Lamb waves propagation in elastic plane layers with a joint strip

The Lamb waves are used for the ultrasonic characterization of welds because of their relative long-range propagation. In this paper, a simplified model of a weld-strip between two identical semi-infinite elastic layers is investigated. The reflected and transmitted ultrasonic fields are expressed by modal series whose coefficients are obtained by application of orthogonality relation. Comparisons with solutions obtained by finite elements wave propagation simulations are made. The energy balance between the incident and the scattered waves is also used to verify the accuracy of the obtained modal amplitudes.     

Propagation properties of elastic waves in semi-infinite phononic crystals and related waveguides

The transmission and reflection coefficients of two-dimensional semi-infinite solid-solid phononic crystal systems and fluid-fluid phononic waveguide structures have been investigated. The numerical results show that the transmission spectra for longitudinally and transversally polarized incident waves are different, and the spectra of the transmission and reflection coefficients of the semi-infinite system agree well with the band structure. The numerical results show that when a guided wave incident, localized modes are excited, and different polarities have different coupling efficiencies with the incident guided wave. At the same time, far from the cutoff frequency, the guided wave couples out of semi-infinite waveguide highly efficiently.     

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.     

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.     

Numerical solutionsfor acoustic Rayleigh wave problems in anisotropic and layered media

A finite difference iterative formulation which has already been applied successfully to acoustic surface wave scattering problems in homogeneous and layered isotropic as well as non-linear media, is extended to cover Rayleigh type mode propagation in anisotropic materials. The transmission, reflection and conversion into bulk modes of Rayleigh waves are studied as a function of relative step height. The waves are incident normally at upward and downward step discontinuities formed by the sudden termination of an uniform aluminium layer on a semi-infinite fused quartz substrate. In terms of the severity of Rayleigh wave scattering, the layered upward step has the most drastic effects, followed by the layered downward and the homogeneous downward steps respectively. Rayleigh wave scattering at a break in a layered waveguide is discussed.     

Modal coupling in acoustic waveguides: planar discontinuities

A new derivation for a scattering matrix for reflection and transmission of higher order modes at the planar junction of two waveguides is presented. The derivation is extended to include finite junction wall impedance and offset waveguides. The resulting matrix equations are analyzed and the physical significance of the matrices is explained. As an example of the theory, analytical expressions for the coupling coefficients at a size change in a rectangular duct are developed and the resulting reflection and transmission coefficients are computed. The results should be of interest to the HVAC noise control community. The paper also shows the effects of modal truncation on the accuracy and convergence of the solution. It is shown that the proper selection of the ratio of the number of modes on either side of the discontinuity is related to the ratio of the characteristic sizes of the waveguides. Finally it is shown that at least one higher mode should be included for reasonable accuracy in the computation of plane wave reflection and transmission coefficients except at the very lowest frequencies.     

Truncating cylindrical wave modes in two-dimensional multiple scattering

When analyzing the two-dimensional multiple scattering of electromagnetic waves by cylinders, the incident, scattered, and transmitted fields need to be represented by infinite sums of cylindrical wave modes. These infinite sums need to be truncated to a finite limit in order to calculate the scattering matrix. The accuracy of the scattered field representation and the stability of the matrix inversion are both critically dependent on the truncation limit. The parameters involved in the scattering are analyzed to determine their effect on the upper and lower bounds of an appropriate modal truncation.     

弹性波斜入射声子晶体的缺陷模及其转型

推导出弹性波斜入射固-固掺杂结构声子晶体的转移矩阵和透射系数公式.计算固-固掺杂结构声子晶体中弹性波的透射系数.得到当横波斜入射时,透射波中横波的缺陷模随着入射角的增大而减弱,横波向纵波的转型随着入射角的增大而增强.当纵波斜入射时,透射波中纵波的缺陷模随着入射角的增大而减弱,纵波向横波的转型随着入射角的增大而增强.     

Modal decomposition method for modeling the interaction of Lamb waves with cracks

The interaction of the low-order antisymmetric (a0) and symmetric (s0) Lamb waves with vertical cracks in aluminum plates is studied. Two types of slots are considered: (a) internal crack symmetrical with respect to the middle plane of the plate and (b) opening crack. The modal decomposition method is used to predict the reflection and transmission coefficients and also the through-thickness displacement fields on both sides of slots of various heights. The model assumes strip plates and cracks, thus considering two-dimensional plane strain conditions. However, mode conversion (a0 into s0 and vice versa) that occurs for single opening cracks is considered. The energy balance is always calculated from the reflection and transmission coefficients, in order to check the validity of the results. These coefficients together with the through-thickness displacement fields are also compared to those predicted using a finite element code widely used in the past for modeling Lamb mode diffraction problems. Experiments are also made for measuring the reflection and transmission coefficients for incident a0 or s0 lamb modes on opening cracks, and compared to the numerical predictions.     

畸形波电磁散射特性分析及其特征识别标识的研究

针对弱非线性的Longuet-Higgins模型在模拟强非线性畸形波海面时所存在的问题,采用修正的相位调制法模拟一维畸形波时间、空间波面,该方法能够实现畸形波的定时定点生成,并且其波形既能保持目标谱的频谱结构,又能较大程度地满足波浪序列的统计特性.同时,基于改进的双尺度(TSM)法及时域有限差分法建立畸形波的电磁散射模型,经过相对平均偏差和均方根偏差误差分析后,基于TSM法研究分析了畸形波及其背景海面波的归一化雷达散射截面(NRCS)的计算结果.实验表明,合成孔径雷达成像中畸形波的NRCS比背景波要小,即畸形波的合成孔径雷达图像成像比背景波要灰暗,因此可以将NRCS作为畸形波的特征识别标识.通过分析研究不同极化方式、入射角、入射频率条件下畸形波与背景波面的电磁散射特性实验数据得出:当二者的NRCS差值大于-11.8 dB及以上时,即认为产生畸形波,这为实际的工程应用提供了参照标准.     

