Scattering of elastic waves by an elastic sphere

The problem of scattering of plane compressional wave by an elastic sphere embedded in an isotropic elastic medium of different material properties is solved. Approximate formulas are derived for the displacement field, stress tensor, stess intensity factors, far-field amplitudes and the scattering cross section. It is assumed that the wave length is large compared to the radius of the scatterer. Various elastostatic limits are also presented.     

Scattering of acoustic waves by movable lightweight elastic screens

This paper computes the insertion loss provided by movable lightweight elastic screens, placed over an elastic half-space, when subjected to spatially sinusoidal harmonic line pressure sources. A gap between the acoustic screen and the elastic floor is allowed. The problem is formulated in the frequency domain via the boundary element method (BEM). The Green's functions used in the BEM formulation permit the solution to be obtained without the discretization of the flat solid–ground interface. Thus, only the boundary of the elastic screen is modeled, which allows the BEM to be efficient even for high frequencies of excitation. The formulation of the problem takes into account the full interaction between the fluid (air) and the solid elastic interfaces.The validation of the algorithm uses a BEM model, which incorporates the Green's functions for a full space, requiring the full discretization of the ground. The model developed is then used to simulate the wave propagation in the vicinity of lightweight elastic screens with different dimensions and geometries. Both frequency and insertion loss results are computed over a grid of receivers. These results are also compared with those obtained with a rigid barrier and an infinite elastic panel.     

Scattering of electromagnetic waves by a coated not perfectly conducting sphere

We consider the low-frequency scattering problem of a plane electromagnetic wave by a sphere, which is covered by a penetrable concentric spherical shell. The medium, occupying the shell, is lossless while on the surface of the core an impedance boundary condition is satisfied. The impedance boundary condition was introduced by Leontovich (Investigations of Radiowave Propagation. Part II, Academy of Science, Moscow, 1948) and it accounts for situations where the obstacle is not perfectly conducting but the exterior field will not penetrate deeply into the scatterer. For the near electromagnetic field we obtain the low-frequency coefficients of the zeroth and the first orders while in the far field we derive the leading non-vanishing terms for the scattering amplitude and the scattering cross-section. Spherical coated obstacles are very important in applications. Small particles in biological suspensions, cells, some human organs, atmospheric particles and granules within composite materials are only a few examples of applied interest in science and technology.     

Propagation of elastic waves in a micropolar sphere

The problem of harmonic wave propagation in a solid micropolar sphere is solved by considering the two scalar and two vector equations governing the motion. Stress free boundary conditions are applied and a characteristic equation is obtained. The characteristic determinant can be resolved into the product of two independent determinants. Two classes of motion are observed which have been analysed in detail.     

Scattering of elastic waves by a crack with spring-mass contact

The scattering problem of elastic waves by a crack with spring-mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack-opening displacements and scattering cross-sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross-sections, even if the mass is small.     

Scattering of elastic waves by a diamond shaped inclusion with cracks

This paper studies the scattering of in-plane compressional and shear waves by a diamond shaped inclusion with cracks using the boundary element method. The special case that the shape of the diamond becomes square is also considered. Numerical calculations are carried out for the limited cases of diamond shaped hole and rigid inclusions, and the effects of frequency and inclusion shape on the scattering cross section and dynamic stress intensity factor are shown in graphical form. The results where the elastic properties of the inclusion are the same as those of the matrix are also discussed.     

Scattering of a plane wave by an anisotropic ferrite-coated conducting sphere

On the basis of the three-dimensional spherical vector wave functions in ferrite anisotropic media, and the fact that the first and second spherical vector wave functions in ferrite anisotropic media satisfy the same differential equations, the electromagnetic fields in homogeneous ferrite anisotropic media can be expressed as the addition of the first and second spherical vector wave functions in ferrite anisotropic media. Applying the continue boundary condition of the tangential component of electromagnetic fields in the interface between the ferrite anisotropic medium and free space, and the tangential electric field vanishing in the interface of the conducting sphere, the expansion coefficients of electromagnetic fields in terms of spherical vector wave function in ferrite medium and the scattering fields in free space can be derived. The theoretical analysis and numerical result show that when the radius of a conducting sphere approaches zero, the present method can be reduced to that of the homogeneous ferrite anisotropic sphere. The present method can be applied to the analyses of related microwave devices, antennas and the character of radar targets.     

Diffraction of elastic waves by an elliptic crack

The integral equation method is used to obtain the scattered field of a normally incident plane wave from an elliptic crack embedded in an isotropic elastic medium. It is shown that the determination of the diffracted field depends on the solution of integro-differential equation. A formal power series solution, in the low frequency limit, is obtained. Expressions are derived for the scattered amplitudes and the dynamic stress intensity factor.     

