On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

The problem of electric and acoustic waves diffraction by a half-plane crack in a transversal isotropic piezoelectric medium is investigated. The crack is assumed to be electric permeable and free of tractions. The so-called “quasi-hyperbolic approximation” [15] is adopted. Applying Laplace transformations and Wiener–Hopf technique a closed form solution is obtained. By the means of Cagniard–de Hoop method a detailed dynamic full electroacoustic wavefield’s investigation is conducted. Mode conversion between electric and acoustic waves, effect of electroacoustic head wave, Bleustein–Gulyaev surface wave and the wavefield structure depending on the type of the incident wave (acoustic or electric) and its angle of incidence are analyzed in details. The dynamic field intensity factors at the crack tip depending on the angle of incidence and on time are derived explicitly. Numerical analysis is presented.     

On diffraction in a piezoelectric medium by a half-plane: The Sommerfeld problem

This paper is concerned with the diffraction problem in a transversely isotropic piezoelectric medium by a half-plane. The half-plane obstacle considered here is a semi-infinite slit, or a crack; both its surfaces are traction free and electric absorbent screens. In a generalized sense, we are dealing with the Sommerfeld problem in a piezoelectric medium.¶The coupled diffraction fields between acoustic wave and electric wave are excited by both incident acoustic wave as well as incident electric wave; and the sound soft and electric "blackness" conditions on the screens are characterized by a system of simultaneous Wiener-Hopf equations. Closed form solutions are sought by employing special techniques. Some interesting results have been obtained, such as mode conversions between acoustic wave and electric wave, novel diffraction patterns in the scattering fields, and the effect of electroacoustic head wave, as well as of surface wave-Bleustein-Gulyaev wave.¶Unlike the classical Sommerfeld problem, in which the only concern is the scattering field of electric wave, the strength of material, e.g. material toughness, is another concern here. From this perspective, relevant dynamic field intensity factors at the crack tip are derived explicitly.     

Artificial boundary conditions for two-dimensional equations of fluid dynamics. 1. Convective wave equation

The article models external flow problems on artificially bounded regions. In the linear approximation we examine the reflection of acoustic waves in a moving medium, incident at various angles on a fixed boundary. We consider the construction of various boundary conditions and estimate their reflecting properties for plane waves and waves from point sources. The plane wave approximation is justified theoretically. A method is proposed for estimating the integral reflection coefficient for waves with a whole range of incidence angles. __________ Translated from Prikladnaya Matematika i Informatika, No. 24, pp. 76–110, 2006.     

Scattering of a plane acoustic wave on a periodic array of piston radiators embedded into a rigid screen

The stationary scattering of a plane acoustic wave on a periodic or a doubly periodic set of piston radiators elastically connected with a rigid screen is considered. The screen separates two half-spaces filled with media possessing different acoustic properties. The model considered takes into account energy losses in the elastic ties between the piston radiators and rigid screen. The problem solution in the case where only one half-space is filled with an acoustic medium is found as a special case. The results of numerically analyzing the reflection coefficients of a plane wave as functions either of the frequency of the incident wave or of the angle of incidence of the plane acoustic wave for different values of the parameters involved are presented. Bibliography: 4 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 125–137. Translated by G. L. Nikitin.     

A solution for transient surface waves of the B-G type in a dissipative piezoelectric crystal

We derive a solution to the problem of shear horizontal electroacoustic surface waves in a piezoelectric half-space. We formulate a time-domain dynamic problem accounting for time dispersion for both electric and elastic fields and use a separation of variables to express the solution in terms of a wave propagator. Transient surface waves of the B-G type are found to propagate with a constant speed and exponentially decay in space. Their amplitude vanishes at large distances from the boundary as the reciprocal of the depth. Dispersive and non dispersive solutions are compared.     

Diffraction of a plane wave by a step discontinuity in an impedance plane

In the present paper, the high-frequency diffraction of a plane wave by a right-angle step discontinuity in an impedance plane is analyzed with the help of the uniform geometric theory of diffraction, beginning with the Maluzhenets solution. The principal term of an asymptotic solution of the problem, which is uniform with respect to the angle of incidence of the plane wave and the angle of observation, is derived. The excitation of primary and multiply diffracted fields radiated from the upper edge, as well as surface waves, is considered (the lower edge does not radiate cylindrical or surface waves owing to a right-angle step). For simplicity, the details of computation are given here for a right-angle step discontinuity. A similar procedure is applied to other examples with more complicated geometry. Bibliography: 7 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 97–108. Translated by V. V. Zalipaev.     

Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack

The problem of interaction of a plane time-harmonic SH-wave with an elastic fiber of quasi-square or quasi-triangular cross section, when an interface crack is present between an infinite elastic matrix and the fiber, is considered. The modified null-field method taking into account the asymptotic behavior of the solution at crack tips is exploited for obtaining numerical results. The effects of fiber shape, fiber/matrix material combination, debonding (crack size), and direction of wave incidence on the scattering amplitude in the far zone are analyzed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 245–254, March–April, 2008.     

压电材料中两平行不相等界面裂纹的动态特性研究

利用Schmidt方法,研究了压电材料中两个平行不相等的可导通界面裂纹对简谐反平面剪切波的散射问题．利用Fourier变换,使问题的求解转换为对两对以裂纹面张开位移为未知变量的对偶积分方程的求解．数值计算结果表明,动态应力强度因子及电位移强度因子受裂纹的几何参数、入射波频率的影响．在特殊情况下,与已有结果进行了比较分析．同时,电位移强度因子远小于不可导通电边界条件下相应问题的结果．     

Propagation of shear waves in piezoelectric “superlattice-substrate” structures

The results of a computer simulation of the dispersion relations for the propagation of shear waves in piezoelectric “superlattice-substrate” structures are analyzed. The superlattice consists of a finite number of layers and is made up of materials with 6mm symmetry. The dispersion relations are obtained using a formulation for periodic hamiltonian systems. This approach makes it possible to account for the anisotropy, the piezoelectric interaction of the mechanical and electric fields, and an arbitrary number of layers in the superlattice. Numerical results are presented for CdS-ZnO layers. Selective spatial localization of acoustic modes is demonstrated for different spectral regions. The effects of the ordering of the superlattice layers, of their number, and of the boundary conditions on the dispersion spectra and on the form of the shear wave motion are examined. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, and Institute of Metal Physics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 148–156, 1999.     

Local solutions to a model of piezoelectric materials

A local existence theorem is proved for a non‐linear coupled system modelling the electromechanical motion of a one‐dimensional piezoelectric body with domain switching. The system is composed by a heat equation describing the behaviour of the number of electric dipoles and by a wave equation governing the dynamic of the electric displacement. The main coupling in the system appears in the time‐dependent velocity of the waves depending on the number of electric dipoles. The proof of the result relies on a time decay estimate satisfied by the number of electric dipoles and an uniform estimate of the solution of the regularized wave equation. Copyright © 2004 John Wiley & Sons, Ltd.     

压电压磁复合材料中界面裂纹对弹性波的散射

利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题．经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式．数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同．     

A Combined Method for Calculating the Field of a Point Source in a Waveguide (Slightly Curved Media)

The two-dimensional problem of propagating the waves generated by a point source in a depth slightly curved waveguide is investigated. The Dirichlet condition is given on the boundary of the waveguide, and also two consistency conditions are defined on the interface between the fluid and the bottom. The velocity of the acoustic wave is assumed to be arbitrarily dependent on the depth of the waveguide and weakly dependent on the trace coordinate. With the help of rather cumbersome transformations, the solution is expressed as a sum of geometric-optical waves, normal waves, and a remainder. Sufficient conditions on the total amount of detached normal and geometric-optical waves are obtained. Bibliography: 2 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 225–234.     

Well-posedness of the poincar�� problem in a cylindrical domain for the higher-dimensional wave equation

It is known that waves (acoustic waves, radio waves, elastic waves, and electric waves) in cylindrical tubes are described by the wave equation. In the theory of hyperbolic-type partial differential equations, boundary-value problems with data on the whole boundary serve as examples of ill-posedness of the posed problems. In this work, it is shown that the Poincar´e problem in a cylindrical domain for the higher-dimensional wave equation is uniquely solvable. A uniqueness criterion for a regular solution is also obtained.     

Influence of a Weak Boundary on the Wave Field of an Approaching Source

The response of a weak interface inside an isotropic elastic medium to an approaching source is considered. It is shown that a strong shear wave arises in the wave field reflected at an angle greater than a critical one. Properties of this wave are studied, and theoretical seismograms describing the contribution of all reflected waves to the total field are presented. Bibliography: 19 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 89–100.     