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.     

An analytical and experimental comparison of optimal actuator and error sensor location for vibration attenuation

Feedforward active control of the flexural waves in a single and L-shaped plate has been analytically and experimentally investigated. The plates are simply supported along two parallel edges, and free at the other two ends. Point forces were used to generate the primary and secondary plate excitations. The plate flexural displacement is described by a combination of a travelling wave solution and a modal expansion. The flexural wave coefficients were determined using the boundary conditions, continuity equations at the driving force locations, and continuity equations at the corner junction for the L-shaped plate. The control actuator and error sensor are optimally located in order to achieve the best control performance.     

On formulation of a transition matrix for electroporoelastic medium and application to analysis of scattered electroseismic wave

On the basis of Pride's theory (1994) which couples Biot's theory for poroelastic medium (1956) and Maxwell equations via flux/force transport equations, we extend Yeh et al. (2004) approach for poroelastic medium to develop a transition matrix for electroporoelastic medium. The transition matrix, which relates the coefficients of scattered waves to those of incident waves, is then derived through the application of Betti's third identity and the associated orthogonality conditions for the electroporoelastic medium. To illustrate the application, a simple case of the scattering problem of a spherical electroporoelastic inclusion, embedded within the surrounding electroporoelastic medium subjected to an incident plane compressional wave is considered.     

Wave propagation characteristics of helically orthotropic cylindrical shells and resonance emergence in scattered acoustic field. Part 1. Formulations

The method of wave function expansion is adopted to study the three dimensional scattering of a plane progressive harmonic acoustic wave incident upon an arbitrarily thick-walled helically filament-wound composite cylindrical shell submerged in and filled with compressible ideal fluids. An approximate laminate model in the context of the so-called state-space formulation is employed for the construction of T-matrix solution to solve for the unknown modal scattering coefficients. Considering the nonaxisymmetric wave propagation phenomenon in anisotropic cylindrical components and following the resonance scattering theory which determines the resonance and background scattering fields, the stimulated resonance frequencies of the shell are isolated and classified due to their fundamental mode of excitation, overtone and style of propagation along the cylindrical axis (i.e., clockwise or anticlockwise propagation around the shell) and are identified as the helically circumnavigating waves.     

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.     

平面电磁波在任意方向运动的介质-介质界面上的反射和透射

研究平面电磁波从一种介质入射到另一种以任意方向运动的介质时,在介质界面上发生的反射和透射现象,从Maxwell方程组、运动界面的边值关系和运动介质的本构关系出发,得到了反射波和透射波电磁场矢量与入射波电磁场矢量的关系的表达式、反射和透射系数,讨论了反射波、透射波与入射波之间的能量关系,电磁波对运动介质作用力的性质,并得出一些新的结论． 关键词：     

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.     

海面冰层对声波的反射和散射特性

北极海面冰层复杂多变,其对声波的反射和散射严重影响冰下水声信道的传输特性,建立海面冰层的声波反射和散射模型对冰下水声通信研究具有重要意义.假设海面冰层为多层固体弹性介质且冰-水界面粗糙,满足微扰边界条件,导出声波从海水介质入射到海面冰层时相干反射系数满足的线性方程组.对相干反射系数随声波频率、掠射角、冰层厚度的变化进行数值分析.进一步引入根据散射声场功率谱密度计算散射系数的方法,改变掠射角,对冰层厚度、散射掠角对散射系数的影响进行研究.     

固-固界面退化特性的超声反射评价方法

提出了一种基于有限宽超声束反射的固-固界面退化特性评价方法,从理论和数值仿真角度进行了分析和计算。将两固体界面间的薄层简化为界面弹簧模型,以界面法向和切向劲度系数表征界面的退化程度。通过数值计算求得有限宽超声纵波束在不同入射角和界面不同退化程度下的反射横波、反射纵波的镜面反射系数。进一步地,通过建立二维有限元模型,仿真研究了有限宽超声纵波束在给定入射角及界面不同退化程度下镜面反射系数的变化规律。结果表明,反射纵波和反射横波的镜面反射系数随有限宽超声纵波束的入射角及界面劲度系数的改变而变化,且存在镜面反射系数随界面劲度系数单调且敏感变化的入射角,据此可准确评价界面的退化程度。     

On the reflection of coupled Rayleigh-like waves at surface defects in plates

The reflection of coupled Rayleigh-like waves from surface defects in elastic plates is investigated experimentally and analyzed on the basis of an analytical model and finite difference simulations. The propagation of Rayleigh-like waves in plates is characterized by an energy transfer to the opposite plate side and back over a distance called the beat length. Experimental results clearly show this beating effect and its dependency on the frequency-thickness product, and excellent agreement is obtained with existing analytical predictions. The propagation and scattering are modeled separately for the fundamental A(0) and S(0) Lamb modes that constitute the incident Rayleigh-like wave. The reflection coefficients from surface slots are investigated using finite difference simulations and the reflected Rayleigh-like wave is obtained by superposition. The theoretical model reveals strong dependencies of the reflected field on the ratio between excitation distance and beat length and on the cutoff frequencies of specific higher Lamb modes. Standard pulse-echo measurements allow for the detection of small defects from a remote transducer location. Good agreement is obtained between the predicted and measured amplitude spectra of the reflected Rayleigh-like wave. The developed model allows for the evaluation of defect location and damaged plate side using a combination of time-of-flight and frequency measurements.