管桩屏障在柱面波源下近场隔振效应的解析求解

基于波函数展开法表示柱面波源自由场,首次提出了一种求解柱面波源下管桩屏障对弹性波隔振效应的解析方法。方法首先考虑柱面波源与管桩屏障的位置关系,采用波函数展开法对入射柱面波进行了0阶Hankel展开表示,并采用任意坐标系间变换的Graf加法定理在任意桩体坐标系中表示,将入射波场和散射波场叠加后通过满足所有桩体的边界条件以求解所有桩体的散射波场。该解析方法分析了柱面波源入射下群桩屏障的隔振效果,首次在排桩隔振问题中考虑了入射波曲率的影响,为柱面波的散射问题提供了理论解答。该文重点讨论了入射波曲率、管桩个数和桩排数等因素对管桩隔振效果的影响,结果表明：整体上管桩屏障对柱面P波的隔振效果优于柱面SV波;柱面波源距离管桩屏障更近时排桩后场地的位移反应显著增大;相比平面波,柱面波源作用下排桩数量的提升对隔振效果的影响较小;三排管桩屏障比两排管桩屏障隔振效果更强,更宜采用三排管桩屏障进行柱面波源的隔振。     

A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity

The theory of coupled plasma, thermal, and elastic waves was used to investigate the wave propagation on semiconductor material with cylindrical cavity during photo-thermoelastic process. An unbounded material, elastic semiconductor containing a cylindrical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of cavity is constrained, and the carrier density is photogenerated by an exponentially decaying pulse boundary heat flux. The eigenvalue approach, together with Laplace transform techniques, was used to obtain the analytical solutions. Numerical computations have been done for a silicon-like semiconductor material, and the results are presented graphically to estimate the effect of the coupling between the plasma, thermal, and elastic waves. The graphical results indicate that the thermal activation coupling parameter is an important phenomenon and has a great effect on the distribution of field quantities.     

带形介质内SH型导波对圆柱孔洞的动力分析

弹性板壳的反平面运动中由缺陷引起的应力集中问题可以按照带形介质中圆柱孔洞对SH型导波的散射问题来分析。首先,构造带形介质中相容导波的形式,即其满足上、下边界应力自由条件。之后,由波函数展开法给出圆柱孔洞散射波的级数表示,根据累次镜像叠加的方法构造由上、下边界反射所形成的相容的散射导波。最后,给定入射导波,由圆柱孔洞边界应力自由的条件来定解波函数级数的系数。数值算例求解了特定导波对圆柱孔洞的散射,给出了圆柱孔洞边沿的动应力分布,讨论了导波阶数、频率以及孔洞位置的影响。     

Propagation of axisymmetric waves on the surface of a cylindrical cavity in elastic medium

A nondamped axisymmetric mode that propagates in an elastic cylindrical waveguide representing an extended cavity with a circular cross section in an infinite homogeneous medium is described. The wave dispersion in this system is analyzed and the similarity with and differences from other elastic media with one boundary are considered, including an infinite round rod and the surface of a half-space (Rayleigh wave). It is shown that, for axisymmetric waves in the cavity, a boundary frequency dependent on the curvature radius always exists, below which the waves are evanescent. A physical interpretation of results is given.     

Scattering of a transversely confined Neumann beam by a spherical particle

Various properties of an electromagnetic wave whose spherical multipole expansion contains only Riccati-Neumann functions are examined. In particular, the novel behavior of the beam phase during diffractive spreading is discussed. When a Neumann beam is scattered by a spherical particle, the diffraction and external reflection portions of the scattering amplitude constructively interfere for large partial waves. As a result, a set of rapidly decreasing beam shape coefficients is required to cut off the partial wave sum in the scattering amplitudes. Because of its strong singularity at the origin, a Neumann beam can be produced by a point source of radiation at the center of a spherical cavity in a high conductivity metal, and Neumann beam scattering by a spherical particle can occur for certain partial waves if the sphere is placed at the center of the cavity as well.     

