Scattering of antiplane shear waves by layered circular elastic cylinder

An exact analytical solution for the scattering of antiplane elastic waves by a layered elastic circular cylinder is obtained. The solution and its degenerate cases are compared with other simpler models of circular cylindrical scatterers. The effects of the geometrical and physical properties of the interphase are studied. Numerical results confirm the existence of a resonance mode in which the scatterer's core undergoes a rigid-body motion when the outer layer of the scatterer is very compliant. This resonance mode has been attributed [Liu et al., Science 289, 1734 (2000)] to a new mechanism for the band gap formed in the extremely low frequency range for phononic crystals made of layered spherical scatterers. Numerical results also show the existence of a similar resonance mode when the outer layer of the scatterer has very high mass density.     

Scattering of electromagnetic waves by a chiral cylinder

We consider the problem of three-dimensional diffraction of electromagnetic waves excited by an elementary source on a chiral infinite cylinder of arbitrary radius. Effective scattering cross sections of a chiral cylinder in the case of two-dimensional diffraction are numerically analyzed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 872–883, October 2008.     

Circumferential waves in a composite circular cylinder

Circumferential waves propagating in a layered, circular cylinder are studied. The cylinder consists of an elastic circular core encased in a hollow, circular cylinder of distinctly different elastic properties. Both smooth and bonded contact are considered. The effect of curvature and layer thickness on the phase velocity of the lowest mode(s) is investigated for both an acoustically softer and an acoustically stiffer layer. When the outer radius of the composite cylinder is unbounded, Stoneley waves are a limiting case as the ratio of the radius of the core to the wavelength increases beyond bounds. When the outer radius is finite, waves in a layer and a half-space result for this limit. Some attention is also directed to the limiting case of small layer thickness to the wavelength ratio. In the limit as this ratio vanishes, the motion of the core reduces to that of Rayleigh waves on the curved surface. For smooth contact, the motion of the core becomes uncoupled from that of the layer for this limiting case, and two distinct modes are seen to exist.     

Scattering of a Gaussian beam by an anisotropically coated circular cylinder

A solution to the problem of Gaussian beam scattering by an anisotropically coated circular cylinder is presented. The incident Gaussian beam source is expanded as an approximate expression in the simple form with a Tayor’s series. The transmitted field in the anisotropically coated region is expressed as a infinite summation of eigen plane waves with different polar angles. The unknown coefficients of the scattered fields are obtained with the aid of the boundary conditions. The infinite series can be truncated under the prerequisite of achieving the solution convergence. Only the case of transverse-electric polarization is discussed. The similar formulation of transverse-magnetic polarization can be obtained by adopting the similar method. Some numerical results are presented and discussed. The result is in agreement with that available as expected when the Gaussian beam degenerates to a plane wave incidence case.     

Acoustic waves emitted by a vortex ring passing near a circular cylinder

Acoustic waves emitted by a vortex ring moving near a circular cylinder have been studied experimentally and theoretically. The vortex rings used in the experiments had a translational speed ν₀ in the range 26 ⪅ ν₀ ⪅ 58 m/s and a radius of about 4·7 mm comparable in size with the cylinder radius. The acoustic pressure signals were detected by four microphones in the far field, and analyzed by digital methods. The observed pressure p obeys the scaling law p ∞ ν₀³L⁻⁴, where L is the impact distance of the vortex path to the cylinder. The observed sound wave is of dipole radiation type, and the direction of the dipole axis rotates as the vortex position changes relative to the cylinder. The direction of the dipole axis is related to that of the normal to the plane of the vortex ring. The instantaneous resultant force exerted on the cylinder by the vortex motion has also been examined, and the magnitude and the direction determined experimentally as a function of time. The theory of vortex sound predicts that the wave profile is proportional to the second time derivative of the volume flux (of a hypothetical potential flow around the cylinder) through the vortex ring. The observed scaling law and dipole directivity of the pressure are in good agreement with the theoretical predictions. The pressure profiles are calculated by using the observed vortex motion. These profiles also agree well with the observed ones, confirming the validity of the theory.     

Scattering of electromagnetic waves by a layer of air plasma surrounding a conducting cylinder

In this paper, the total scattering and back-scattering cross-sections (respectively represented by and _b) of an air plasma layer surrounding a conducting cylinder are studied. The plasma layer can be turned ON and OFF to allow for a comparison between the scattering cross-section of the bare cylinder and the plasma covered cylinder. The plasma layer is generated at atmospheric pressure, which results in a very highly collisional case. The scattered fields are calculated using a cylindrical expansion, with coefficients satisfying the appropriate boundary conditions, and which are a function of the refractive index of the air plasma. The results of our study are presented as plots of the total scattering cross-section, , and back-scattering cross-section, _b, versus frequency. The scattering cross-section gives an average characteristic of the scattering process from obstacles. Once the scattering cross-section is known, the actual scattered energy per unit length per second can be calculated by multiplying by the incident energy per unit area per second.     

Scattering from a coated nihility circular cylinder placed in chiral metamaterial

The scattering of electromagnetic plane wave from a coated nihility circular cylinder placed in chiral metamaterial is investigated. The nihility cylinder is coated with chiral or chiral-nihility metamaterial and the medium hosting the coated cylinder is also considered as chiral or chiral-nihility metamaterial. The vector wave equation is used to find out the solution for the fields scattered from the concentric chiral ciruclar cylinders immersed in chiral metamaterial. Inner chiral cylinder is reduced to nihility cylinder taking permittivity and permeability approaching to zero with chirality parameter equal to zero. Coated perfect electric conductor (PEC)/perfect magnetic conductor (PMC) are obtained by taking very large value of permittivity/permeability of the inner cylinder. Numerical results for fields reflected from coated nihility cylinder are compared with those obtained for coated PEC/PMC cylinder. Our results for the special case of dielectric coated nihility/PEC cylinders in free space are shown to be in agreement with already published results thus validating the scheme of analysis.     

