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.     

Energy considerations of plane and cylindrical hydromagnetic variable energy blast waves

Numerical results describing the propagation of plane and cylindrical blast waves with time dependent energy inputs in an ideal gas in presence of an axial magnetic field have been obtained by modified similarity method. These results are in agreement with Patrick's [6] experimental observations of non-existence of ordinary shock waves. For strong shocks the hottest region is located near the piston, whereas for weaker shocks the front becomes the hottest. The presence of magnetic field, however, reduces the temperature in the shocked region, except near the piston where it increases. An increase in magnetic field leads to an increase in shock velocity. Predicted variations of the percentages of magnetic, internal and kinetic energies with shock strength support the experimental observations of Kolb [3]. With increase in, equipartition between kinetic and internal energies is seen to shift towards higher shock strength.

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Zusammenfassung Für die Ausbreitung von ebenen und zylindrischen Stoßwellen mit zeitabhängiger Energiezugabe in einem idealen Gas in Gegenwart eines achsialen Magnetfeldes sind numerische Resultate mit Hilfe einer modifizierten Ähnlichkeitsmethode erhalten worden. Die Ergebnisse sind in Übereinstimmung mit den experimentellen Beobachtungen von Patrick [6] über die Nicht-Existenz von gewöhnlichen Stoßwellen. Für starke Stöße liegt das heißeste Gebiet in der Nähe des Kolbens, bei schwächeren Stößen nahe zur Stoßfront. Die Gegenwart des Magnetfeldes vermindert die Temperatur in der Stoßzone mit Ausnahme der Region in Kolbennähe, wo die Temperatur steigt Erhöhung des Magnetfeldes erhöht die Stoßgeschwindigkeit. Die berechneten Änderungen der Anteile der magnetischen, inneren und kinetischen Energien mit der Stoßstärke unterstützen die Beobachtungen von Kolb [3]. Mit der Zunahme von wird die Gleichverteilung der kinetischen und der inneren Energie gegen höhere Stoßstärken verschoben.

     

On the use of variational methods in steady magneto-gas dynamics

Zusammenfassung Nachdem gezeigt wurde, unter welchen Bedingungen die Ableitung einer Potentialgleichung in der Magnetogasdynamik möglich ist, wird diese diskutiert. Da sie beim Übergang vom unterkritischen in den überkritischen Bereich den Typ ändert, ist das Variationsverfahren die einzige Möglichkeit, eine geschlossene Lösung für beide Bereiche zu erhalten. Es wird das zur Potentialgleichung gehörige Variationsproblem abgeleitet und für die Umströmung eines Zylinders mitk=1,5 gelöst. Die beiden Figuren (Figur 1 im Maßstab 133 und Figur 2 im Maßstab 116,6) stellen die Strömungslinien und die Linien gleicher Mach-Zahl für einen Zylinder mit dem RadiusR=1m bei einem MagnetfeldH=10000 und einer AnströmgeschwindigkeitU=500 m/sec dar.

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The research reported in this paper has been made possible by the support of the United States Government.     

Propagation of shear waves in homogeneous and inhomogeneous fibre-reinforced media on a cylindrical Earth model

The present paper is concerned with the propagation of shear wave in a cylindrical structure comprised of two concentric media by two distinct cases. In first case, media are homogeneous and in second case, media are heterogeneous. The heterogeneities are caused due to the radial variation in both the media distinctly. The dispersion relation for shear wave propagation in homogeneous and heterogeneous, fibre-reinforced media have been derived analytically in the closed form using Debye Asymptotic Expansion and verified with the existing literature and classical results. Numerical computation and graphical demonstration have been carried out to show the remarkable effect of various parameter viz. fibre-reinforcement, heterogeneities and radii ratio of the media on the intensity of frequency of shear wave propagation against the dimensionless wave number. A comparative study between the reinforcement and isotropic material with or without heterogeneity has been discussed extensively and unravel some important peculiarities.     

Propagation of high-frequency harmonic elastic waves excited by surface perturbation of a noncircular cylindrical cavity

A ray method based on geometrical optics is applied to solve the problem of propagation of harmonic elastic waves excited by the perturbation of the surface of a noncircular cylindrical cavity. Stresses are computed under plane strain conditions for a cavity in the form of a parabolic cylinder and for a cylindrical cavity with a Munger oval section subjected to a uniform, surface load or a surface load which is a cosinusoidal function of the angle.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 75–82, 1987.     

Propagation of torsional waves in tubular bones

By considering the material inhomogeneity and anisotropy of osseous tissues, the propagation of torsional waves in tubular bones has been studied in this paper. An exact closed form solution is presented. The electric and magnetic fields induced by the travelling torsional waves in tubular bones are also derived by accounting for the piezoelectricity of osseous material. Making use of the derived analytical solution, and the experimentally determined constants for osseous tissues, numerical values of the phase velocities and attenuation coefficients are calculated for different frequencies in the ultrasonic range. Further, the effects of material damping and inhomogeneity on the attenuation and phase velocities of the waves are examined.     