The scattering of electro-elastic waves by a spherical piezoelectric particle in a polymer matrix

This paper is devoted to the study of scattering of plane harmonic waves by a piezoelectric sphere with spherical isotropy embedded in an unbounded isotropic polymer matrix. The scattered displacement field and the electric potential in the matrix are expressed in terms of spherical vector wave functions and spherical harmonic functions, respectively. For the field points inside the inhomogeneity, new displacement functions are introduced. Expansion of the new displacement functions and the electric potential in terms of spherical harmonic functions, the equations of motion and electrostatic lead to four second order ordinary differential equations (odes), where three of them are coupled. The coupled system of odes is solved by the generalized Frobenius series. This approach is readily used to handle low and high frequencies. Three different types of piezoelectric inhomogeneities, PZT-4, PZT-5H, and BaTiO₃ are considered and the associated piezoelectric effects on the electro-mechanical fields, differential and total scattering cross-sections are addressed.     

Response of acoustic imaging systems using convergent leaky waves to cylindrical flaws

A theoretical study of imaging systems utilizing focused leaky surface acoustic waves (SAWs), and their response to certain kind of defects is presented. In particular, circular cylindrical inhomogeneities with axes perpendicular to the surface are considered. The scattering of the SAW from this cylinder is formulated with some approximations. The surface wave incident on the inhomogeneity is initially found as an angular spectrum of plane waves. However, to apply the boundary conditions at the cylindrical surface, the incident field has to be transformed into a superposition of cylindrical waves. Similarly, the scattered field, which is found in the form of outgoing cylindrical SAWs, is converted back to a plane wave spectrum. A formula is obtained for the transducer output voltage in terms of the position and the radius of the cylinder, and it is suitable for computer evaluation. By considering various locations for the cylinder, the sensitivity of the system around the focal point is studied. By comparing the output voltages for cylinders of different radii, the sensitivity of the system to the size of the inhomogeneity is examined. The numerical results are in agreement with the experimental observations.     

Multiple Scattering of Thermal Waves from a Subsurface Cylindrical Inclusion in Semi-infinite Functionally Graded Materials Using Non-Fourier Model

In this study, a theoretical method is applied to investigate the multiple scattering of thermal waves and temperature field resulting from a subsurface cylindrical inclusion in a semi-infinite functionally graded material (FGM). The adiabatic boundary condition at the semi-infinite surface is considered. The thermal waves are excited at the surface of semi-infinite functionally graded materials by modulated optical beams. The model includes the multiple scattering effects of the cylindrical thermal wave generated by the line heat source. According to the wave equation of heat conduction, a general solution of scattered thermal waves is presented. Numerical calculations illustrate the effect of subsurface inclusion on the temperature and phase change at the sample surface under different physical and geometrical parameters. It is found that the temperature above the conducting cylindrical inclusion decreases because of the existence of the inclusion. The effect of the inclusion on the temperature and phase change at the surface is also related to the non-homogeneous parameter of FGMs, the wave frequency of thermal waves, and the distance between the inclusion and the semi-infinite surface. Finally, the effect of the relaxation time of buried inclusion on the temperature and phase change at the surface is examined.     

Green's-function method for the analysis of propagation in holey fibers

A Green's-function method is employed to provide a rigorous analysis to the propagation and coupling phenomena in holey fibers. The analysis is carried out for an arbitrary grid of circular air holes of the fiber guide, while the electromagnetic field is taken to be a vector quantity. Application of the Green's-function concept leads to a coupled system of equations incorporating as unknowns the field expansion coefficients to cylindrical wave functions within the air holes. The propagation constants of the guided waves are computed accurately by determining the singular points of the corresponding system's matrix. Field distribution and dispersion properties of guided modes as well as coupling phenomena between parallel-running holey fibers are investigated, and numerical results are presented.     

Cavitation erosion as a kind of dynamic damage

The purpose of this work is to show that the spherical shock waves arising in a liquid during cavitation bubble collapse can lead to formation of deep needle-like pits on the solid surface. The nature of dynamic damage during cavitation erosion is the spallation caused by interference of rarefaction waves. Rarefaction at spherical wave impact arises when the velocity of contact surface boundary becomes less than the speed of sound in a target. If the tension caused by the focused rarefaction wave exceeds the spall strength of material, channel spall cracks can arise. At low pulsed loading, spall cracks are formed in a dynamic fatigue mode. Needle-like damage arises upon focusing rarefaction waves. In terms of our model, a system of cylindrical spall cracks is consecutively formed around a deeper axial spall needle-like crack. Upon subsequent loading, each crack acts as a source of new rarefaction wave. Newly formed cylindrical spall cracks suppress the growth of the cracks of previous generation and give birth to the cracks of next generation. A distinctive feature is that the cracks are first formed at the periphery of damageability zone, subsequent cracks having a lower depth.     

