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.

     

Interaction of acoustic waves and piezoelectric structures

In the paper, we investigate the basic transmission problems arising in the model of fluid‐solid acoustic interaction when a piezo‐ceramic elastic body ( Ω ⁺ ) is embedded in an unbounded fluid domain ( Ω ^? ). The corresponding physical process is described by boundary‐transmission problems for second order partial differential equations. In particular, in the bounded domain Ω ⁺ , we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω ^? , we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

A representation of acoustic waves in unbounded domains

Compact, time‐harmonic, acoustic sources produce waves that decay too slowly to be square‐integrable on a line away from the sources. We introduce an inner product, arising directly from Green's second theorem, to form a Hilbert space of these waves and present examples of its computation.¹ © 2005 Wiley Periodicals, Inc.     

Scattering of acoustic waves by inhomogeneous obstacles

The scattering of acoustic waves, produced by a continuously–stratified layer, is investigated through a Volterra integral formulation in the Fourier–transform domain. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.

     

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.     

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.     

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.     

Dispersion relations of elastic waves in two-dimensional tessellated piezoelectric phononic crystals

A type of two-dimensional tessellated piezoelectric phononic crystal is theoretically studied in this paper, formed by homogeneous piezoelectric and inhomogeneous functionally graded rectangular columns. Firstly, the propagation properties of in-plane and anti-plane Bloch waves in each piezoelectric rectangular column are systematically investigated. Furthermore, the total transfer matrices of Bloch waves are obtained based on transfer matrices of homogeneous piezoelectric and inhomogeneous functionally graded rectangular columns. Finally, the Bloch theorem is used to obtain the dispersion relations of in-plane and anti-plane Bloch waves. The influences of non-dimensional geometrical parameters and gradient profile functions on the dispersion relations are discussed based on the graphically numerical results. Under a special value of modal parameter, the dispersion surfaces and curves of in-plane Bloch waves approximatively have plane and axis symmetries respectively, and an approximate total band-gap of anti-plane Bloch waves arise. The theoretical models and numerical discussions will provide a direct guidance of multi-material 3D printing for inhomogeneous periodic structures with dispersion and band-gaps properties.     

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.     

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.