The penetrable coated sphere embedded in a point source excitation field

A low frequency acoustic wave field emanates from a given point and fills up the whole space. A penetrable lossy sphere with a coeccentric spherical core, which is also penetrable and lossy but characterized by different physical parameters, disturbs the given point source field. We obtain zeroth- and first-order low frequency solutions of this scattering problem in the interior of the spherical core, within the spherical shell, and in the exterior medium of propagation. We also derive the leading nonvanishing terms of the normalized scattering amplitude, the scattering cross-section as well as the absorption cross-section. The special case of a penetrable sphere is recovered either by equating the physical parameters that characterize the media in the shell and in the exterior, or by reducing the radius of the core sphere to zero. By letting the compressional viscosity of the medium in the interior sphere, or in the shell, go to zero, we obtain corresponding results for the lossless case. The incident point source field is so modified as to be able to obtain the corresponding results for plane wave incidence in the limit as the source point approaches infinity. It is observed that a small scatterer interacts stronger with a point source generated field than with a plane wave. A detailed analysis of the influence that the geometrical and the physical parameters of the problem have on the scattering process is also included. An interesting conclusion is that if the point source is located at a distance more than five radii of the scatterer away from it, then no significant changes with the plane excitation case are observed.     

Estimates for low-frequency elastic scattering by a rigid body

When a plane elastic wave is scattered by a rigid body the surface integral of the traction, projected along the direction of polarization of the incident wave, provides the leading low-frequency approximation for the scattering amplitudes. Two kinds of lower and upper bounds for the surface traction integral are given. One is based on the geometrical characteristics of the scatterer and is expressed in terms of corresponding values of the best fitting interior and exterior confocal triaxial ellipsoids. The case of best fitting interior and exterior spheres is examined as a special case. These bounds are sharp in the sense that they both become equalities when the scatterer degenerates to an ellipsoid. The other kind of lower and upper bounds involve the capacity of the scatterer. All estimates were obtained by using the generalized Dirichlet and Thomson Principles of Potential Theory in Elastostatics. Furthermore, all constants appearing in the bounds are given in terms of the ratio of the phase velocities for the transverse and the longitudinal wave. An upper bound for scattering by a cube at normal incidence is also included.This work was done while both authors were visiting the Department of Mathematics of The University of Tennessee at Knoxville. The second author wishes to acknowledge partial support from The University of Tennessee Science Alliance.     

Acoustic scattering and radiation problems, and the null-field method

The best known methods for solving the scattering and radiation problems of acoustics are integral-equation methods. However, it is also known that the simplest of these methods yield equations which are not uniquely solvable at certain discrete sets of frequencies (the irregular frequencies). In this paper, we shall analyse an alternative method (the null-field method, or T-matrix method). We prove that the infinite system of null-field equations always has precisely one solution, i.e. the unphysical irregular frequencies do not occur with this method. Moreover, we also prove that the solution of the original boundary-value problem can always be determined (at any point exterior to the scatterer) from the solution of the null-field equations. We prove these results in two dimensions, for two radiation problems (the exterior Neumann problem and the exterior Dirichlet problem) and two scattering problems (scattering by a sound-hard body and scattering by a sound-soft body); similar results can be proved in three dimensions. We also prove some subsidiary results, concerning the solvability of certain boundary integral equations and the completeness of certain sets of radiating wave-functions, and give a discussion of related numerical techniques.     

Wave reflection from a periodically composed half-space

The character of wave motions in geometrical settings of a periodic nature and their interplay with primary and secondary waves in the exterior of partly space-filling configurations receive prominence in the theories of x-ray and electron diffraction. It is customary to focus attention on the free or natural wave motions in unbounded media with a periodic bias prior to estabishing the self-consistent solution for specific excitations in composite media. An integrated, rather than sequential, approach to problems in the latter category is recommended and detailed here in connection with the incidence of plane waves on a half-space with periodic composition normal to its boundary; and is shown, in particular, to furnish directly a superior means of calculating the reflection coefficient.This work was supported in part by Office of Naval Research Contract Nonr-225(74).     

SERIES SOLUTION FOR SCATTERING OF PLANE SH－WAVES BY MULTIPLE SHALLOW CIRCULAR－ARC CANYONS

ＳＥＲＩＥＳＳＯＬＵＴＩＯＮＦＯＲＳＣＡＴＴＥＲＩＮＧＯＦＰＬＡＮＥＳＨ－ＷＡＶＥＳＢＹＭＵＬＴＩＰＬＥＳＨＡＬＬＯＷＣＩＲＣＵＬＡＲ－ＡＲＣＣＡＮＹＯＮＳＦａｎｇＹｉｎｇｇｕａｎｇ（房营光）（Ｇｕａｎｇｄｏｎｇ｀ＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌ...     

