Propagation of high-frequency harmonic elastic waves from an axially symmetric cavity

An asymptotic ray method is developed for studying propagation of high-frequency harmonic elastic waves from a smooth, convex, axially symmetric cavity. The dynamic stresses near a prolate spheroidal cavity, to whose surface is applied a normal, angle-independent load, are investigated as a specific numerical example. It is shown that account of three terms of the ray series makes it possible to find quite accurate solutions even when the wave length is comparable with the cavity sizes.Translated from Teorr eticheskaya i Prikladnaya Mekhanika, No. 18, pp. 87–95, 1987.     

Reflection of harmonic elastic waves from a convex cylindrical cavity of arbitrary section

We describe an approach to the solution of problems of reflection of harmonic elastic waves from a convex indrical cavity of arbitrary section, on the basis of Debye ray, series. We obtain a system of linear algebraic equations to determine the constants of integration and expressions for determining the stresses in the elastic medium surrounding the convex cylindrical cavity. We give the results of computation of the stresses that arise as a result of the action of a planar harmonic rarefaction wave on a cylindrical cavity in the shape of elliptic and parabolic cylinders and on a cylindrical cavity whose section is a Munger oval. Four figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 10–16, 1991.     

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.Received: December 12, 2001     

Diffraction of sound waves by a rigid cylindrical cavity of finite length with an internal impedance surface

A rigorous solution is presented for the problem of diffraction of plane harmonic sound waves by a cavity formed by a terminated rigid cylindrical waveguide of finite length whose interior surface is lined by an acoustically absorbent material. The solution is obtained by a modification of the Wiener-Hopf technique and involve an infinite series of unknowns, which are determined from an infinite system of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem and their effects on the diffraction phenomenon are shown graphically.     

Scattering of plane harmonic waves on a cylindrical cavity with an elliptical cross section in an orthotropic medium

The diffraction of a plane longitudinal harmonic wave on a cavity with a smooth curvilinear cross section in a rectilinearly orthotropic medium is solved by using small perturbations in the elastic moduli and introducing generalized wave potentials. Results are presented from a numerical analysis of the dynamic stresses in the near diffraction field and at the boundary of an elliptical cavity including variations in the relative incident wavelength, eccentricity of the cavity, and degree of anisotropy of the medium. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 102–110, 1999.     

Propagation of torsional waves in a circular elastic rod

Zusammenfassung Das Problem eines unendlichen kreiszylindrischen Halbstabes, dessen Endquerschnitt mit beliebigen Torsionsspannungen belastet ist, wird auf Grund der strengen dreidimensionalen Elastizitätstheorie gelöst. Die Lösungsmethode besteht aus einer Integraltransformationstechnik mit asymptotischer Inversion für eine frequenzmodulierte Stufenfunktion. Die Ergebnisse zeigen, dass die Gültigkeit eines «dynamischen Saint-Venant-Prinzips» von der betreffenden Frequenzkomponente abhängt.

---

---

This work was initiated while the author was still employed by the IBM Corp. at Endicott, New York.     

Reflection of a harmonic elastic wave from a convex axisymmetric cavity

An approach based on Debye ray series is proposed to solving the problem of reflection of harmonic elastic waves from a convex axisymmetric cavity. Numerical results are reported for the stresses that arise when a plane harmonic pressure wave hits a flattened spheroidal cavity.Institute of Mechanics of the Ukrainian Academy of Sciences. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 60–68, 1989.     

Propagation of elastic waves in certain composites

Conclusions 1. Relationships have been obtained for determining nine elastic characteristics of orthotropic composite materials from the properties of the starting components and the assigned reinforcement scheme.2. Formulas are given for calculating the propagation velocity of three types of elastic flat waves for an arbitrary direction in one of the planes of elastic symmetry of a uniform orthotropic material.3. It has been shown that the velocity of the first arrival of a packet of ultrasonic vibrations which is recorded in an experiment is equal to the velocity of motion of the wave front in a limitless medium even for rather thin (5–10 mm) fiberglass-plastic specimens with unidirectional or cross-reinforced schemes.4. The dependences of elastic properties and rates of propagation of elastic vibrations on direction which are calculated theoretically from the properties of the starting components and the reinforcement scheme agree satisfactorily with experimental results.Translated from Mekhanika Polimerov, No. 3, pp. 531–536, May–June, 1978.     

Propagation of waves from spherical and cylindrical cavities

Résumé L'auteur examine la propagation des ondes d'une cavité sphérique ou cylindrique dans une substance avec une isotropie transversale et curviligne. Il traite d'une manière assez détaillée le cas particulier d'un solide infini dans lequel existe un trou sphérique ou cylindrique, et les résultats numériques sont donnés sous une forme graphique pour le trou cylindrique avec un démarrage à fonction type unitaire.     

