Leaky helical flexural wave backscattering contributions from tilted water-filled cylindrical shells

Helical flexural waves on a bluntly truncated tilted water-filled cylindrical steel shell in water are found to give large contributions to the backscattering above the coincidence frequency. The presence of the water inside the shell increases the damping of the leaky wave when short tone bursts are used. The magnitude of the scattering is found by modifying a ray analysis developed for empty shells. When longer bursts are used, some of the internally radiated energy (corresponding to the case of one internal chord) is superposed on the ordinary helical ray backscattering. This occurs as a consequence of the internal excitation of helical rays.     

Backscattering of transients by tilted truncated cylindrical shells: time-frequency identification of ray contributions from measurements

Impulse backscattering measurements by a thick-walled finite cylindrical shell are examined in the time-frequency domain to identify and characterize individual ray contributions from generalized Lamb waves excited on the shell. Previous experiments and analysis in the frequency-aspect angle domain [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)] indicate that large backscattering enhancements occur in the midfrequency region for the shell tilted at large angles. Presently this experimental data is examined in the time-frequency domain for selected angles of incidence. Individual ray contributions are evident and their evolution over aspect angle is discussed. The most prominent contribution is due to the meridional ray of the a0 leaky Lamb wave. This feature distinctly highlights the truncation of the shell and is found over a range of aspect angles spanning 200 degrees for the frequencies examined. Also observed are periodic features corresponding to end-reflected helical waves of the a0-. These scattering features are significantly different from those reported for thin-walled finite cylinders at low frequencies. The present results may be useful for target identification and localization and as a comparison tool for high-frequency computational scattering models.     

Meridional ray backscattering enhancements for empty truncated tilted cylindrical shells: measurements,ray model,and effects of a mode threshold

Narrow-band backscattering experiments are used to characterize a meridional ray enhancement on a tilted, finite empty cylindrical shell having a blunt truncation. The meridional ray of the lowest order flexural leaky Lamb wave is examined, which has previously been shown to lead to large backscattering enhancements for excitation frequencies near and above the shell's coincidence frequency. The measurements are used to validate a convolution formulation ray theory describing the far-field backscattered amplitudes. Comparisons are also made with an approximate partial wave series solution for the finite cylindrical shell. The amplitude of the meridional ray enhancement is dependent on the nature of the reflection of the leaky wave from the shell truncation. While the peak measured amplitude agrees with predictions at low frequencies, experiments indicate the enhancement is degraded at high frequencies and exhibits an abrupt drop near the frequency of the mode threshold (cutoff) for the next-highest flexural mode. The nature of the leaky wave end reflection is examined using an approximate calculation of the energy reflection coefficient for leaky waves on a semi-infinite free plate. Results suggest the observed degradation is the result of mode conversion effects.     

Leaky helical flexural wave scattering contributions from tilted cylindrical shells: ray theory and wave-vector anisotropy.

At sufficiently high frequencies, cylindrical shells support a wave whose properties are analogous to those of the lowest antisymmetric Lamb wave on plates. When the shell is in water and the frequency exceeds the coincidence frequency, the flexural wave is a leaky wave that can be a major contributor to the scattering by tilted shells [G. Kaduchak, C. M. Wassmuth, and C. M. Loeffler, J. Acoust. Soc. Am. 100, 64-71 (1996)]. While the meridional ray-scattering contributions for such leaky flexural waves were previously modeled, the helical contribution can also be significant. A ray theory for those contributions is compared with the exact partial wave series (PWS) solution for infinitely long empty shells. The agreement between the ray theory and the PWS is only possible when a weak anisotropy of the flexural wave parameters is included in the evaluation of the ray theory. The anisotropy is determined numerically from the roots of a denominator in the PWS because approximations for the anisotropy from thin-shell mechanics are not applicable significantly above the coincidence frequency.     

