Acoustical scattering by multilayer spherical elastic scatterer containing electrorheological layer

A computational procedure for analyzing acoustical scattering by multilayer concentric spherical scatterers having an arbitrary mixture of acoustic and elastic materials is proposed. The procedure is then used to analyze the scattering by a spherical scatterer consisting of a solid shell and a solid core encasing an electrorheological (ER) fluid layer, and the tunability in the scattering characteristics afforded by the ER layer is explored numerically. Tunable scatterers with two different ER fluids are analyzed. One, corn starch in peanut oil, shows that a significant increase in scattering cross-section is possible in moderate frequencies. Another, fine poly-methyl methacrylate (PMMA) beads in dodecane, shows only slight change in scattering cross-sections overall. But, when the shell is thin, a noticeable local resonance peak can appear near ka=1, and this resonance can be turned on or off by the external electric field.     

Parametric instabilities of a viscous liquid layer covered by a thin elastic plate under vertical periodic motion

Parametric instabilities of a horizontal liquid layer with a finite depth covered by a thin elastic plate under a vertical periodic motion are investigated with account taken of the viscosity of the liquid layer. The primary regions and the secondary ones of dynamic instabilities are determined by using the equation of a thin elastic plate including the normal component of the viscous stress, but not the tangential component of it. The critical amplitude of the imposed oscillation, beyond which a parametric instability occurs (that is, the neutral stability curves) is found in the space of the frequency and amplitude of the imposed vertical oscillation. These results are confirmed by experimental ones for a liquid layer of glycerine covered with a thin rubber plate.     

Rayleigh wave scattering from a vertical edge of isotropic substrates

The paper numerically studies the harmonic Rayleigh wave scattering at the 90-degree corner of isotropic substrate. The finite element method is used. The main attention is paid to two cases. The first one is the apex of the substrate corner is rounded off. The second one consists in that a layer of foreign material is deposited on the face which scatters the Rayleigh wave. The dependence of the reflection and the transmission coefficients on the Poisson ratio, the angle of incidence, the fillet radius, and the layer thickness are obtained. It is found that if the Rayleigh wave is incident perpendicularly to the substrate border, then the fillet of small radius as compared to the wavelength increases the reflection coefficient and decreases the transmission coefficient by factors 1.3–1.8. At normal incidence, the Poisson ratio does not change qualitatively the dependence of the reflection and transmission coefficients on the fillet radius. But the Poisson ratio can substantially affect the angle dependence of these coefficients if the wave is incident obliquely on the corner rounded off. It is also found out that a layer can modify the conditions of scattering such that the incident wave is totally reflected without transmission and conversion into bulk waves in a wide interval of angle of incidence, although, in principle, the bulk wave generation is allowed within a part of this angle interval.     

Resonance theory of elastic wave scattering from a cylindrical cavity

Resonant excitation of a fluid-filled cylindrical cavity in an elastic medium by an incident compressional wave is investigated on the basis of the resonance theory of nuclear scattering. It is shown that the scattering amplitude consists of a series of narrow resonances super-imposed upon, and interfering with, a broad background that corresponds to the scattering from an empty cavity. The resonances may be analyzed in a most enlightening fashion by studying them separately in each partial wave of the normal-mode series. They are seen to correspond to excitations of the eigenvibrations of the cavity fluid caused by a phase-match of “creeping waves”, similar to the “Regge poles” of nuclear physics.     

Generation of a single normal wave by a vertical linear array in the water layer

The possibility of the acoustic energy emission into a single normal wave by a vertical linear array in a homogeneous water layer is considered for the case of the array aperture being smaller than the layer thickness.     

Distorted wave eikonal approximation for elastic electron-atom scattering

By treating the static field of the atom exactly and using the eikonal wavefunction to bring in the couplings to all remaining atomic states, a simple formula for elastic scattering amplitude is derived. Its usefulness is demonstrated by applying it to electron—hydrogen scattering.     

Effects of interface energy on scattering of plane elastic wave by a nano-sized coated fiber

In the framework of surface elasticity theory, the scattering of plane compressional and shear waves by a single nano-sized coated fiber embedded in an elastic matrix is studied using the method of eigenfunction expansion. The dynamic stress concentration factors along the interface between the coated fiber and the matrix induced by the plane elastic wave and scattering cross section are derived and numerically evaluated. The interface stress, inhomogeneous material constants and thickness of the coated layer on the scattering of the elastic wave become much more important when the radius of the coated-fiber is reduced to the nanometer scale. These were confirmed by the use of numerical results. Our results can aid in understanding the dynamic mechanical properties of nano-composites. The proposed method has potential applications in the characterization of the interfacial layer that links reinforced fibers to their matrix.     

Mean-field T-matrix approach to elastic wave scattering by small and point-like objects

The T-matrix of a small inclusion embedded in a homogeneous matrix is calculated for vector elastic waves. The theory relies on an approximation of the local stress and momentum inside the inclusion by volumetric averages, which allows the summation of the full multiple-scattering series. The limiting case of a point scatterer is discussed. The mean-field T-matrix and its point limit both satisfy the elastodynamic version of the optical theorem. The accuracy of the results is discussed by comparison with some exact solutions for spheres. In particular, the mean-field T-matrix allows the approximate modeling of low-frequency resonances by small, high-contrast objects. The present theory could be applied to the multiple scattering of elastic waves by a collection of small or fuzzy resonant scatterers.     

