Acoustic radiation force of a solid elastic sphere immersed in a cylindrical cavity filled with ideal fluid

An expression for the acoustic radiation force function on a solid elastic spherical particle placed in an infinite rigid cylindrical cavity filled with an ideal fluid is deduced when the incident wave is a plane progressive wave propagated along the cylindrical axis. The acoustic radiation force of the spherical particle with different materials was computed to validate the theory. The simulation results demonstrate that the acoustic radiation force changes demonstrably because of the influence of the reflective acoustic wave from the cylindrical cavity. The sharp resonance peaks, which result from the resonance of the fluid-filled cylindrical cavity, appear at the same positions in the acoustic radiation force curve for the spherical particle with different radii and materials. Relative radius, which is the ratio of the sphere radius and the cylindrical cavity radius, has more influence on acoustic radiation force. Moreover, the negative radiation forces, which are opposite to the progressive directions of the plane wave, are observed at certain frequencies.     

刚性角隅内圆柱壳结构声辐射特性研究

本文对流场中处于刚性角隅内圆柱壳结构振动-声辐射问题进行研究．基于双反射方法，推导了位于两个垂直刚性壁面角隅区内圆柱壳结构的振动-声辐射方程．以此为基础，开展受线环向激励力作用的圆柱壳结构的振动-声辐射特性的数值计算．研究了刚性角隅内圆柱壳结构布置位置及计算频率对声辐射功率、声指向性的影响．计算结果可为分析含复杂声学边界的结构声振问题提供技术支持．     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Size Estimation of Fatigue Crack Appearing at Bolt Joints of Aluminum Alloy Plates by Synchronized SAW Measurement

The synchronized ultrasonic measurement with the surface acoustic wave (SAW) was carried out during the fatigue testing of bolted specimens of the aluminum alloy in synchronization with a fatigue cycle. The stationary SAW measurement was also carried out in the fatigue testing under pausing the fatigue tester at the mean load. In both measurements, the intensity of the scattered wave gradually increased with the number of fatigue cycles in the fretted region ahead of a bolt hole due to surface roughness, and the steep increment occurred following appearance and propagation of the fatigue crack. The steep increment was detected earlier in the synchronized measurement than that in the in-process measurement. In the synchronized SAW measurement, the intensity of the reflection from the fatigue crack increased with increasing stress level in the fatigue cycle. Then, the crack length was estimated with the intensity change of the reflection from the crack in the fatigue cycle following the Elber’s model modified by Suresh on the crack opening and closure following the stress intensity factor. The method developed in the present work shows the potential of the synchronized surface acoustic wave measurement as a tool for the early detectability of the fatigue crack as well as for the evaluation of crack opening/closure behavior in the bolted joint.     

基于电磁声激励Lamb波的裂纹深度检测

本文采用电磁声传感器接收单一S₀模态激励,测量Lamb波在板中不同深度的槽形裂纹处的反射与透射,用于对已知扩展长度的表面裂纹进行深度测量。然后分析了Lamb波模态的频散与波动特性,由超声Lamb波的波结构,近似计算了S₀模态入射到裂纹时的反射系数。计算结果与实验结果一致。结果表明,Lamb波在有限长裂纹处的反射系数可采用二维模型中的反射系数求解公式近似求解。采用电磁超声传感器接收单一S₀模态激励,重复测量稳定性高,适用于Lamb波反射系数的测量。Lamb波的反射系数与裂纹深度有很好的对应关系,可用于板表面已知长度裂纹的深度测量。     

Acoustic radiation force on a rigid cylinder in an off-axis Gaussian beam near an impedance boundary

The exact equations of the axial and transverse acoustic radiation force functions of a Gaussian beam arbitrarily incident on an infinite rigid cylinder close to an impedance boundary and immersed in an ideal fluid are deduced by expressing the incident wave, the scattering wave and the boundary reflected wave in terms of the cylindrical wave function. The effects of the beam waist, the sound reflection coefficient, the cylinder position and the distance from the impedance boundary on the acoustic radiation force are studied using numerical simulations. The simulation results show that the amplitude of the acoustic radiation force function increases with beam width. Moreover, the values of the acoustic radiation force in both the axial and transverse directions reach those of a plane wave when the beam width is considerably larger than the wavelength of the Gaussian beam. The properties of the impedance boundary and the position of the cylinder in the Gaussian beam have a considerable effect on the magnitude and direction of the force. The simulation results, particularly in the case of a transverse force, indicate the presence of a negative acoustic radiation force that is related to the nondimensional frequency and position of the cylinder in the Gaussian beam.     