Backscattering enhancements for tilted solid plastic cylinders in water due to the caustic merging transition: observations and theory

Bulk shear and longitudinal waves give rise to important contributions to the scattering of ultrasound by tilted finite plastic and rubber cylinders in water. This occurs in situations where either the shear or longitudinal speed is less than the speed of sound in the surrounding water. At a certain critical tilt angle, large backscattering enhancements are observed for finite cylinders, where the wave vector can reverse direction upon reflection from the cylinder truncation. The scattering process is analogous to the enhancement produced by the merging of rainbow caustics of primary rainbow rays in the scattering of light by long dielectric cylinders, also known as the caustic merging transition [C. M. Mount, D. B. Thiessen, and P. L. Marston, Appl. Opt. 37, 1534-1539 (1998)]. A ray theory was developed to model the backscattering mechanism at the critical tilt angle. It employs the idea of the Bravais effective refractive index, convenient for constructing ray diagrams for the projections of rays in the base plane of the cylinder. There is general agreement between the theory and the experiment down to relatively low ultrasonic frequencies (ka as small as 10). The enhancement is the most significant backscattering contribution for a wide range of tilt angles.     

Backscattering enhancements from Rayleigh waves on the flat face of a tilted solid cylinder in water

When the face of a finite solid elastic cylinder is ensonified by an acoustic wave, a variety of backscattering contributions associated with acoustic wave coupling into elastic waves are observed. A significant backscattering enhancement is observed for tilts such that the acoustic wave is incident on the face of the cylinder in the vicinity of the coupling angle for launching Rayleigh waves across the face. The observed backscattering indicates that the Rayleigh waves are reflected at the edge of the face and subsequently radiate acoustic waves in the backscattering direction. The measured backscattering is compared to an approximate theoretical prediction. Approximating the focusing of the Rayleigh wave after reflection at the (circular) edge by a Gaussian beam pressure distribution on the cylinder's face yields simple expressions for the amplitude which are consistent with the measurements. In the vicinity of end-on incidence, other backscattering contributions due to the reflection of waves traveling down the length of the cylinder are observed. There is also evidence of a face-traversing longitudinal wave for slightly tilted cylinders.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Acoustic backscattering enhancements resulting from the interaction of an obliquely incident plane wave with an infinite cylinder

Background and objective

The analysis of the acoustic backscattering enhancements from tilted cylinders is of particular importance in determining some of the (visco)elastic properties of the cylinder, and/or its surrounding fluid in ultrasonic non-destructive evaluation (NDE) and imaging (NDI) applications. Previous related investigations on an aluminum cylinder limited to incidence angles varying from 0° to 40°, revealed the existence of an anomalous “pseudo-Rayleigh” mode (above the critical Rayleigh angle) identified as the rigid-body translational dipole (n = 1) mode. The objective here is to provide a complete investigation on the backscattering enhancements for incidence angles larger than 40° for various elastic and viscoelastic cylinder materials.

Method

Using the partial-wave series solution for the linear scattering by an infinite circular cylinder, the acoustic backscattering from isotropic elastic and viscoelastic (polymer-type) cylinders excited by an obliquely incident plane acoustic wave is investigated. Total and resonance backscattering form functions are calculated for several elastic and viscoelastic cylinder materials immersed in water versus the angle of incidence 0° ? α < 90°. The “pure” resonance peaks are isolated by subtracting a rigid background from the total form function, so the associated resonance modes are properly identified.

