Dyadic Green's function of a sphere with an eccentric spherical inclusion

An exact, analytical solution to the problem of point-source radiation in the presence of a sphere with an eccentric spherical inclusion has been obtained by combined use of the dyadic Green's function formalism and the indirect mode-matching technique. The end result of the analysis is a set of linear equations for the vector wave amplitudes of the electric Green's dyad. The point source can be anywhere, even within the aforesaid nonspherical body, and there is no restriction with regard to the electrical properties in any part of space. Several checks confirm that this solution obeys the energy conservation and reciprocity principles. Numerical results are presented for an electric Hertz dipole radiating from within an acrylic sphere, which contains an eccentric spherical cavity.     

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.     

Generalized Lorenz-Mie theory for a sphere with an eccentrically located spherical inclusion

Abstract

The theory of interaction between an arbitrary electromagnetic shaped beam and a sphere with an eccentrically located spherical inclusion is presented. This theory is built as a synthesis between two available theories (i) the generalized Lorenz-Mie theory for a homogeneous sphere (illuminated by an arbitrary shaped beam) and (ii) the theory of interaction between a plane wave and an eccentrically stratified dielectric sphere.     

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.     

Stresses in a thick plate containing an eccentric spherical inclusion or cavity part II

Summary Part II of the paper presents a solution for the problem of a thick plate containing an eccentric rigid spherical inclusion when the plate is subject to a stress system symmetrical about the axis of revolution of the plate.

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Spannungen in einer dicken Platte mit exzentrischem kugelförmigem Einschluß oder Loch

Zusammenfassung Der zweite Teil der Arbeit bringt eine Lösung des Problems der dicken Platte mit extrentrischem, starrem kugelförmigem Einschluß unter drehsymmetrischer Belastung.

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With 2 Figures     

Scattering of a spherical acoustic field from an eccentric spheroidal structure simulating the kidney-stone system

Summary.  We consider the acoustic scattering of time-harmonic spherical waves from an eccentric non coaxial spheroidal structure simulating the kidney-stone system. The proposed analysis is based on the application of the translational addition theorem for spheroidal wave functions. The resulting theoretical model is frequency-independent. Numerical results concerning the applicability of our approach are also presented. Received September 20, 2002 Published online: March 20, 2003     

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 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, stress 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.     

Electromagnetic-wave scattering by a sphere with multiple spherical inclusions

An exact solution to the problem of electromagnetic-wave scattering from a sphere with an arbitrary number of nonoverlapping spherical inclusions is obtained by use of the indirect mode-matching technique. A set of linear equations for the wave amplitudes of the electric field intensity throughout the inhomogeneous sphere and in the surrounding empty space is determined. Numerical results are calculated by truncation and matrix inversion of that set of equations. Specific information about the truncation number pertaining to the multipole expansions of the electric field intensity is given. The theory and the accompanying computer code successfully reproduce the results of other pertinent papers. Some numerical results [Borghese et al., Appl. Opt. 33, 484 (1994)] were not reproduced well, and that discrepancy is discussed. Our numerical investigation is focused on an acrylic sphere with up to four spherical inclusions. This is the first time that numerical results are presented for a sphere with more than two spherical inclusions. Interesting remarks are made about the effect that the look direction and the structure of the inhomogeneity have on backscattering by the acrylic host sphere.     

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 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 antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface

Summary We present analytical solutions for the scattering of an antiplane shear wave by a piezoelectric circular cylinder with an imperfect interface. We first consider the simple case in which the imperfection is homogeneous along the interface. Two typical imperfect interfaces are addressed: 1) mechanically compliant and dielectrically weakly conducting interface, and 2) mechanically compliant and dielectrically highly conducting interface. The expressions for the directivity pattern and scattering cross-section of the scattered shear waves are derived. We then investigate the more difficult problem in which the imperfection is circumferentially inhomogeneous along the interface. A concise expression for an inhomogeneously compliant and weakly conducting interface is derived by means of matrix notation. Numerical examples are presented to demonstrate the effect of the imperfection and the circumferential inhomogeneity of the interface on the directivity patterns and scattering cross-sections of the scattered shear wave. The circumferentially inhomogeneous interface is also utilized to model the interface where an arbitrary number of cracks exist. Results show that when every part of the interface is rather compliant, large low-frequency peaks of the scattered cross-sections, which correspond to the resonance scattering, can be observed no matter if the interface is homogeneous or inhomogeneous. The appearance of large low-frequency peaks can be well explained by estimating the natural frequency of the corresponding reduced mass-spring system where the cylinder is assumed as a rigid body. Peaks of the scattered cross-sections spanning from low frequencies to high frequencies can be observed for a cylinder with a partially debonded interface.     

Detachment of an elastic matrix from a rigid spherical inclusion

An approximate theoretical treatment is given for detachment of an elastomer from a rigid spherical inclusion by a tensile stress applied to the elastomeric matrix. The inclusion is assumed to have an initially-debonded patch on its surface and the conditions for growth of the patch are derived from fracture energy considerations. Catastrophic debonding is predicted to occur at a critical applied stress when the initial debond is small. The strain energy dissipated as a result of this detachment, and hence the mechanical hysteresis, are also evaluated. When a reasonable value is adopted for Young's modulus E of the elastomeric matrix, it is found that detachment from small inclusions, of less than about 0.1 mm in diameter, will not occur, even when the level of adhesion is relatively low. Instead, rupture of the matrix near the inclusion becomes the preferred mode of failure at an applied stress given approximately by E/2. For still smaller inclusions, of less than about 1 m in diameter, rupture of the matrix becomes increasingly difficult, due to the increasing importance of a surface energy term. These considerations account for the general features of reinforcement of elastomers. Small-particle fillers become effectively bonded to the matrix, whereas larger inclusions induce fracture near them, or become detached from the matrix, at applied stress that can be calculated from the particle diameter, the strength of adhesion, and the elasticity of the matrix material.     

Scattering of a Hermite-Gaussian beam field by a chiral sphere.

Scattering of a Hermite-Gaussian beam field by a chiral sphere is analyzed. A Hermite-Gaussian beam field is expressed as a superposition of multipole fields at complex-source points. Electromagnetic fields are expanded in terms of the spherical vector wave functions. The unknown expansion coefficients for the scattered field and the internal field are determined by the boundary conditions. As numerical examples, the scattered near fields of the beam incidence are calculated, and the effects of the chirality and the radius of the chiral sphere on the fields are examined. The results for a Gaussian beam incidence are also compared with those of a plane-wave incidence.