Scattering of pulsed Rayleigh surface waves by a cylindrical cavity

A pulsed Rayleigh surface wave of prescribed shape is incident on a cylindrical cavity which is parallel to both the plane free surface and the plane wave front. Multiple reflections at the cylindrical and plane free surface are considered and the resulting displacements and stress components are calculated in the surrounding of the cavity by approximately summing infinite double sums. Use is made of the stationary loading case simulated by a periodic train of wave pulses and its time Fourier series representation and of expansions of all incident and reflected waves in terms of cylindrical wave functions. For reflection, the free surface of the half-space is approximated by a fictitious convex (or concave) cylindrical surface of “large” radius. The wave pattern due to a single pulse loading is constructed from the stationary solution by enforcing homogeneous initial conditions in the half-space ahead of the single loading pulse and by prescribing a wide spacing in the periodically set-forth train of pulses. The numerical results for stresses and dynamic stress magnification factors are especially useful for the interpretation of recent measurements in dynamic photoelasticity.     

Asymptotic modeling of Helmholtz resonators including thermoviscous effects

We systematically employ the method of matched asymptotic expansions to model Helmholtz resonators, with thermoviscous effects incorporated starting from first principles and with the lumped parameters characterizing the neck and cavity geometries precisely defined and provided explicitly for a wide range of geometries. With an eye towards modeling acoustic metasurfaces, we consider resonators embedded in a rigid surface, each resonator consisting of an arbitrarily shaped cavity connected to the external half-space by a small cylindrical neck. The bulk of the analysis is devoted to the problem where a single resonator is subjected to a normally incident plane wave; the model is then extended using “Foldy’s method” to the case of multiple resonators subjected to an arbitrary incident field. As an illustration, we derive critical-coupling conditions for optimal and perfect absorption by a single resonator and a model metasurface, respectively.     

A Refined Asymptotic Model of Fluid-Structure Interaction in Scattering by Elastic Shells

A refined asymptotic model of fluid-structure interaction in scattering by elastic shells is proposed. The model takes into consideration transverse compression of a shell by a fluid and some other phenomena. As an illustration, scattering of a plane acoustic wave by a circular cylindrical shell is considered. Comparison of numerical data corresponding various approximate approaches is provided. This revised version was published online in July 2006 with corrections to the Cover Date.     

Cylindrical cavity expansion in compressible Mises and Tresca solids

The elastoplastic field induced by quasi-static expansion in steady-state plane-strain conditions of a pressurized cylindrical cavity (cylindrical cavitation) is investigated. Material behavior is modeled by Mises and Tresca large strain flow theories formulated as hypoelastic. Both models account for elastic-compressibility and allow for arbitrary strain-hardening (or softening). For the Mises solid analysis centers on the axially-hydrostatic assumption (axial stress coincides with hydrostatic stress) in conjunction with a controlled error method. Introducing an error control parameter we arrive at a single-parameter-dependent quadrature expression for cavitation pressure. Available results are recovered with particular values of that parameter, and an optimal value is defined such that the cavitation pressure is predicted with high accuracy. For the Tresca solid we obtain an elegant solution with the standard model when no corner develops in the yield surface. Under certain conditions however a corner zone exists near the cavity and the solution is accordingly modified revealing a slight difference in cavitation pressure. Comparison with numerical solutions suggests that the present study establishes cylindrical cavitation analysis on equal footing with existing studies for spherical cavitation.     

Application of the reciprocity theorem to scattering of surface waves by a cavity

Scattering of surface waves by a cylindrical cavity at the surface of a homogenous, isotropic, linearly elastic half-space is analyzed in this paper. In the usual manner, the scattered field is shown to be equivalent to the radiation from a distribution of tractions, obtained from the incident wave on the surface of the cavity. For the approximation used in this paper, these tractions are shifted to tractions applied to the projection of the cavity on the surface of the half-space. The radiation of surface waves from a normal and a tangential line load, recently determined by the use of the reciprocity theorem, is employed to obtain the field scattered by the cavity from the superposition of displacements due to the distributed surface tractions. The vertical displacement at some distance from the cavity is compared with the solution of the scattering problem obtained by the boundary element method (BEM) for various depths and widths of the cavity. Comparisons between the analytical and BEM results are graphically displayed. The limitations of the approximate approach are discussed based on the comparisons with the BEM results.     

