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.     

Leaky helical flexural wave backscattering contributions from tilted cylindrical shells in water: observations and modeling

For tilt angles smaller than the meridional ray coupling condition previously investigated [S. F. Morse et al., J. Acoust. Soc. Am. 103, 785-794 (1998)], flexural helical waves on cylindrical shells can significantly enhance the backscattering. These contributions are compared and modeled here for an empty cylinder. Experiments using tone bursts were performed on a tilted stainless steel shell to investigate the contributions caused by flexural leaky Lamb waves above the coincidence frequency of the shell. In some of the measurements the tone bursts were of sufficient duration to superpose helical wave contributions of successive circumnavigations, along with the meridional contribution near the critical tilt, to arrive at a quasi-steady-state backscattering amplitude for the cylinder. These measurements are compared with an approximate numerical partial-wave series solution and a ray theory as a function of the tilt angle. The data for ka = 20 follow the basic shape of the ray theory and the relevant features of the partial-wave model. They illustrate the importance of the interference of successive helical wave contributions. Measurements (also as a function of the tilt angle) using tone bursts that were sufficiently short to separate the earliest helical wave contribution from later contributions also support the ray theory.     

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.     

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.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

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.     

Coherent waves in a multiply scattering poro-elastic medium obeying Biot's theory

Twersky's theory is generalized to multiple scattering by a uniform random distribution of cylinders in a poro-elastic medium. The high-frequency regime only, where no dispersion effects occur in the absence of scatterers, is investigated in the frame of Biot's theory. The scatterers lie within a slab of the host medium, and an incident wave gives rise to a fast longitudinal coherent wave, a slow longitudinal one, as well as a shear one in the slab. The dispersion equations of those three coherent waves are derived. The shear coherent wave propagates independently of the other two, while the longitudinal coherent waves obey a coupled dispersion equation involving conversion terms. Numerically speaking, coupling effects are significant only when forward scattering by a single cylinder of the fast wave into the slow one (or the slow wave into the fast) is larger than forward scattering with no conversion.     

Scattering of electromagnetic wave from perfect electromagnetic conductor cylinders placed in un-magnetized isotropic plasma medium

The two dimensional analytical formulation of scattering of electromagnetic wave from a perfect electromagnetic conductor (PEMC) cylinder placed in un-magnetized isotropic plasma medium is presented. The extended classical scattering theory is used. The incident wave is taken as linearly polarized wave. The analytical theory is formulated for parallel polarization (TM) and also for perpendicular polarization (TE). The numerical computation results show that backscattering and forward scattering are sensitive to electron density and effective collision frequency of plasma medium. We placed different types of cylinders (PEC, PMC and PEMC) in un-magnetized plasma medium and concluded that stealth capability of plasma increases with the placement of PEMC cylinder in plasma medium.     

The influence of large-scale seafloor slope and average bottom sound speed on low-grazing-angle monostatic acoustic scattering

Variations in large-scale seafloor slope and average seabed sound speed account for a significant portion of the variations in scattering intensity observed in low-grazing-angle monostatic reverberation. Numerical modeling using a finite-difference solution to the elastic wave equation is used to quantify the effect of these large-scale parameters in interpretations of reverberation data. For hard rough seafloor (e.g., basalt), the results of the modeling suggest that the monostatic backscattering strength increases with increasing large-scale seafloor slope up to a slope of about 15 degrees dipping toward the incident direction. Once the grazing angle of the incident wavefield exceeds the critical grazing angle for the flat reference seafloor the backscattering intensity increases only slowly with increasing grazing angle. Similarly, average subseafloor sound speed has a significant effect. Seafloor with low sound speeds characteristic of soft bottoms (e.g., sediment) generate significantly weaker backscatter signals than seafloor with sound speeds characteristic of hard bottoms (e.g., basalt). The difference is that the shear waves can always be passed into soft bottoms because even for a flat seafloor there is no shear wave critical grazing angle.     

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…     

浅海小掠射角的海底界面声反向散射模型的简化

在浅海,尤其是负梯度声速剖面和海面较为平静的浅海波导,海底界面反向散射是浅海混响的主要来源.经验散射模型只适用于分析浅海混响平均强度衰减特性,而基于物理机理建立的反向散射模型克服了这一缺陷,但同时也引入了其受地声模型约束的问题.本文结合了海底反射系数的三参数模型,对浅海远场海底反向散射模型进行了简化,以减少地声模型的输入参数.理论分析了海底反射系数的相移参数可以描述海底对声场的散射作用,无需任何海底地声参数的先验知识.通过对海底反向散射模型近似简化,结果表明在临界角附近和甚小掠射角范围内的海底粗糙界面反向散射模型的角度特性和强度特性受海底沉积层的影响不同:在临界角附近,海底反向散射的角度特性受海底反射系数的相移参数加权,而其散射系数则近似与相移参数无关;对于甚小掠射角,海底反向散射的角度特性近似与海底反射系数的相移参数无关,其散射系数则近似与相移参数的4次方成正比.     