On the mechanisms of heat transport across vacuum gaps

Heat exchange between closely positioned bodies has become an important issue for many areas of modern technology including, but not limited to, integrated circuits, atomic force microscopy, and high-density magnetic recording, which deal with bodies separated by gaps as narrow as a few nanometers. It is now recognized that heat transport across a gap of sub-micron width does not follow the Stefan–Boltzmann law, which is based on a conventional theory developed for sufficiently wide gaps. This paper describes the structure of thermally excited electromagnetic fields in arbitrarily narrow gaps, and it also shows that heat can be carried across narrow vacuum gaps by acoustic waves. The structure of the acoustic wave fields is also described, and it is shown that they become the dominant heat carriers in gaps narrower than a certain critical width, which is estimated to be a few nanometers. For example, consider a vacuum gap between silicon half-spaces. When the gap’s width is below a critical value, which is about 7.5 nm, the contribution of acoustic waves must be taken into account. Assuming that the wavelength of thermally excited acoustic waves is of order 1 nm, it may be possible to estimate the contribution of acoustic waves to heat transport across gaps with 4 nm < h < 7.5 nm by the kinetic theory, but for narrower gaps with h < 4 nm, this approximation is not valid, and then the full wave theory must be used. Also for gaps narrower than about 2.5 nm, there is no need to take into account electromagnetic radiation because its contribution is negligible compared to that of acoustic waves.     

The inverse scattering problem for a prolate acoustically rigid solid of revolution

In a harmonic mode of scattering of planar acoustic waves we study the problem of determining the shape of a prolate acoustically rigid solid of revolution. From experimental measurements we assume that the complex amplitude of inverse scattering is known on a discrete set of test wave numbers in directions that are nearly perpendicular to the axis of revolution of the scatterer. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 124–130.     

Fatigue life investigation using non-destructive testing methods

Experimental investigations of the fatigue life prediction of two different specimen forms made from steel 42CrMo4 are described. The fatigue load is defined as a cyclic loading with constant and non constant amplitudes in tension range and with different stress ratios. This loading range leads to a high cyclic fatigue behaviour of both specimens. During the test, the growth of the fatigue crack is monitored using two different non-destructive methods, namely acoustic emission and the electric resistance. The acoustic emission is used for detecting sound waves as a result of dissipation of elastic energy during microcracks and cracks growth, as well as for the detection of the place of crack initiation. The electric resistance is used for the monitoring and quantitative investigation of the crack growth. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exact analysis for mode III cracks between two dissimilar magnetoelectroelastic layers

This paper develops a closed-form solution for an interface crack in a layered magnetoelectroelastic strip of finite width. The strip is subjected to anti-plane mechanical and in-plane electric and magnetic fields. Explicit expressions for the stress, electric, and magnetic fields, together with their intensity factors, are obtained for two extreme cases of an impermeable and a permeable cracks. The stress intensity factor does not depend on the electromagnetic boundary conditions assumed for the crack. However, the electrically and magnetically permeable boundary conditions on the crack profile have a significant influence on the crack-tip electromagnetic field intensity factors. Solutions for some special cases, such as a central crack, an edge crack, two symmetric collinear cracks, and a row of collinear interface cracks, are also obtained in closed forms. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 763–784, November–December, 2008.     

Numerical solution of integral equations of first and second kind in scalar and vector problems of diffraction on a cube

We consider the problem of numerical simulation of the scattering of acoustic and electromagnetic waves on a cube whose edge ha s length up to 8 wave lengths of the incident wave. We describe a scheme using a representation of the boundary integral equation in the form of an operator convolution equation on the symmetry group of the cube. We compare the results of numerical solution of integral equations of first and second kind for scalar and vector problems of diffraction of a plane wave on a cube. Translated fromProblemy Matematicheskoi Fiziki, 1998, pp. 36–45.     

Construction of the solutions of linear hyperbolic systems using laguerre geometric-optic expansions

We discuss a technique for expanding the solution of a linear hyperbolic system of differential equations in a series of Laguerre functions behind the wave front. Solving the original linear system is reduced to solving the eikonal equation that describes the behavior of the wave front and a sequence of transfer systems that describe the Laguerre spectrum. The application of the technique is illustrated using the examples of one-dimensional acoustic and thermoelastic waves. Translated fromMatemetichni Metodi ta Fiziko-Mekhanichni Polya. Vol. 40, No. 2, 1997, pp. 39–43.