弹性波散射与多重散射的T矩阵方法

研究弹性波散射与多重散射的T矩阵方法。首先,基于Helmholtz体内和体外公式推导了对应于圆柱型散射体的T矩阵元素的具体表达式;接着分析了在含多个随机分布圆柱型散射体的随机非均匀介质中弹性波的多重散射并给出在统计平均意义下的相干波的定义以及波速和衰减系数计算公式;最后,针对Ge/Al、Sic/Al复合材料用Matlab进行了编程和数值计算;计算单个柱型散射体的散射截面以及随机非均匀介质中相干波的速度和衰减系数,分析了这种介质的频散特性。     

pFFT快速边界元方法模拟三维声散射

研究了用pFFT快速边界元方法模拟声散射问题的关键技术。采用Burton—Miller方程消除了声学边界元方法中外问题解的不唯一现象。为此,文中研究了采用常量元时该方程中超奇异积分的计算方法。最后,通过对平面声波的刚性圆球声散射的数值模拟,验证了建立的声学pFFT快速边界元方法。     

Experimental comparison of measurement techniques for drop size distributions in liquid/liquid dispersions

An online measurement technique for drop size distribution in stirred tank reactors is needed but has not yet been developed. Different approaches and different techniques have been published as the new standard during the last decade. Three of them (focus beam reflectance measurement, two-dimensional optical reflectance measurement techniques and a fiber optical FBR sensor) are tested, and their results are compared with trustful image analysis results from an in situ microscope. The measurement of drop sizes in liquid/liquid distribution is a major challenge for all tested measurement probes, and none provides exact results for the tested system of pure toluene/water compared to an endoscope. Not only the size analysis but also the change of the size over time gives unreasonable results. The influence of the power input on the drop size distribution was the only reasonable observation in this study. The FBR sensor was not applicable at all to the used system. While all three probes are based on laser back scattering, the general question of the usability of this principle for measuring evolving drop size distributions in liquid/liquid system is asked. The exterior smooth surface of droplets in such systems is leading to strong errors in the measurement of the size of the drops. That leads to widely divergent results. A different measurement principle should be used for online measurements of drop size distributions than laser back scattering.     

ANALYSIS ON ACOUSTICAL SCATTERING BY A CRACKED ELASTIC STRUCTURE

The acoustical scattering by a cracked elastic structure is studied. The mixed method of boundary element and fractal finite element is adopted to solve the cracked structure-acoustic coupling problem. The fractal two-level finite element method is employed for the cracked structure, which can reduce the degree of freedoms (DOFs) greatly, and the boundary element method is used for the exterior acoustic field which can automatically satisfy Sommerfeld‘s radiation condition. Numerical examples show that the resonance frequency is lower with the crack‘s depth increase, and that the effect on the acoustical field by the crack is particularly pronounced in the vicinity of the crack tip. This mixed method of boundary element and finite element is effective in solving the scattering problem by a cracked structure.     

An efficient numerical method for exterior and interior inverse problems of Helmholtz equation

The generalized pulse-spectrum technique (GPST), an efficient and versatile inversion algorithm, is used with adaptive grids to solve both exterior (scattering) and interior (cavity) boundary-shape inverse problems of two-dimensional Helmholtz equation. Numerical simulations of nontrivial examples are carried out to test the feasibility and to study the general characteristics of GPST without the real measurement data. It is found that GPST does efficiently produce very good results.     

应用分形有限元方法于外域声场计算

应用二级分形有限元方法计算了外域声场. 用一人工边界把外域声场分为两部分,人工边界以内使用常规有限元方法,人工边界以外的无限大区域使用分形有限元方法.使用分形有限元方法的优点是：一方面形成几何自相似网格使得相邻层之间的单元刚度矩阵和质量矩阵具有非常简单的关系;另一方面引用自动满足无限远辐射条件的全域插值函数把节点自由度变换为一组广义坐标,因而计算量可以大大减少. 数值算例表明：该方法对于计算无限大外域声场是有效的.     

Overall constitutive description of symmetric layered media based on scattering of oblique SH waves

This papers investigates the scattering of oblique shear horizontal (SH) waves off finite periodic media made of elastic and viscoelastic layers. It further considers whether a Willis-type constitutive matrix (in temporal and spatial Fourier domain) may reproduce the scattering matrix (SM) of such a system. In answering this question the procedure to determine the relevant overall constitutive parameters for such a medium is presented. To do this, first the general form of the dispersion relation and impedances for oblique SH propagation in such coupled Willis-type media are developed. The band structure and scattering of layered media are calculated using the transfer matrix (TM) method. The dispersion relation may be derived based on the eigen-solutions of an infinite periodic domain. The wave impedances associated with the exterior surfaces of a finite thickness slab are extracted from the scattering of such a system. Based on reciprocity and available symmetries of the structure and each constituent layer, the general form of the dispersion and impedances may be simplified. The overall quantities may be extracted by equating the scattering data from TM with those expected from a Willis-type medium. It becomes evident that a Willis-type coupled constitutive tensor with components that are assumed independent of wave vector is unable to reproduce all oblique scattering data. Therefore, non-unique wave vector dependent formulations are introduced, whose SM matches that of the layered media exactly. It is further shown that the dependence of the overall constitutive tensors of such systems on the wave vector is not removable even at very small frequencies and incidence angles and that analytical considerations significantly limit the potential forms of the spatially dispersive constitutive tensors.     