Electromagnetic wave scattering from a random medium layer with a random interface

Abstract

The problem of electromagnetic wave scattering from a random medium layer with a random interface is considered. The layer has planar boundaries on average. Assuming that both the random perturbations of the interface and the random fluctuations of permittivity of the medium are small, a first-order perturbation solution to the scattered field is obtained. Using this solution, the bistatic scattering coefficients γ_αβ are calculated and expressed in a compact and meaningful form. The various terms that constitute γ_αβ are identified with distinct scattering processes. Since it is often of particular interest, the special case of backscattering is considered. Finally, the results are compared with those of others.     

Note on wave propagation through a periodic rectangular wave-guide containing ferrite slabs

Wave propagation through a rectangular wave-guide loaded with periodic ferrite slabs has been considered. Numerical computations for the ratio of amplitudes and the phase shift has been made for the first three harmonics only.I take this opportunity of thanking Dr. S. C.Dasgupta and Dr. S. S.Baral for suggesting this investigation and for their guidance in preparing this note. I also wish to express my gratitude to the C.S.I.R. for financial support as a Senior Research Fellow.     

Propagation of flexural wave in periodic beam on elastic foundations

The propagation properties of flexural wave in the periodic beam on elastic foundations are studied theoretically. The wavenumbers and traveling wave characteristics in the beam on elastic foundations are analyzed. Basing on the equations of motion, the complex band structures and frequency response function are calculated by the transfer matrix method. And the Bragg and locally resonant gaps properties and the effects are researched. A gap with low frequency and wide range can exist in a beam on elastic foundations.     

The scattering of waves by a periodic surface

The paper derives a general formula for the scattering of electromagnetic (or sound) waves from a periodic, perfectly conducting (or perfectly rigid) surface. No restrictions are imposed on the angle of incidence, the size of the surface or the degree of roughness. Except for the basic Kirchhoff approximation, the method is exact. The results confirm, generalise or correct special cases obtained by more complicated methods.

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Matching of asymptotic models in scattering of a plane acoustic wave by an elastic cylindrical shell

Scattering of a plane harmonic acoustic wave by an elastic cylindrical shell is considered. The procedure based on matching of asymptotic models is developed. The long-wave models (the Kirchhoff-Love theory (or its refinement) and the long-wave high-frequency approximation) are exploited in the vicinities of zero frequency and thickness resonance frequencies, whilst the model of a fluid-loaded flat elastic layer is utilized outside the aforementioned vicinities. Comparison with the exact solution demonstrates that the proposed approach is highly efficient for total synthesis of the scattered pressure as well as for uniform approximation of the resonant curves associated with partial modes.     

Pure elastic resonance scattering of an obliquely incident plane acoustic wave by a submerged infinite cylinder

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Intensities of fine-structure components due to light scattering at a transverse elastic wave

The splitting and intensity are estimated for the doublet produced by scattering of a light wave at hypersonic transverse shear vibrations in a liquid of high shear viscosity. It is shown that observation of the fine structure of the Rayleigh line at fairly high temperatures is prevented by the very small magnitude of the splitting and the strong damping of the transverse vibrations. The intensity of these components is very small at low temperatures, so they can be observed only with a source having very narrow and intense lines.     

Modified null field method for elastic wave scattering from a partially debonded fiber-SH-waves

Debonded fibers influence the macro-mechanical behavior of fiber-reinforced composite materials. Debonded fibers contribute to the initiation and growth of cracks at the fiber/matrix interface. To examine such problems, the scattering of elastic SH-waves (problem of anti-plane strain) from debonded fibers is studied with a numerical method which can handle the mixed boundary conditions on the partially bonded fiber. A modification of the null field of T-matrix method is developed for this purpose. The modification is achieved by the introduction of a mathematical surface. The simultaneous solution of the integral representations of the field scattered by the mathematical surface and the actual fiber surface give rise to sufficient equations that permit solution of the debonded fiber problem. The scattering cross-section and the far field amplitude are calculated as a function of frequency, fiber properties and debonding area. This will be of interest in structural applications where such cross-sections can be used to compute the dynamical effective properties of damaged composites.     

平面声波斜入射到水中无限长圆柱壳体的纯弹性共振散射

斜入射情况下水中弹性圆柱壳体的共振声散射问题至今还很少被研究。本文导出了平面声波斜入射时水中无限长圆柱壳体纯弹性共振散射函数的简单而明显的表达式。针对中空铝圆柱壳体(b/a=0.8)详细计算了不同入射角时纯弹性共振散射的分波共振谱,同时还给出了远场反向散射形态函数及其刚硬背景隔离,发现形态函数受吻合频率的影响很大。文中详细计算了斜入射时无固次复频率平面上的共振复极点分布,并由此计算了不同入射角时各阶共振模式,特别是附加共振模式所对应螺旋环绕波的相速度频散曲线。这些结果十分有助于认识声波斜入射下圆柱壳体的共振和再辐射的物理本质。