Results and conclusion

The plots of the partial-wave series reveal acoustic backscattering enhancements (not shown in previous investigations) generally occurring at ka? 0.1 at a critical angle α_c bounded by the longitudinal and shear waves coupling angles θ_L=sin^-1(c/c_L) and θ_S=sin^-1(c/c_S) such that θ_L<α_c<θ_S (where c_L and c_S are the phase velocities of the longitudinal and shear waves inside the elastic cylinder, and c is the speed of sound in the surrounding medium). It is shown here that the backscattering enhancements with a critical angle θ_L<α_c<θ_S result from the excitation of the monopole (n = 0) resonance mode. Moreover, additional acoustic backscattering enhancements still occur in the range 1 ?ka? 6 even though the angle of tilt is greater than the Rayleigh wave coupling angle θ_R=sin^-1(c/c_R) (where c_R is the Rayleigh wave velocity in an elastic half-space). The resonance scattering theory shows that such additional enhancements are associated with the excitation of a dipole (n = 1) resonance mode which may result from the interference of meridional and/or helical waves propagating along the cylinder’s surface. It is therefore essential to consider tilt angles ranging from normal to end-on incidence for a complete analysis of the backscattering by elastic and viscoelastic cylinders.     

周向重叠三分螺旋折流板换热器壳侧性能试验研究

对倾斜角为20°、24°、28°和32°的单头以及32°的双头周向重叠三分螺旋折流板换热器和弓形折流板换热器的传热和压降性能进行了测试,换热器采用公共壳体和可更换管芯结构。采用壳侧轴向雷诺数和轴向欧拉数分别作为反映壳侧流量和阻力系数的无因次参数。试验结果显示在试验范围内周向重叠三分螺旋折流板换热器壳侧换热系数、壳侧压降和综合性能指标都随着倾斜角增大而减小;倾斜角20°方案的性能指标最佳,其平均壳侧努塞尔数和轴向欧拉数与弓形折流板方案的数值之比分别为1.123和0.45;双头螺旋折流板方案的换热系数和压降都大于同样倾斜角的单头螺旋折流板方案,但两者的综合性能较接近。     

充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

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

I.IntroductionTheResonanceScattcringThcory(RST)asanimportantmethodtoana1yzeacousticscat-teringofsubmergede1asticbodieswascxtcnsivelyuscdforcy1indrica1andspherica1geometries,inc1udingsolidstructuresandho11owoncs.RSTismain1yappliedtostudytheresonancescat-teringspcctra(oracousticspcctra)ofanc1astictargctcxcitedby'theinciderttacousticwavesoastOidentifythetargct.Tocxtracttheresonancescattcringspcctra,anappropriatebackgroundsuchasrigidbackgroundorsoftonemust-besubtractcd.Expcrimenta1ly,theReson…     

Contribution of steep irregularities to the radio-brightness temperature of the ocean

We propose a new mechanism of a change in the brightness temperature of the ocean due to the contribution from steep mesoscale waves and estimate the contribution of such waves to the brightness temperature of the ocean. A steep wave is simulated by an inclined surface. The estimates show that variations in the radio-brightness temperature due to steep irregularities can reach several kelvins at low grazing angles. For short observation distances and low grazing angles, the brightness temperature has bursts similar to those observed in the case of backscattering. These bursts occur when breaking waves hit the observation area. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 3, pp. 217–223, March, 2000     

Negative group velocity Lamb waves on plates and applications to the scattering of sound by shells

Symmetric Lamb waves on plates exhibit anomalies for certain regions of frequency. The phase velocity appears to be double-valued [M. F. Werby and H. Uberall, J. Acoust. Soc. Am. 111, 2686-2691 (2002)] with one of the branches having a negative group velocity relative to the corresponding phase velocity. The classification of the symmetric plate modes for frequencies appearing to have a double-valued phase velocity is reviewed here. The complication of a double-valued velocity is avoided by examining mode orthogonality and the complex wave-number spectra. Various authors have noted an enhancement in the backscattering of sound by elastic shells in water that occurs for frequencies where symmetric leaky Lamb waves (generalized to case of a shell) have contra-directed group and phase velocities. The ray diagram for negative group velocity contributions to the scattering by shells [G. Kaduchak, D. H. Hughes, and P. L. Marston, J. Acoust. Soc. Am. 96, 3704-3714 (1994)] is unusual since for this type of mode the energy on the shell flows in the opposite direction of the wave vector. Circumnavigation of the shell is not required for the leaky ray to be backward directed.     