Resonance scattering of elastic waves by an elastic inclusion in an elastic matrix. Numerical calculations

The scattering of an incident plane ultrasonic (longitudinal) wave by an elastic spherical inhomogeneity contained within an elastic matrix is studied. The emphasis is on the computation and analysis of basic multiple cases that result when different material behaviours are present in the matrix and in the inclusion. These calculations are useful in underwater acoustic applications. The behaviors are dominated by the soft or rigid backgrounds of the resonance scattering theory (RST). The first three multiple coefficients appearing in the expansions for the total elastodynamic fields developed around the inhomogeneity during the scattering process have been calculated in suitable frequency bands in all the cases considered. The examination of modulus, the real parts, and the imaginary parts of these (complex) coefficients under the RST approach allows the quantitative assessment of the conditions under which monopole or dipole resonances will occur and their relative magnitudes. The decomposition of the multiple coefficients into their resonance and background portions shows that it is the upward frequency shift of the background curves that controls the dominance of either radial (monopole) or translation (dipole) oscillations of the inclusion. This has an effect on the dispersion curves of the composite, which develop optical as well as acoustical branches. The real and imaginary parts of the multiple coefficients are respectively proportional to the attenuation and the effective wave speed in this simple inhomogeneous composite.     

Scattering of torsional waves by a spherical cavity in a long circular elastic cylinder

Summary. The axisymmetric wave equation is solved for the problem of torsional elastic waves scattered by a spherical cavity located symmetrically in an infinitely long circular cylinder. Using Fourier transforms, the problem is reduced to the solution of an infinite system of simultaneous equations, which is suitable for the numerical solution. The numerical results on the transmission and reflection coefficients are shown for various values of sphere radius and frequency. Equation of energy conservation is utilized to check the numerical procedure.     

Scattering of SH waves by an arbitrarily orientated closed crack

The 2D problem of a time-harmonic plane shear horizontal (SH) wave scattered by a finite closed crack in an isotropic material is presented in the paper. The crack is arbitrarily orientated with regard to the incident wave. A spring model based on the assumption that the traction components on the crack surfaces are linearly related to the crack opening displacement (COD) is used to model the closed crack. The problem is formulated in a set of boundary integral equations which contains the CODs as unknowns. Numerical examples are presented for the CODs, elastodynamic stress intensity factors, and the scattered displacement field for various parameters, such as spring stiffness, crack sizes and crack orientations. The results show that both the crack closure and orientation have significant effects on the scattered displacement field for the closed crack.     

Scattering of a pulsed wave by a sphere with an eccentric spherical inclusion

A dielectric sphere with an eccentric spherical dielectric inclusion and an incident amplitude-modulated plane electromagnetic wave constitute an exterior radiation problem, which is solved in this paper. A solution is obtained by combined use of the Fourier transform and the indirect-mode-matching method. The analysis yields a set of linear equations for the wave amplitudes of the frequency-domain expansion of the electric-field intensity within and outside the externally spherical inhomogeneous body; that set is solved by truncation and matrix inversion. The shape of the backscattered pulse in the time domain is determined by application of the inverse fast Fourier transform. Numerical results are shown for a pulse backscattered by an acrylic sphere that contains an eccentric spherical cavity. The effects of cavity position and size on pulse spreading and delay are discussed.     

Diffraction of shear waves by an edge crack in an elastic wedge

Low frequency diffraction of plane harmonic shear (SH) wave by an edge crack in an elastic wedge of arbitrary vertex angle is studied. Kontorowich-Lebedev transform is used to solve the mixed boundary value problem under consideration. For low frequency case, i.e. wavelength large compared to the length of the crack, the displacement field is obtained by successive approximation of the resulting Wiener-Hopf equation. For the limiting case of an elastic half space the results agree with those obtained by the method of matched asymptotic expansions.     

Comparative solutions for a punch problem of an elastic sphere encapsulated in an elastic shell

One of the major causes of mechanical damage incurred in agricultural commodities is attributed to the frequent impacts they receive in harvesting and handling. In agricultural operations, in general, only the local contact phenomenon is considered and the effect of wave propagation is ignored. The punch problem is a special case in the class of contact problems that is of particular practical interest in the impact loading encountered in fruit handling and harvesting.Two potential methods are proposed for analysing the deformation of an elastic sphere encapsulated in an elastic shell and subjected to punch loading. Numerical evaluation of both models showed that the results are comparable. Although more examples related to different geometries and loadings would be required to substantiate the data, the results provide a useful tool for the selected specific geometry which is very common in agriculture. Because good agreement was obtained between the two methods, the choice of which to implement should be made according to the specific problem in question. The Boussinesq method is a more rigorous mathematical approach and, as such, offers a better insight into the actual behaviour of the domain under given boundary conditions. Its utilization is limited to well defined geometrics because of the complexity involved. The finite element method is capable of handling irregular shapes but requires large computer memory for an exact solution. Both methods have been successfully implemented in a practical agricultural problem in an attempt to decrease the mechanical damage encountered during mechanized fruit harvesting.     