Hydroelastic analysis of gravity wave interaction with submerged horizontal flexible porous plate

The present study deals with the surface gravity wave interaction with submerged horizontal flexible porous plate under the assumption of small amplitude water wave theory and structural response. The flexible porous plate is modeled using the thin plate theory and wave past porous structure is based on the generalized porous wavemaker theory. The wave characteristics due to the interaction of gravity waves with submerged flexible porous structure are studied by analyzing the complex dispersion relation using contour plots. Three different problems such as (i) wave scattering by a submerged flexible porous plate, (ii) wave trapping by submerged flexible porous plate placed at a finite distance from a rigid wall and (iii) wave reflection by a rigid wall in the presence of a submerged flexible porous plate are analyzed. The role of flexible porous plate in attenuating wave height and creating a tranquility zone is studied by analyzing the reflection, transmission and dissipation coefficients for various wave and structural parameters such as angle of incidence, depth of submergence, plate length, compression force and structural flexibility. In the case of wave trapping, the optimum distance between the porous plate and rigid wall for wave reflection is analyzed in different cases. In addition, effects of various physical parameters on free surface elevation, plate deflection, wave load on the plate and rigid wall are studied. The present approach can be extended to deal with acoustic wave interaction with flexible porous plates.     

Analytical extension of Finite Element solution for computing the nonlinear far field of ultrasonic waves scattered by a closed crack

Nonlinear scattering of ultrasonic waves by closed cracks subject to contact acoustic nonlinearity (CAN) is determined using a 2D Finite Element (FE) coupled with an analytical approach. The FE model, which includes unilateral contact with Coulomb friction to account for contact between crack faces, provides the near-field solution for the interaction between in-plane elastic waves and a crack of different orientations. The numerical solution is then analytically extended in the far-field based on a frequency domain near-to-far field transformation technique, yielding directivity patterns for all linear and nonlinear components of the scattered waves. The proposed method is demonstrated by application to two nonlinear acoustic problems in the case of tone-burst excitations: first, the scattering of higher harmonics resulting from the interaction with a closed crack of various orientations, and second, the scattering of the longitudinal wave resulting from the nonlinear interaction between two shear waves and a closed crack. The analysis of the directivity patterns enables us to identify the characteristics of the nonlinear scattering from a closed crack, which provides essential understanding in order to optimize and apply nonlinear acoustic NDT methods.     

Nonstationary shock reflection over nonstraight surfaces: an approach with a method of multiple steps

Shock reflection phenomena over nonstraight surfaces have been investigated. The models used in this experiment are ordinary circular cylindrical concave and convex wedges and step-like wedges which simulate the former. The step-like wedges were used to investigate the process of reflected-wave formation over circular cylindrical wedges (method of multiple steps). The reflected-wave structure has been photographed with a schlieren apparatus. The formation of the reflected wave over circular cylindrical wedges is physically well understood by comparing it with shock reflection over step-like wedges. In particular, the reason why the reflected wave over a concave circular cylindrical wedge is very weak away from the reflection point is elucidated. Moreover, the structure and the formation mechanism of the so-called transitioned regular reflection (TRR) are illustrated in detail. As a by-product, based on acoustic theory, analytical formulae for the transition wedge angle are found. They are in good agreement with experiments. Received Received 28 February 1996 / Accepted 7 August 1996     

Acoustic scattering from baffled membranes that are backed by elastic cavities

An elastic membrane backed by a fluid-filled cavity in an elastic body is set into an infinite plane baffle. A time harmonic wave propagating in the acoustic fluid in the upper half-space is incident on the plane. It is assumed that the densities of this fluid and the fluid inside the cavity are small compared with the densities of the membrane and of the elastic walls of the cavity, thus defining a small parameter . Asymptotic expansions of the solution of this scattering problem as →0, that are uniform in the wave number k of the incident wave, are obtained using the method of matched asymptotic expansions. When the frequency of the incident wave is bounded away from the resonant frequencies of the membrane, the cavity fluid, and the elastic body, the resultant wave is a small perturbation (the “outer expansion”) of the specularly reflected wave from a completely rigid plane. However, when the incident wave frequency is near a resonant frequency (the “inner expansion”) then the scattered wave results from the interaction of the acoustic fluid with the membrane, the membrane with the cavity fluid, and finally the cavity fluid with the elastic body, and the resulting scattered field may be “large”. The cavity backed membrane (CBM) was previously analyzed for a rigid cavity wall. In this paper, we study the effects of the elastic cavity walls on modifying the response of the CBM. For incident frequencies near the membrane resonant frequencies, the elasticity of the cavity gives only a higher order (in ) correction to the scattered field. However, near a cavity fluid resonant frequency, and, of course, near an elastic body resonant frequency the elasticity contributes to the scattered field. The method is applied to the two dimensional problem of an infinite strip membrane backed by an infinitely long rectangular cavity. The cavity is formed by two infinitely long rectangular elastic solids. We speculate on the possible significance of the results with respect to viscoelastic membranes and viscoelastic instead of elastic cavity walls for surface sound absorbers.     

