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.     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

Scattering and active acoustic control from a submerged piezoelectric-coupled orthotropic hollow cylinder

A general exact analysis for three-dimensional scattering of a time-harmonic plane-progressive sound wave obliquely incident upon an arbitrarily thick bilaminated circular hollow cylinder of infinite extent, which is composed of a cylindrically orthotropic axially polarized piezoelectric inner layer perfectly bonded to an orthotropic outer layer, is presented. An approximate laminate model in the context of the so-called state space formulation along with the classical T-matrix solution technique involving a system global transfer matrix is employed to solve for the unknown modal scattering and transmission coefficients. Numerical example is given for an air-filled and water-submerged two-layered elasto-piezoelectric hybrid (steel/PZT4) hollow cylinder insonified by an obliquely incident unit-amplitude plane sound wave. Following the acoustic resonance scattering theory (RST), the total form function amplitude together with the associated global scattering, the far-field inherent background, and the resonance scattering coefficients of the nth normal mode are computed as a function of dimensionless frequency for selected angles of incidence, piezoelectric layer thickness parameters, and electrical boundary conditions (i.e., open/closed circuit or active). Also, the electrical voltage coefficients required for partial or complete cancellation of the reflected sound field are calculated. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.     

Scattering of plane acoustic waves by a transversely isotropic cylindrical shell—application to material characterization

Scattering of obliquely incident plane acoustic wave by an air-filled, transversely isotropic cylindrical shell immersed in water is investigated theoretically and experimentally. The normal mode expansion technique is employed for analyzing the scattering field, and then resonance modes of the shell appearing in modal scattering form functions are identified performing the resonance scattering analysis. Dispersion curves for Sholte-Stoneley, SH and Lamb waves are obtained and their characteristics are interpreted. Calculated backscattering and resonance spectra as well as dispersion curves are compared with those from ultrasonic experiments for two composite samples having the same nominal composition but fabricated under different conditions. Sensitive change of the dispersion curves is observed for both normal and oblique incidences, which demonstrates the feasibility of systematic inverse evaluation of damage or elastic constants of the composite shell using data from the acoustic scattering measurements.     

Dynamic viscoelastic effects on sound wave scattering by an eccentric compound circular cylinder

The classical method of separation of variables in conjunction with the translational addition theorem for cylindrical wave functions are employed to obtain an exact solution for two-dimensional interaction of a harmonic plane acoustic wave with an infinitely long (visco)elastic circular cylinder which is eccentrically coated by another (visco)elastic material and is submerged in an ideal unbounded acoustic medium. The novel features of Havriliak-Negami model for dynamic viscoelastic material behaviour are used to take the rheological properties of the coating (and/or core) material into consideration. The analytical results are illustrated with numerical examples in which a steel rod eccentrically coated with (an eccentric steel shell filled with) dissipative materials of distinct viscoelastic properties is insonified by plane sound waves at selected angles of incidence. The effects of incident wave frequency, angle of incidence, core eccentricity and dynamic viscoelastic material properties on the backscattered form function spectra are examined. Limiting cases are considered and fair agreements with available solutions are obtained.     

On Multiple Scattering of Radiation by an Infinite Grating of Dielectric Circular Cylinders at Oblique Incidence

A rigorous analytical representation for the multiple scattering coefficients of the fields radiated by an infinite grating of dielectric circular cylinders excited by an obliquely incident plane electromagnetic wave is derived in terms of the “well-known scattering coefficients of an isolated dielectric cylinder at oblique incidence” and “Schl?milch series”. In addition, a generalized sum-integral grating equation is acquired for the multiple scattered amplitude of a cylinder at oblique incidence in the grating in terms of the scattering coefficients of the insulating dielectric circular cylinder at oblique incidence.      

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.     

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.     

Polarization characteristics of an electromagnetic wave scattered from a slightly random surface: +45° polarized incidence

Abstract

The present paper deals with the scattering of an obliquely polarized electromagnetic (EM) wave from a slightly rough surface, which is assumed to be a two-dimensional (2D), homogeneous and isotropic Gaussian random field. In contrast to the cases of TE(s) and TM(p) polarized incidence, the scattering profile for an obliquely polarized incidence is not symmetric with respect to the incident plane, despite the fact that the random surface is statistically isotropic.     

Theoretical and experimental validation of UTD applied to electromagetic-wave scattering by circular cylinders

The scattering of obliquely incident electromagnetic waves by a perfectly conducting circular cylinder is analyzed. In this paper the accuracy of a high-frequency asymptotic model based on the Uniform Theory of Diffraction (UTD) is investigated by comparing UTD simulations with results obtained from the exact eigenfunction solution for plane-wave incidence.UTD results are also compared with results from experiments carried out at 50 GHz, for various cylinder radii and for different linear wave polarizations. Excellent agreement between the measurement results and the theoretical ones is obtained.     

蒙特卡洛方法计算材料表面激发参数

电子非弹性散射平均自由程（IMFP）是用表面电子能谱进行表面化学定量分析时极为重要的一个参数,它可以用测量的弹性峰电子能谱分析以及蒙特卡洛模拟来确定.为了更加精确地确定电子非弹性散射平均自由程,必须对弹性峰电子能谱中的表面激发效应进行修正,通常使用介电响应理论方法计算得到的表面激发参数.然而,通过理论计算得到的表面激发参数不能包含电子在材料内部输运过程中弹性散射的影响,进而影响所测的电子非弹性散射平均自由程的准确度.在这个工作中,我们采用蒙特卡洛方法来确定包含弹性散射效应时的表面激发参数.所得到的表面激发参数在不同能量、角度情况下,尤其是在弹性散射效应显著的60°以上的大角度入射、出射情况下,都与实验测量值符合得非常好.基于这些新确定的表面激发参数,可以在弹性峰电子能谱测量中获得更为准确的电子非弹性散射平均自由程数据.     