Shock waves in an elastic pipeline

The formation of shock waves from the solitary Gaussian and hyperbolic waves in an elastic pipeline has been investigated. It is shown that the parameters of these waves — the path length and the time of formation — differ insignificantly from the analogous parameters of the shock waves formed from the sine waves. The evolution of the discontinuity surface in these shock waves has been considered. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 3, pp. 489–495, May–June, 2008.     

Scattering of elastic waves by spherical inclusions with applications to low frequency wave propagation in composites

Scattering of plane elastic waves by a spherical inclusion is considered. A unified method of solution is presented which treats compressional and shear incidence on a similar basis. Explicit results are given for Rayleigh scattering. We apply the results of the single scattering problem to the propagation of low frequency waves in a composite containing a dilute concentration of spherical inclusions. Explicit formulae are given for the effective wave speeds and attenuations when the inclusions are voids. Both the compressional and shear wave speeds decrease initially as a function of frequency.     

Scattering of Beltrami fields by an orthorhombic dielectric-magnetic sphere immersed in a chiral medium

The T matrix method can be formulated to study Beltrami planewave scattering by a sphere composed of an orthorhombic dielectric magnetic material immersed in a chiral medium. Whereas an orthorhombic dielectric-magnetic material whose permeability dyadic is a scalar multiple of its permittivity dyadic is pathologically unirefringent and anisotropic. A chiral medium characterized by either a left-handedness or a right-handedness in its microstructure is birefringent and not anisotropic. The backscattering efficiency has an undulating behaviour with increase in electrical size and is highly affected by constitutive anisotropy of the sphere. Multiple lobes appear in theplots of the differential scattering efficiency when the incident ?eld is left-circularly polarized wave. Peaks of curves of the backscattering effciency appear at lower frequencies for an incident left-circularly polarized wave and at higher frequencies for a right-circularly polarized wave incidence, if the sphere is impedance-matched to the ambient chiral medium.     

Scattering of a surface wave by a submerged sphere

Summary The problem of the scattering of a surface wave in a nonviscous, incompressible fluid of infinite depth by a fully submerged, rigid, stationary sphere has been reduced to the solution of an infinite set of linear algebraic equations for the expansion coefficients in spherical harmonics of the velocity potential. These equations are easily solved numerically, so long as the sphere is not too close to the surface. The approach has been to formulate the problem as an integral equation, expand the Green's function, the velocity potential of the incident wave, and the total velocity potential in spherical harmonics, impose the boundary condition at the surface of the sphere, and carry out the integrations. The scattering cross section has been evaluated numerically and is shown to peak for values of the product of radius and wave number somewhat less than unity. Also, the Born approximation to the cross section is obtained in closed form.Supported by the Department of the Navy, Naval Sea Systems Command under Contract No. N00017-72-C-4401.     

Scattering of shear waves by a rigid cylinder in an inhomogeneous medium

We consider the problem of scattering of shear (SV) waves by a rigid circular cylinder embedded in an inhomogeneous medium, in which density and shear modulus vary as the power of the distance from the center of the cylinder. The problem is investigated by the method of dual integral transformation. The resulting integrals are evaluated asymptotically to obtain the time solution. Numerical computations are done to investigate the behaviour of reflection co-efficients and divergence factors for shear and compressional waves respectively. The results show that the expectations in case of a homogeneous earth are also valid in the heterogeneous case.     

阻抗球体表面的空气耦合声波的波束形成

1引言 在利用传声器阵列进行语音声源定位的研究中存在着阵列较大不利于实际应用的问题.这是因为波束宽度与阵列尺寸成反比:波束宽度越窄,阵列指向性越好.因而研究如何在小阵列尺寸的情况下获得较窄波束,具有较大应用价值.实际应用中,均匀圆形阵列测向范围为[-180°,180°],有较广的应用.将传声器阵列围绕球体均匀放置后可得到具有更好性能的波束[1].本文对球体周围的声场作了进一步的具体研究,在此基础上分析了不同的球体情况对声场和波束形成的影响,并进行了比较.