弹性波绕任意形状界面孔的散射

求解了弹性波绕任意形状界面孔的散射问题．通过入射波、反射波或折射波及孔的散射波场的叠加,得到了界面孔在SH波绕射下的总波场．总波场波函数的级数项待定系数可采用边界配点法来确定,该法不受边界正交性的限制,能够适用于任意形状的边界．最后,对界面椭圆孔进行了实例计算,得到了椭圆孔边的动应力集中系数．     

Scattering of guided waves by circumferential cracks in composite cylinders

A somewhat generalized numerical procedure is used in this paper to study the problem of wave scattering by circumferential cracks in composite pipes. The study is motivated by the need to develop a model for the quantitative, ultrasonic non-destructive evaluation of cracks in pipes. For this purpose, a stiffness-based Rayleigh–Ritz type approach is employed first to obtain the approximate wave numbers and wave modes. Using the wave function expansions of the incident and scattered fields in the axial direction and decomposing the problem into separate symmetric and anti-symmetric problems, a three-dimensional wave scattering problem is reduced to two, independent two-dimensional problems over the circular cross-section. Both these problems can be reduced further to quasi-one-dimensions by discretizing the cross-section into finite elements and using a transfer matrix approach in the circumferential direction. This simplification greatly reduces the computational time. A comparison of the results for an isotropic pipe demonstrates the reliability and accuracy of the modified numerical procedure. Numerical results for the reflection and transmission coefficients of different incident wave modes are also presented for a 2-ply composite pipe with a crack. The crack may have an arbitrary circumferential length and radial depth. Simple extrapolations from one wave to another wave, separately incident on a crack, are demonstrated to be impossible due to different mode conversions by the crack.     

Dynamic interaction of an eccentric multipole cylindrical radiator suspended in a fluid-filled borehole within a poroelastic formation

Acoustic radiation and the dynamic field induced by a cylindrical source of infinite extent, undergoing angularly periodic and axially-dependent harmonic surface vibrations, while eccentrically suspended in a fluid-filled cylindrical cavity embedded within a fluid-saturated porous elastic formation, are analyzed in an exact manner. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation, is of practical importance with a multitude of possible applications in seismo-acoustics. The formulation utilizes the novel features of Biot dynamic theory of poroelasticity along with the translational addition theorem for cylindrical wave functions to obtain a closed-form series solution. The basic dynamic field quantities such as the resistive and the reactive components of the modal acoustic radiation impedance load on the source in addition to the radial and transverse stresses induced in the surrounding formation by an eccentric pulsating/oscillating cylinder in a water-filled borehole within a water-saturated Ridgefield sandstone medium are evaluated and discussed. Special attention is paid to the effects of source eccentricity, excitation frequency, and mode of surface oscillations on the modal impedance values and the dynamic stresses. Limiting cases are considered and good agreements with available solutions are obtained.     

SH波绕界面孔的散射

用波函数展开方法研究了SH波绕界面孔的散射问题。由入射、反射和透射波组成的自由波场与孔的散射场叠加成总波场。按照一定方式将两个半平面散射波场延拓于全平面，通过Hankel-Fourier展开方法求得了任意形状孔散射场的级数解。以椭圆形孔为例计算了孔边缘的动应力集中系数。     

The low frequency scatter of SH waves by a rough interface in an elastic plate

The study of the reflection and transmission of low frequency SH waves incident upon a rough interface in an elastic plate is undertaken by employing a theory of acoustic wave scattering from rough surfaces originally due to Biot and subsequently generalised to the case of elastic media. In this theory the interface is replaced by a distribution of voids/asperities whose individual size is small compared to the excitation wavelength. We plot the absolute values of the reflection and transmission coefficients versus frequency when a single symmetric SH plate mode is used as the input excitation. The different types of inclusions are used to simulate the rough surface are the hollow, fluid filled and aluminum spheres. Lastly, the loss of energy due to scattering is also estimated for the different inclusion distributions considered.