Active control scheme for improving mass resolution of film bulk acoustic resonators

High mass resolution of sensors based on film bulk acoustic resonators (FBARs) is required for the detection of small molecules with the low concentration.An active control scheme is presented to improve the mass resolution of the FBAR sensors by adding a feedback voltage onto the driving voltage between two electrodes of the FBAR sensors. The feedback voltage is obtained by giving a constant gain and a constant phase shift to the current on the electrodes of the FBAR sensors. The acoustic energy produced by the feedback voltage partly compensates the acoustic energy loss due to the material damping and the acoustic scattering, and thus improves the quality factor and the mass resolution of the FBAR sensors. An explicit expression relating to the impedance and the frequency for an FBAR sensor with the active control is derived based on the continuum theory by neglecting the influence of the electrodes. Numerical simulations show that the impedance of the FBAR sensor strongly depends on the gain and the phase shift of the feedback voltage, and the mass resolution of the FBAR sensor can greatly be improved when the appropriate gain and the phase shift of the feedback voltage are used. The active control scheme also provides an effective solution to improve the resolution of the quartz crystal microbalance (QCM).     

Similarity solutions of energy and momentum boundary layer equations for a power-law shear driven flow over a semi-infinite flat plate

The problem of a steady forced convection thermal boundary-layer driven by a power-law shear is investigated. The search for similarity solutions reduces the problem to a couple of ordinary differential equations containing three parameters: the exponent of the decaying exterior velocity profile, the exponent of the power-law prescribing the thermal condition on the wall and Prandtl number. The effects of these parameters on the existence and form of similarity solution are investigated and the functional dependence of the local Nusselt number on these parameters is reported and discussed. An analysis of the assumptions usually accepted to derive similarity solutions is also reported in order to show the range of values of the exterior velocity power-law exponent for which such solutions may exist.     

A discontinuous Galerkin method with plane waves and Lagrange multipliers for the solution of short wave exterior Helmholtz problems on unstructured meshes

Recently, a discontinuous Galerkin method with plane wave basis functions and Lagrange multiplier degrees of freedom was proposed for the efficient solution of the Helmholtz equation in the mid-frequency regime. This method was fully developed however only for regular meshes, and demonstrated only for interior Helmholtz problems. In this paper, we extend it to irregular meshes and exterior Helmholtz problems in order to expand its scope to practical acoustic scattering problems. We report preliminary results for two-dimensional short wave problems that highlight the superior performance of this discontinuous Galerkin method over the standard finite element method.     

含裂纹弹性结构对声散射作用研究

研究了含裂纹的弹性结构对声的散射作用.应用分配形有限元和边界元相结合的方法于含裂纹的结构声相互作用问题.利用二级分形有限元方法对含裂纹结构进行离散,这将使得自由度大为减少;使用边界元方法计算外域散射声场,这将自动满足无限远辐射边界条件.数值结果初步表明:(1)随着裂纹深度的增加,结构声耦合系统的共振频率将下降;(2)裂纹附近的声场所受的影响更为明显.     

Improved algorithm of light scattering by a coated sphere

An efficient numerical algorithm for computing the light scattering by a coated sphere is proposed. The calculation of relevant functions by different recurrence algorithms is discussed. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by prior methods. Exemplifying results such as extinction efficiency, scattering efficiency, light scattering intensity as well as calculation speed are provided. The results show that this algorithm is efficient, fast, numerically stable and accurate.     

Analysis of a plate containing an elliptic inclusion with eigencurvatures

Summary An infinite plate containing an elliptic subregion in which a uniform eigencurvature is prescribed is analyzed. The problem is formulated by using the classical plate theory. Employing the Maysel's relation, an integral-type solution to the equilibrium equation is expressed in terms of the eigencurvature. Closed-form solutions of the displacement and corresponding resultant moment are obtained for interior points as well as for exterior points of the ellipse. An infinite plate containing an elliptic inhomogeneity in which a uniform eigencurvature is prescribed is also considered. The disturbance of the displacement and corresponding resultant moment due to the inhomogeneity is determined by the equivalent eigencurvature method. Solutions of a circular finite plate with uniform eigencurvature in a circular zone are also obtained analytically. Received 30 September 1997; accepted for publication 3 February 1998     

Asymptotic and numerical study of a surface breaking crack subject to a transient thermal loading

An asymptotic algorithm is applied to the problem of a finite, thermo-elastic solid containing a surface breaking crack, when the exterior surface is subjected to oscillatory thermal loading. This algorithm involves the study of a model problem. An analytical and numerical study of this model problem of a thermo-elastic half space containing a surface breaking crack and subjected to oscillatory thermal loading is presented. The crack surface is traction free. In particular, the amplitude of the stress intensity factor at the crack vertex is found as a function of the crack depth and the frequency of thermal oscillation.     

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.