Evaluation of fluid-filled fractures during acoustic measurements on tube waves

The problem of reflection, transmission, and conversion of the tube wave on a fracture intersecting a borehole is investigated. We consider the case where an acoustic sonde is placed inside a borehole and the fracture separates two different elastic half-spaces and is filled with a porous material. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 324, 2005, pp. 121–128.     

Dispersion of lamb waves in a three-layer plate made from compressible materials with finite initial deformations

A three-layer plate made from compressible elastic materials with finite initial deformations caused by compressive forces applied to their faces is considered. By using the three-dimensional linearized theory of propagation of elastic waves in bodies with initial stresses, the propagation of Lamb waves in this plate is investigated.     

Interaction of acoustic waves with shock waves in elastic solids

Summary Transmission and reflexion of plane acoustic waves through a longitudinal shock wave in elastic isotropic solids are investigated. As a result, the amplitude of the transmitted and reflected waves and the jump of the acceleration of the shock are explicitly determined.

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Résumé On envisage la transmission et la réflexion d'une onde acoustique plane par une onde de choc longitudinale dans les solides élastiques isotropes. On détermine explicitement l'amplitude des ondes transmises et réflechies et le saut de l'acceleration du choc.

     

Decay instability of electron acoustic waves

Eulerian and particle in cell (PIC) simulations are used to investigate the decay instability of electron acoustic waves (EAWs). An EAW is a nonlinear wave with a carefully tailored trapped particle population, that can be excited by a relatively low driver amplitude, if the driver is applied resonantly over many trapping periods. The excited EAW rings at nearly constant amplitude long after the driver is turned off, provided the EAW has the longest wavelength that fits in the plasma. Otherwise, the EAW decays to a longer wavelength EAW, through a vortex-like trapped particle population merging.     

On the asymptotic linearization of acoustic waves

The initial value problem of a certain generalization of the nonlinear, dispersive wave equations with dissipation is rigorously studied. The solutions of the equations can be found exactly up to in certain norms. The essential use is made of the fact that this equation is asymptotically linearizable to i.e., the equations can be mapped to an equation which differs from a linearizable equation only in terms which are of An application of the equations to unidirectional small amplitude acoustic waves is discussed. The general methodology used here can also be applied to other asymptotically linearizable equations.

     

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.     

Dispersion of torsional waves in initially stressed multilayered circular cylinders

Within the framework of a piecewise homogeneous body model, with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the propagation of torsional waves in prestressed multilayered circular cylinders is investigated. The elasticity relations for cylinder components are given through the Murnaghan potential. The influence of variations in the geometric and mechanical parameters of the cylinders on the dispersion curves is analyzed.     

Minnaert resonances for acoustic waves in bubbly media

Through the application of layer potential techniques and Gohberg–Sigal theory we derive an original formula for the Minnaert resonance frequencies of arbitrarily shaped bubbles. We also provide a mathematical justification for the monopole approximation of scattering of acoustic waves by bubbles at their Minnaert resonant frequency. Our results are complemented by several numerical examples which serve to validate our formula in two dimensions.     

The excitation of symmetric and antisymmetric lamb waves in a piezoelectric strip by surface electrodes

Solutions of the problems of the excitation by surface electrodes of symmetric and antisymmetric Lamb waves in a strip of piezoelectric material are obtained. The solutions of the problems are reduced to systems of singular integral equations in auxiliary functions, proportional to the jump in charge density at the electrodes. Approximate solutions of the systems of singular integral equations are obtained by the Bubnov-Galerkin method using Chebyshev polynomials of the first kind. The results of numerical calculations of the electro-elastic fields for a strip of cadmium sulphide are given.     

On an inverse problem for acoustic and seismic waves

Two basic inverse problems for determining the constitutive relation in an attenuating medium from given absorption behavior of plane waves in the medium are dealt with in the frequency domain by methods of complex analysis. In particular the case of a prescribed constant internal friction function over the seismic frequencies is considered in detail.     

Scattering of acoustic waves on a sloping beach

A classical problem of acoustics is considered by the Sommerfeld-Maliuzhinets method. All geometric waves are computed explicitly. For diffracted waves, a numerical procedure based on a uniquely solvable Fredholm integral equation is elaborated. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp. 57–64. Translated by B. V. Budaev.     

Spherical model on thermoelastic generation of acoustic waves

Summary Existing theories on the thermoelastic generation of acoustic waves do not yield satisfactory agreement with experimental data. A new spherical model is therefore proposed, where the transient heating, caused by a laser impact, is represented by the three-dimensional heat pole. An analytical solution of the thermoelastic pressure wave could be derived. The good agreement of our spherical model with the experimental results is demonstrated.

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Zusammenfassung Bestehende Theorien über die thermoelastische Erzeugung von Schallwellen ergeben keine befriedigende Uebereinstimmung mit experimentellen Daten. Es wird deshalb ein neues sphärisches Modell vorgeschlagen, wo die schlagartige Aufheizung, erzeugt durch einen Lasereinschuss, durch den dreidimensionalen Wärmepol dargestellt wird. Eine analytische Lösung für die thermoelastische Druckwelle konnte hergeleitet werden. Die gute Uebereinstimmung unseres sphärischen Modells mit den experimentellen Resultaten wird demonstriert.

     

Dispersion of elastic waves in the contact-impact problem of a long cylinder

Numerical dispersion of two-dimensional finite elements was studied. The outcome of the dispersion study was verified by the numerical and analytical solutions to the longitudinal impact of two long cylindrical bars. In accordance with the results of the dispersion analysis it was demonstrated that the quadratic elements showed better accuracy than the linear ones.     

Solitary waves in a tapered prestressed fluid-filled elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed increases with distance for positive tapering while it decreases for negative tapering.     

Solitary waves in a tapered prestressed fluid-filled elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible inviscid fluid the evolution equation is obtained as the Korteweg-de Vries equation with a variable coefficient. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed increases with distance for positive tapering while it decreases for negative tapering.