Enhanced and specular backscattering in random media

We study scalar waves probing a heterogeneous medium whose parameters are modeled in terms of a statistically isotropic random field. The medium is terminated by an oblique interface at one end (the bottom) and pressure release type boundary conditions at the other end (the top). The tilt of the bottom interface is relatively small so that the dominant contributions to the wave field are confined to a paraxial tube. This study generalizes the basic formulation in terms of Itô–Schrödinger equations in a one-dimensional deterministic background, describing the macrostructure, to one in which the background is more complicated. It provides the first step toward the analysis of scattered waves in general background media modulated by a random microstructure. We discuss in detail the enhanced backscattering phenomenon or weak localization in this setting, with a tilted interface imbedded in the random medium, and find that the backscattering cone does not depend on the tilt. We also find that the enhanced backscattering phenomenon is not affected by the replacement of a specular interface with a diffusive interface.     

Measurement of the absolute n p scattering differential cross section at 194 MeV

We describe a double-scattering experiment with a novel tagged neutron beam to measure differential cross sections for np backscattering to better than +/-2% absolute precision. The measurement focuses on angles and energies where the cross section magnitude and angle dependence constrain the charged pion-nucleon coupling constant, but existing data show serious discrepancies among themselves and with energy-dependent partial-wave analyses. The present results are in good accord with the partial-wave analyses, but deviate systematically from other recent measurements.     

Scattering from a ribbed finite cylindrical shell with internal axisymmetric oscillators

A theoretical formalism is elaborated to determine the acoustic field scattered from a finite cylindrical shell reinforced by a set of ribs with internal axisymmetric oscillators, the locations and properties of which can vary arbitrarily along the cylinder axis. Analytical expressions are derived for the scattered pressure and approximate expressions are proposed to calculate the backscattered field. Some applications have been carried out to investigate the problem of backscattering from a periodically ribbed finite cylindrical shell in the presence of rib aperiodicity or axisymmetric internal oscillators. The modifications of the main features associated with scattering from helical and Bloch-Floquet waves are examined and numerical results are presented with respect to the mean rib spacing and to the total mass of the internal structures.     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Nonresonant mechanism of scattering of electromagnetic waves by sea surface: Scattering by steep sharpened waves

We develop an asymptotic theory of nonresonant backscattering of electromagnetic waves in the X-band by the ocean surface. Small-height (5÷20 cm) breaking surface waves with sharpened edges are assumed to be the main cause of nonresonant scattering. Using the methods of physical optics and geometrical theory of diffraction, we calculate the contribution of breaking sharpened waves to the scattering cross section for two orthogonal polarizations of electromagnetic scattering. It is shown that the main contribution to the backscattering is from the mirror reflection from the leading edge of such a wave, and the sharpness of the wave edge leads to the fact that the backscattering cross section of horizontally polarized radiation can exceed that of the vertically polarized radiation. Institute for Space Research, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 42, No. 3, pp. 240–254, March 1999.     

Numerical analysis of bulk conical waves in anisotropic cylinders; application to stiffness tensor measurement

A point source-point receiver technique, based on laser generation and laser detection of acoustic waves, allows determination of mechanical properties of an anisotropic cylinder. The nature of the material and the geometry of the sample give a dispersive behaviour to the diffracted waves and make the acoustic signature difficult to interpret. To overpass the intricacies, wave fronts (conical waves in the volume and helical waves on the surface) are synthesized from signals provided by scanning the primitive line of the cylinder with a laser point source. In order to distinguish between direct bulk conical waves and other contributions in the acoustic response, some considerations on line surface waves and on reflected bulk conical waves are supplied. The identification of the stiffness tensor components, based on the inversion of the bulk waves phase velocities, is applied to signals simulated for a composite material.