Electromagnetic scattering by an aggregate of spheres

We present a comprehensive solution to the classical problem of electromagnetic scattering by aggregates of an arbitrary number of arbitrarily configured spheres that are isotropic and homogeneous but may be of different size and composition. The profile of incident electromagnetic waves is arbitrary. The analysis is based on the framework of the Mie theory for a single sphere and the existing addition theorems for spherical vector wave functions. The classic Mie theory is generalized. Applying the extended Mie theory to all the spherical constituents in an aggregate simultaneously leads to a set of coupled linear equations in the unknown interactive coefficients. We propose an asymptotic iteration technique to solve for these coefficients. The total scattered field of the entire ensemble is constructed with the interactive scattering coefficients by the use of the translational addition theorem a second time. Rigorous analytical expressions are derived for the cross sections in a general case and for all the elements of the amplitude-scattering matrix in a special case of a plane-incident wave propagating along the z axis. As an illustration, we present some of our preliminary numerical results and compare them with previously published laboratory scattering measurements.     

On the propagation of waves from spherical and cylindrical cavities in anisotropic materials

The propagation of waves from a spherical or cylindrical cavity in an inhomogeneous anisotropic elastic solid is considered. In the first instance, integral transforms are used to provide solutions to specific boundary value problems involving elastic media exhibiting certain inhomogeneities. It is then noted that the Bergman integral operator method provides a more general analysis. Finally, an asymptotic approach having a wide range of application is discussed and employed to construct wavefront and high-frequency expansions for the solution field in general media.     

Three‐dimensional BEM for scattering of elastic waves in general anisotropic media

Based on the full‐space Green's functions, a three‐dimensional time‐harmonic boundary element method is presented for the scattering of elastic waves in a triclinic full space. The boundary integral equations for incident, scattered and total wave fields are given. An efficient numerical method is proposed to calculate the free terms for any geometry. The discretization of the boundary integral equation is achieved by using a linear triangular element. Applications are discussed for scattering of elastic waves by a spherical cavity in a 3D triclinic medium. The method has been tested by comparing the numerical results with the existing analytical solutions for an isotropic problem. The results show that, in addition to the frequency of the incident waves, the scattered waves strongly depend on the anisotropy of the media. Copyright © 2003 John Wiley & Sons, Ltd.     

Scattering of SH-waves by an interface cavity

Summary. The scattering of the SH-wave and dynamic stress concentrations near an arbitrary cavity situated at the planar interface separating two different elastic media are investigated. The total wave field can be obtained by superposition of the free field and the scattered field. The free field is composed of the incident, reflected and refracted waves. The scattered wave fields in adjacent media are expressed respectively, and the method of wave functions expansion is applied to obtain the solutions for these fields. The scattered wave functions can be expanded into Hankel-Fourier series with unknown coefficients. In solving for the unknown coefficients according to the boundary conditions for the total wave field at the interface and at the cavity wall, the non-orthogonality makes the system of equations for the unknown coefficients infinite and coupling each other. Another key point is to extend each scattered wave field from its own half-plane domain into the full plane domain by a certain way keeping the total wave field unchanged for the non-orthogonal Fourier integrals around the cavity. Finally, the scattering of the SH wave by an interface ellipse with different ratios between long and short axis is considered, and the distributions of dynamic stress concentration factors at the cavity wall are presented.     

Transformation of radially traveling cylindrical waves between two skew cylindrical coordinate systems

The transformation of radially traveling cylindrical waves between two cylindrical coordinate systems with skew (nonparallel) axes is derived for the first time to our knowledge. The analytical procedure is based on the complex integral representation of the Hankel function and appropriate contour deformation and change of variables to obtain a final Fourier transform expression of the cylindrical wave in the new system. Scalar and vector waves are considered. This new result is a powerful tool for the rigorous analysis of scattering and coupling in nonparallel optical fiber configurations.     

Dynamic Stress around Two Interacting Cylindrical Nano-Inhomogeneities with Surface/Interface Effects

On the basis of continuum surface elasticity, two interacting cylindrical nano-inhomogeneities with surface/interface effect in a small-sized solid under anti-plane shear waves are investigated, and the dynamic stress around the nano-inhomogeneities is analyzed. The wave function expansion method is used to expressed the wave field around the two nano-inhomogeneities. The total wave field is obtained by the addition theorem for cylindrical wave function. Through analysis, it is found that the distance between the two nano-inhomogeneities shows great effect on the dynamic stress in nano composites. The effect of the distance is also related to the properties of the nano-inhomogeneities and the interface, the wave frequency, and the incident angle of shear waves. To show the accuracy of the results for certain given parameters, comparison with the existing results is also given.     