Transient scattering by a circular cylinder

The scattering of transient plane waves by a circular cylinder is studied by using the Kirchhoff time-retarded potential boundary integral equation method. Two distinct problems are solved: (i) surface velocity potentials (or pressures) are found for rigid cylinders scattering ramp, ramp-step and Gaussian incident potential (or pressure) waves and (ii) surface velocities are found for free boundary (pressure release) cylinders scattering ramp, ramp-step and Gaussian incident velocity waves. The numerical schemes for both boundary conditions are very similar; since the same influence coefficients are used they differ only by a sign in the final formulation. Numerical results are readily obtained for the first few transit times. This approach is complementary to the usual modal approach in that it is best suited to early time values where the modal solutions converge most slowly.     

Scattering matrices of Lamb waves at irregular surface and void defects

Time-harmonic solution of Lamb wave scattering in a plane-strain waveguide with irregular thickness is investigated based on stair-step discretization and stepwise mode matching. The transfer relations of the transmission matrices and reflection matrices are derived in both directions of the waveguide. With these, an explicit expression of the scattering matrix is derived. When the scattering region of an inner irregular defect is geometrically divided into several parts composed of sub-waveguides with variable thicknesses and void regions with vertical free edges corresponding to the plate surfaces, the scattering matrix of the whole region could then be derived by modal matching along the artificial boundaries, as explicit functions of all the scattering matrices of the sub-waveguides and reflection matrices of the free edges. The effectiveness of the formulation is examined by numerical examples; the calculated scattering coefficients are in good accordance with those obtained from numerical simulation models.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Scattering of elastic waves by multiple elastic circular cylinders with imperfect interface

In the current paper a general method is presented for the rigorous solution for the scattering of elastic waves by a cluster of elastic circular cylinders of infinite length. The interface separating the cylinder from the surrounding media is considered to be homogeneous imperfect. Specifically, the tractions are continuous but the displacements are discontinuous and proportional in terms of interface stiffness parameters to their respective traction components. Using the exact theory of multipole expansion, analytic solutions for the scattered and internal fields excited by an incident plane P-wave, an incident cylindrical P-wave and an incident plane SV-wave are derived.

Numerical results for directivity patterns and scattering cross-sections are presented for a finite hexagonal array of elastic circular inclusions with imperfect interface. The results show that the sequence of maxima and minima in the curves of scattered cross-sections becomes more undistinguishable as the interface becomes more imperfect. Also, the results reveal that large low-frequency peaks of the scattered cross-sections, which correspond to resonance scattering, can be observed for both the low-velocity and high-velocity elastic cylinders with extremely imperfect interface while the small high-frequency peaks of the scattered cross-sections can appear for low-velocity elastic cylinders with relatively perfect interface. Furthermore, the results clearly show that the interaction effects between cylinders cannot be ignored for an incident plane SV-wave as compared to an incident plane P-wave. More importantly is the fact that the reciprocity relations, which hold for elastic wave scattering by a single cylinder, no longer apply for elastic wave scattering by multiple cylinders.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

Scattering of an arbitrarily oriented dipole field by an infinite and a finite length PEMC circular cylinder

Electromagnetic scattering from an infinite and a finite length PEMC circular cylinder, illuminated by an arbitrarily oriented dipole, is investigated theoretically. An electric dipole as a source of excitation is considered first, and then a magnetic dipole as a source of excitation is treated. In contrast to the case of an axially directed dipole, it is shown that no additional terms are needed to incorporate the cross-polarized component of the field for the case of radial and circumferential dipoles. Numerical verifications are presented to verify the validity of derived results and numerical code by comparing results with the published literature.      

Scattering by a homogeneous anisotropic-coated conducting elliptic cylinder

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a homogeneous anisotropic elliptical shell is obtained. The conducting elliptic cylinder and the shell have the same eccentricity. The transmitted and scattered fields of the anisotropic shell are expressed as Mathieu functions in elliptic coordinates. The unknown coefficients of the scattered and transmitted fields are solved with the aid of the boundary conditions and the Galerkin's method. Only the transverse magnetic (TM) polarization is presented and the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented and discussed. As expected the result is in agreement with that available when the coated elliptic cylinder degenerates to a coated circular one.     

Scattering characteristics of Lamb waves from debondings at structural features in composite laminates

This article investigates the scattering characteristics of Lamb waves from a debonding at a structural feature in a composite laminate. This study specifically focuses on the use of the low frequency fundamental antisymmetric (A(0)) Lamb wave as the incident wave for debonding detection. Three-dimensional finite element (FE) simulations and experimental measurements are used to investigate the scattering phenomena. Good agreement is obtained between the FE simulations and experimental results. Detailed parameter studies are carried out to further investigate the relationship between the scattering amplitudes and debonding sizes. The results show that the amplitude of the scattered A(0) Lamb wave is sensitive to the debonding size, which indicates the potential of using the low frequency A(0) Lamb wave as the interrogating wave for debonding detection and monitoring. The findings of the study provide improved physical insights into the scattering phenomena, which are important to further advance damage detection techniques and optimize transducer networks.