沙丘粗糙面的二次极化电磁散射

研究了新月形沙丘粗糙面的二次极化电磁散射. 结合射线追踪理论, 由一次散射面元的反射场照射到二次散射面元, 采用基尔霍夫近似推导了二次散射面元的二次极化散射场. 计算结果表明二次极化散射结果在特定的角度和类型范围内有显著影响. 在电磁波射向背风坡时可以发现其同极化散射截面在入射角较大时大于其他入射方向的结果, 入射角在休止角附近时的交叉极化散射截面出现峰值, 以及前后狭长沙丘之间的二次极化散射特别突出. 本文结果可用于反演分析沙漠地区的风场信息. 关键词： 新月形沙丘 二次极化散射 射线追踪 休止角     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.     

Free vibration of circular cylinders of variable thickness

Flexural vibrations of finite length circular cylinders with shear diaphragm ends and symmetric circumferential wall thickness variations are described by using the Rayleigh-Ritz method. Both symmetric and asymmetric solutions are presented. Only circumferential variations in the wall radial dimension are considered; the method is amenable, however, to consideration of longitudinal variations in wall thickness as well. The cylinder wall thickness variation is described as a Fourier series and the vibration is described as a series of modes of a uniform cylinder with the same mean radius. The theory has been applied to a cylinder whose inner bore is circular but is non-concentric with the circular outer surface. The mode shapes have been investigated experimentally by using time-averaged holograms of the vibrating cylinder and the results compare well with the predictions of the theory. The frequencies of the modes agree with the theoretical predictions to within 2%.     

水中微小波纹圆柱体声散射低频共振调控

塑料类高分子材料甲基丙烯酸甲酯-亚克力(PMMA)圆柱中亚音速Rayleigh波低频隧穿共振可引起反向散射增强,在低频标准散射体设计等领域具有重要应用价值.提出一种微弱形变的规则波纹表面结构,可实现水中PMMA圆柱反向散射低频共振频率的无源调控.利用微扰法推导了水中微弱形变规则波纹圆柱反向散射低频共振频率偏移的近似解,讨论了波纹微扰系数、周期对规则波纹圆柱共振频率偏移的影响规律.基于Rayleigh波相位匹配方法分析了低频共振频率偏移的机理.研究表明:微弱形变规则波纹圆柱中亚音速Rayleigh波沿微弱形变波纹表面传播,与光滑圆柱体相比,传播路径的改变引起Rayleigh波传播相位变化,导致了Rayleigh波低频共振频率发生偏移.最后开展了微弱形变规则波纹圆柱体声散射特性水池实验,获取了其反向散射共振频率,明显观察到了规则波纹圆柱共振频率偏移现象,与理论预报结果吻合较好.     

Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement

This paper Presents numerical simulations, theoretical analysis, and millimeter wave experiments for scattering from one-dimensional very rough surfaces. First, numerical simulations are used to investigate the effects of roughness spectrum, height variation, interface medium, polarization, and incident angle on the backscattering enhancement. The enhanced backscattering due to rough surface scattering is divided into two cases; the RMS height close to a wavelength and RMS slope close to unity, and RMS height much smaller than a wavelength with surface wave contributions. Results also show that the enhancement is sensitive to the roughness spectrum. Next, a theory based on the first- and second-order Kirchhoff approximation modified with angular and propagation shadowing is developed. The theoretical solutions provide a physical explanation of backscattering enhancement and agree well with the numerical results. In addition to the scattering of a monochromatic wave, the analytical results of the broadening and lateral spreading of a pulsed beam wave scattering from rough surfaces are also discussed. Finally, the existence of backscattering enhancement from one-dimensional very rough conducting surfaces with exact Gaussian statistics and Gaussian roughness spectrum is verified by a millimeter-wave experiment. Experimental results which show enhanced backscattering for both TE and TM polarizations for different angles of incidence are presented.     

椭圆柱体对任意入射极化的电磁波的散射

基于电磁场的多尺度变换理论,得到了以导体椭圆柱为例的电磁波任意极化,任意垂直入射到目标上的散射场的解析式.将所得结果应用于计算圆柱目标的散射场,结果与文献完全一致.对椭圆柱体的散射宽度随入射波方位角,电磁波频率以及目标尺寸的变化进行了仿真.结果表明,在垂直于电磁波的方向上观测时,椭圆柱的垂直尺寸对散射有较大的影响,电磁波水平极化时散射最强.所用算法适用于介质椭圆柱等目标的散射特性研究,所得结果为目标尺寸、形状遥感电磁测量等实际应用提供了理论依据.     

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。      

考虑界面状况时柱状弹性固体的声波散射

导出了求解母材料固体中镶嵌的柱状弹性固体(两固体间存在界面薄层)声波散射系数的一般表达式.根据Flax的共振散射理论,对背向散射谱中的共振模式进行了识别.利用模拟界面薄层的弹簧模型,考察了界面层切向劲度常数K_T对共振模式形态的影响 关键词： 声波散射 共振模式 界面     

串列双圆柱时均流场特性分析

对Re=12000,间距比L/D=1.167,2.333,3.500和4.667的串列双圆柱后方速度场进行了实验测量,分析串列双圆柱后方不同剖面处的速度分布规律和湍流度分布规律.并通过流函数理论模型对小间距比串列双圆柱后方流场进行了分析,得出如下结论:与单圆柱相比,当串列双圆柱间距比较小时,后方圆柱的自由剪切层明显向内...