Propagation of plane waves in microstretch fluid

The propagation of plane harmonic waves are studied in a microstretch fluid medium. It is found that five basic waves can propagate at distinct speeds in an infinite linear homogeneous isotropic microstretch fluid. Out of these five waves, one is a longitudinal micro-rotational wave, two are coupled longitudinal waves and remaining two are coupled transverse waves. The longitudinal micro-rotational wave travels independently and is not influenced by the microstretching of the medium, while the coupled longitudinal waves arise due to the presence of microstretching and coupled transverse waves arise due to the presence of micro-rotation in the medium. Speed of propagation of all the waves are found to be complex valued and dispersive at low frequency, but almost non-dispersive at high frequency. Due to complex valued speeds of propagation, all the waves are attenuating but differently. Coupled sets of longitudinal waves reduce to a longitudinal wave of micropolar fluid in the absence of microstretching. Reflection phenomena of a set of coupled longitudinal waves incident obliquely at the free surface of a microstretch fluid half-space has been investigated. Closed formulae for the reflection coefficients are presented and computed numerically for a particular medium. The real and imaginary parts of the complex speeds of all the waves and their corresponding attenuation coefficients have also been studied numerically and depicted graphically against frequency parameter.     

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 spiral waves in anisotropic media: from waves to stripes

The effects of anisotropic diffusion on the propagation of spiral waves in excitable media are studied numerically by means of time-linearized methods in very refined meshes and with very small time steps. It is shown that the anisotropy of the inhibitor's diffusivity tensor does not play as important role on wave propagation as that of the activator. It is also shown that the off-diagonal components of the activator's diffusivity tensor cause stretching of the activator's concentration along the principal directions of this tensor, and that a large difference between the diffusion coefficients in the x- and y-directions may result in the spiral wave annihilation and stripe formation.     

On a cylindrical blast ware propagating in a conducting gas

Zusammenfassung Die Ähnlichkeitslösung von Lin für starke zylindrische Stösse wird verallgemeinert für den Fall, dass der Stoss in einem Plasma und in einem Magnetfeld parallel zur Zylinderachse sich ausbreitet.     

Propagation of internal waves in a three-layer liquid

The propagation o f internal harmonic waves in a three-layer liquid is examined in a linear approximation for arbitrary wave numbers. A travelling wave sohaion is obtained and a dispersion equation is derived. The roots of the dispersion equation and the dependence of the solution on the ratio of the densities of the liquids are examined in detail. The phase and group velocities are plotted as functions of wavelength and graphs of the various wave modes are presented. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 170–174, 1999.     

Propagation of longitudinal viscoelastic waves in a three-layer medium

The nonstationary problem of propagation of a longitudinal plane one-dimensional stress wave through a plane-parallel viscoelastic layer of finite thickness separating two linear elastic half-spaces with different properties is solved in the linear formulation. A plane wave traveling in one of the half-spaces is normally incident on the boundary of the layer (one-dimensional problem). The field in the other elastic half-space, excited as a result of the multiple reflection of the fronts from the boundaries of the layer, is investigated. Graphs of the small displacements at a given point of the elastic half-space are presented. The solution of the problem is based on the dynamic correspondence principle formulated by Bland [3].Central Scientific-Research Institute of Machine Building, Moscow. Translated from Mekhanika Polimerov, No. 1, pp. 151–156, January–February, 1971.     

Propagation of acoustic waves in a fibrous fluid-filled material

The homogenization method is used for the analysis of acoustic wave propagation in a unidirectional fibrous material for the acoustic control of the fiber arrangement in manufacturing composites. Acoustic equations for a rigid periodic structure filled by a nonviscous fluid are obtained by two-dimensional asymptotic expansions. A regular square and triangular arrangement of the fibers with a round cross-section are considered. The analysis reveals that the velocity of acoustic waves is significantly affected by both the volume content and the fiber arrangement.Moscow State Academy of Chemical Engineering, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 651–655 September–October, 1997.     

Propagation of electromagnetic waves in a nonlinear dielectric slab

The early phases of propagation of a large amplitude electromagnetic disturbance in a nonlinear dielectric slab embedded between two linear media are investigated by the method of characteristics. This disturbance is triggered by the arrival of an electromagnetic shock wave at one of the interfaces. Reflection and transmission of an arbitrary signal when it arrives at one of the slab boundaries is characterized in terms of nonlinear reflection and transmission coefficients for the interface. No restrictions are placed on the form of the constitutive laws of the material comprising the slab. By introducing, for the nonlinear dielectric, a class of model equations, an exact solution to the characteristic equations which describes the interaction of a centered wave with anarbitrary oncoming signal is obtained. Solutions for the electromagnetic fields are derived for the special case in which the incident disturbance interacts with the reflected signal from the slab interface. A particular case of the disturbance propagating across a nonmagnetic slab is also examined.     

Propagation of TM waves in a Kerr nonlinear layer

TM electromagnetic waves propagating through a nonlinear homogeneous isotropic unmagnetized dielectric layer located between two homogeneous isotropic half-spaces are studied. The nonlinearity in the layer obeys the Kerr law. The problem is reduced to a system of nonlinear ordinary differential equations. A dispersion relation for the propagation constants is derived. The results are compared with those in the case of a linear layer.     

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.

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