两维位置灵敏探测器的能量和动量响应函数刻度

用弹性散射对多通道(e,2e)谱仪两维位置灵敏探测器的能量和动量响应函数进行了刻度,从位置灵敏探测器输出的两维位置信息中获得了弹性散射的能谱和角度谱,估计了在当前实验条件下的能量分辨和角度分辨.同时,我们用正交多项式的最小二乘法拟合得到了谱仪单路的能量和动量响应函数.     

Absorption of flexural waves by a pair of mechanical resonator chains mounted on a plate

The scattering of flexural waves by two chains of mechanical resonators characterized by effective admittances is considered. In the first (lower) chain, the effective admittance is represented by a susceptance, whereas, in the second (upper) chain, the resonators are characterized by a complex admittance. The spatial periods of the chains are identical. A plane harmonic flexural wave is obliquely incident on the upper chain, and the scattered field formed by the chains is expressed as a superposition of homogeneous and inhomogeneous Bragg spectra. Intense scattering of the incident wave only occurs in the case of mutual compensation of the resonator susceptance and the radiation admittance. A pair of chains with periods not exceeding the half-wavelength of the flexural wave represents an effective insulator for this wave. In the half-space behind the first chain, the zeroth spectral component of the scattered field completely cancels the resonance-frequency incident flexural wave. Let the second chain be positioned at one of the displacement antinodes of the total field formed by the incident field and the zeroth scattered spectrum. Then, if the active components of the effective admittance of resonators belonging to the second chain are identical to the radiation admittance, the incident flexural wave is completely absorbed by the resonators.     

Acoustic scattering from cylindrical shells: Guided waves and resonances of the liquid column

Recent studies of acoustic scattering have allowed the explanation of the existence of additional lines in the resonance spectrum of an elastic solid cylinder immersed in water by the examination of natural modes. A first group of natural modes, related to the propagation of the circumferential waves (Rayleigh, Whispering Gallery waves), is detected when the cylinder is insonified perpendicularly to its axis. A second group of natural modes related to the guided waves which propagate in the direction parallel to the axis of the cylinder is detected when it is insonified obliquely. In this Paper, the authors examine the acoustic scattering from cylindrical shells filled with a fluid (air or liquid) by the method of isolation and identification of resonances (MIIR). It allows resonance spectra to be obtained; in addition, the mode number, n, given by the identification, makes it possible to separate the resonances into different series. It is possible to explain the experimental resonance spectra of a liquid-filled tube insonified perpendicularly to its axis with a non-perfect directive transducer, by the calculation of the eigenfrequencies of the different parts of the target. The authors show the great importance of the guided waves along the axis and of the resonances of the liquid column when the shell is filled with a liquid. The resonance spectra of liquid-filled targets and the reradiation patterns giving by MIIR, i.e. after the end of excitation, are shown for the first time.     

Reflection and scattering from laser-irradiated solid targets at a wavelength of 0.44 μm

Studies of the reflectivity and spectral behaviour of the light scattered from plane solid targets irradiated with the third harmonic of the iodine laser (λ = 0.44 μm) in the intensity range 10¹² to 10¹⁵ W/cm² are reported. The complex spectra of the scattered light observed with normally and obliquely incident laser light provide evidence of stimulated scattering processes. The results are compared with current theories on stimulated Brillouin scattering.     

Acoustic scattering by an elastic elliptic cylinder in water: numerical results and experiments

The acoustic scattering from an elastic elliptic cylinder immersed in water and excited by a normally incident plane wave is considered in this paper. The purpose is to determine, theoretically and experimentally, the pressure scattered by this cylinder. A model based on the theory of elasticity is described briefly. It consists in carrying out expansions in Fourier series of the expressions relating to the conditions of continuity (displacements and constraints) at the surface of cylinder. These expressions form a system of equations. The resolution of this system enables us to obtain the scattering coefficient, then the pressure scattered by the cylinder. The numerical results obtained from this model are compared with experimental results obtained by means of an experimental short-pulse method presented in the literature. An good agreement between the results is noted.     

脉冲平面波斜入射旋转对称体电磁散射的FDTD算法

提出一种应用时域有限差分算法求解脉冲平面波斜入射时旋转对称体散射问题的方法.对斜入射脉冲平面波在圆柱坐标系下进行分解、应用总场/散射场连接边界、PML吸收边界条件.通过与矩量法分析结果的比较,验证了该方法的有效性.     

Diffraction of an obliquely incident wave beam by a rectangular aperture

The diffraction problem of an obliquely incident wave beam on a rectangular aperture can be reduced to that of normal incidence by expressing the incident wave beam in a form convenient for the discussion of the problem. In this paper the diffraction field is obtained by using this expression. The field is then expanded into a series of beam mode functions. The expansion coefficient of the series can be expressed in a simple form. A numerical example of the coefficient is shown for the diffraction by a half plane.     

Proton-proton elastic scattering and nucleon resonance production at high energies

Angular distributions of proton-proton elastic scattering have been measured for incident beam momenta of 10.0, 12.0, 14.2 and 24.0 GeV/c over a range of lab scattering angles from 12 to 152 mrad. This is equivalent to a range of four-momentum transfer squared from about 0.1 to 6.7 GeV² at the highest momentum. Nucleon resonance production in the two-body reaction p + p → p + X has been studied at 24.0 GeV/c incident momentum from 13.5 to 112 mrad by measuring the proton momentum spectra from the elastic peak down to a momentum corresponding to a missing mass of about 2.6 GeV. The new data are compared with previous results and theoretical models.