Off-axis Holographic Zone Plates Recorded and Reconstructed by Cylindrical Wavefronts

Theoretical aspects of off-axis holographic zone plate recording using two cylindrical waves, with arbitrary angled focal lines, and replay of such holograms with a cylindrical or spherical wave are discussed in the narrow-beam approximation. Expressions for the distances and orientations of focal lines of generally reconstructed astigmatic beams are given, and conditions for obtaining spherical waves are analysed. The results have been verified by experiments using photographic emulsion (Agfa-Gevaert Holotest 10E56 plates) as the recording material. In particular, experimentally obtained parameters of the reconstructed astigmatic beam and the spherical wave are found to be in good agreement with theoretical results.     

流体饱和半空间中埋置球面P1、P2和SV波源动力格林函数

基于Biot流体饱和孔隙介质理论,采用Hankel积分变换方法,在频域内求解了流体饱和半空间中埋置球面P1、P2和SV波源的动力格林函数。首先由Hankel积分变换将空间域内球面波展开为波数域内柱面波的叠加;然后在半空间表面对称位置虚拟放置一同样大小的球面波源,这样对于球面膨胀波源(P1和P2波源),地表剪应力为零,但存在非零正应力和孔隙水压,对于球面剪切波源(SV波源),地表正应力和孔隙水压为零,但存在非零剪应力;最后叠加球面波源、虚拟波源和残余半空间表面应力产生的动力响应,即可求得流体饱和半空间中埋置球面波源波数域内的动力响应,空间域内埋置球面波源的动力格林影响函数则由Hankel逆变换求得。该文给出的球面波源动力格林函数,为建立以球面P1、P2和SV波动力格林函数为基本解的间接边界元方法,求解饱和多孔介质中三维轴对称弹性波散射问题奠定了基础。     

Axisymmetric waves in electrohydrodynamic flows

The formation of nonlinear axisymmetric waves on inviscid irrotational liquid jets in the presence of radial electric fields is considered. Gravity is neglected but surface tension is considered. Electrohydrodynamic waves of arbitrary amplitude and wavelength are computed using finite-difference methods. Particular attention is paid to nonlinear traveling waves. In the first class of problems, an electric field generated by placing the liquid jet inside a hollow cylindrical electrode held at constant voltage, its axis coinciding with that of the jet, is studied. The jet is assumed to be a perfect conductor whose free surface is stressed by the electric field acting in the hydrodynamically passive annulus. In the second class of problems, the annular gas is a perfect conductor that transmits a constant voltage onto the liquid/gas surface. The liquid axisymmetrically wets a constant-radius cylindrical rod electrode placed coaxially with respect to the hollow outer electrode, and held at a different constant voltage. The fluid dynamics and electrostatics need to be addressed simultaneously in the inner region. Axisymmetric interfacial waves influenced by surface tension and electrical stresses are computed in both cases. The computations are capable of following highly nonlinear solutions and predict, for certain parameter values, the onset of interface pinching accompanied with the formation of toroidal bubbles. For given wave amplitudes, the results suggest that, for the former case, the electric field delays bubble formation and reduces wave steepness, while for the latter case the electric field promotes bubble formation, all other parameters being equal.     

Analytical calculation of blast-induced strains to buried pipelines

The aim of this paper is to introduce a robust methodology for the analytical calculation of strains in flexible buried pipelines due to surface point-source blasts. Following a brief bibliographic overview regarding the characteristics of ground waves produced by surface explosions, a method used to model wave propagation with radial attenuation and spherical front is presented. Strains due to P- and Rayleigh waves, which dominate the waveform generated by an explosion, are accordingly calculated by modeling the pipeline as a three-dimensional (3-D) cylindrical thin shell and ignoring soil–structure interaction. To simplify the design procedure, a set of easy-to-use relations for the calculation of maximum strains and their position along the pipeline axis is supplied. The derived expressions are evaluated through comparison against 3-D dynamic numerical analyses, field strain measurements in flexible pipelines due to a series of full scale blasts, and state-of-practice design methods. Comparisons show that the proposed methodology provides improved accuracy at no major expense of simplicity, as well as the advantage of properly accounting for the effect of local soil conditions.