite material, impacts some other elastic material. It is assumed that the dynamic response of the slab can be approximated by that of one of the model materials introduced in the first part of this study. It is shown that this is possible for a whole host of materials. These include polycrystalline solids, metals when subjected to high pressure, water, explosive products, gases and yarns as well as elastic-plastic, rigid-plastic and rigid-elastic materials. (Modified author abstract), See also report dated May 72, AD-746 642.

An analysis is presented for linear elastic wave propagation normal to the laminations of a periodically laminated porous composite. The porosity is randomly distributed throughout one constituent and is composed of small spherical voids. This type of porosity is called randomly periodic and produces Rayleigh scattering where the wavelength of the incident wave is much larger than the void diameter. Porosity also reduces the wave speed in a constituent and thereby affects geometric dispersion. A DISSIPATIVE EQUATION OF MOTION IS DEVELOPED FOR POROUS MATERIAL THAT INCLUDES A POROSITY-DEPENDENT WAVE SPEED AND A SCATTERING TERM THAT PROVIDES SPATIAL ATTENUATION. This equation is then used for a constituent of a composite, and a dispersion relation and pulse solution are obtained to determine the significance of porosity in a laminated composite. It is concluded that Rayleigh scattering produces a small damping effect in far-field pulse shapes and small-void porosity can be adequately simulated with an effective wave speed. (Author-PL)