Propagation of cylindrical blast waves in magneto-gas dynamics

Résumé Nous obtenons, dans cet article, des solutions sous forme finie, pour une explosion en ligne dans un milieu ou la pression, la densité et le champ magnétique axial sont des constantes. La surface de choc, cylindrique, se déplace vers l'extérieur, a travers le gaz au repos, et l'énergie totale de l'onde n'est pas constante, mais varie lentement avec le temps.     

Propagation of weakly guided waves in a Kerr nonlinear medium using a perturbation approach

The equations are represented in a simplified format with only a few leading terms needed in the expansion. The set of equations are then solved numerically using vector finite element method. To validate our algorithm, we analyzed a two-dimensional rectangular waveguide consisting of a linear core and nonlinear identical cladding. The exact nonlinear solutions for three different modes of propagations, TE0, TE1, and TE2 modes are generated and compared with the computed solutions. Next, we investigate the effect of a more intense monochromatic field on the propagation of a “weak” optical field in a fully three-dimensional cylindrical waveguide.     

Torsional oscillations of a circular stamp on an elastic layer with a cylindrical cavity

The problem of torsional oscillations of a stamp that is linked with an elastic stratum which contains a cylindrical cavity is considered. The problem is formulated in the form of conjugate integral equations that are related to the integral Weber transforms. The conjugate equations are reduced to an equivalent Fredholm equation of the second kind.Translated from Dinamicheskie Sistemy, No. 9, pp. 54–59, 1990.     

Vertical oscillations of a circular die on an elastic half-space with a cylindrical cavity

The problem on vertical oscillations of a circular die with a plane base that freely lies on an elastic half-space and contains a cylindrical cavity, whose axis is perpendicular to the plane of the base of the die and passes through its center, is considered. The problem is formulated in the form of paired integral equations that are related to integral Weber transforms. The paired equations are reduced to an equivalent Fredholm equation of the second kind. Some results of numerical calculations of amplitude-frequency characteristics of oscillations of the die are given. A comparative analysis with a known solution of an analogous problem for a continuous elastic half-space is given.Translated from Dinamicheskie Sistemy, No. 8, pp. 30–36, 1989.     

Propagation of shear waves in a semi-infinite elastic waveguide with a local constriction

A procedure is proposed for computing longitudinal-shear stresses and displacements in a semi-infinite waveguide with two lateral cutouts. Numerical results are reported for the stresses on the cutout contours and for the transmission coefficient of the elastic wave.Sumy Branch, Khar'kov Polytechnical Institute. Translated from Dinamicheskie Sistemy, No. 10, pp. 14–20, 1992.     

Vertical oscillations of multimass system on elastic half space with a cylindrical cavity

A problem on oscillations of a multimass system (MS) is considered on an elastic half space with a cylindrical cavity. Equations of motions of an MS are given, which are modeled by masses that are connected by springs and dampers. A motion of the half space with a cavity is characterized by a transmitting function,which is known from a solution of a contact problem with vertical oscillations of a die on the half space given. The conditions of interrelation of the MS with the base close the system of algebraic linear equations for determining amplitudes of oscillations of each element of the MS. Translated from Dinamicheskie Sistemy, No. 7, pp. 13–18, 1988.     

Propagation of Scholte-Gogoladze surface waves along a curved fluid-solid interface

A high-frequency ray theory is presented for a type of small-amplitude waves (termed Scholte-Gogoladze waves), localized in a thin layer around an interface between elastic and fluid domains. The interface is assumed to be smooth, with typical radii of curvature much larger than the excitation wavelength. The technique employed in the paper is based on a boundary-layer version of the classical WKB-expansion (see V. M. Babich and N. Ya. Kirpichnikova, The Boundary-Layer Method in Diffraction Problems (Springer, Berlin 1979)). Bibliography: 20 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 229–246.     

A semi-analytical method of solving problems of the high-frequency diffraction of elastic waves by cracks

A semi-analytical approach is proposed for constructing an effective solution of the problem of high-frequency diffraction of elastic waves by a crack in an isotropic plane. It essentially consists of separating the strongly oscillating solution of the main integral equation of the problem, which holds uniformly over the whole crack length for high oscillation frequencies. The solution is sought in the form of the product of a strongly oscillating function, corresponding to the qualitative behaviour of the solution, and a certain slowly varying unknown modulating function, which also becomes the main unknown in the initial equation. It is shown that, to find this new unknown function correctly, it is sufficient to take an order of magnitude smaller number of collocation points than for the direct approach.