Scattering of water waves by axisymmetric bodies in a channel

Methods are presented for the calculation of wave forces on a vertically axisymmetric body arbitrarily placed within a channel. Integral representations of singular solutions of the Helmholtz equation, called channel multipoles here, are derived and these allow straightforward solution of the scattering problem for a vertical cylinder extending throughout the depth. In contrast to previous methods there is no need to sum series of images. These multipoles are also used in deriving an approximate solution valid when the radius of the cylinder is small relative to the wavelength and channel width.To solve for arbitrary shaped axisymmetric bodies, a plane-wave approximation is developed based on the assumption that the wavelength is much less than the channel width. Comparisons with the accurate solution for a vertical cylinder suggest that this approximate method performs well even when this assumption is clearly violated. The results of calculations of wave forces on a truncated cylinder are also given.All of the methods described may be applied just as easily to the case of an off-centre body as to a centrally-placed body.     

Root function solutions in a nucleation theory considering small cluster mobility

It is shown that discrepancies between current nucleation theory and experimental results for incomplete condensation can be surmounted if dimers and trimers are assumed to be highly mobile on the substrate surface so that most of them are captured by larger clusters. This new conception of nucleation kinetics can be described by a system of rate equations for which approximate analytical solutions are given. A peculiar feature of these solutions is the dependence of the nucleus density on a root of the deposition time. The results are compared with experimental data for gold on NaCl; in spite of some open questions the agreement is fairly good.     

The orthogonal projection method for the numerical solution of a field problem

A numerical method, based on the orthogonal projection method of Hilbert space, is given. Two approximate solutions, which bound the exact solution from above and below, are described. The error of the approximate solution is calculated directly. An example of a calculation of temperature field in a nuclear reactor shell is presented.     

The electrostatic problem for the SAW interdigital transducers inan external electric field. II. Periodic structures

For pt.I see ibid., vol.43, no.6, pp.1150-9 (1996). An exact solution of the electrostatic problem for calculating the surface charge and electric field distributions in an arbitrary periodic interdigital transducer (IDT) is given using the results of our companion paper. An arbitrary external electric field may be specified along the electrode structure with the unit cell containing one electrode, or several electrodes, of different widths. The potentials of the electrodes that may be specified are also arbitrary. It is shown that in the case without an external field, the solution includes all the known results as special cases. The case of shorted electrodes in the external electric field is investigated in detail. The surface charge and electric field distributions are calculated for a spatially harmonic external field with an arbitrary wavenumber. The results of the calculations are represented graphically for various ratios between the period of the electrode structure and the wavelength of the external field for the case of a unit cell containing one or two electrodes of different widths     

Optical field study of near-field optical recording with a solid immersion lens

The use of a solid immersion lens (SIL) is an important technique for increasing areal density in optical recording. Here an approximate method is presented for analyzing the optical fields in a SIL above a half-space and a SIL above a multilayer recording medium. Both propagating and evanescent components are included in the distribution of fields below the SIL. An approximate closed-form expression is given for the decay of the intensity away from the SIL surface above a half-space. In the case of a SIL above a recording medium the model describes the strong oscillations that are observed in the reflected Kerr rotation and ellipticity as the medium spacing is varied. These oscillations are attributed to standing waves in the propagating field component.     

Transient Disturbance in a Half Space Under Thermoelasticity with Two Relaxation Times Due to Moving Internal Heat Source

In this paper transient waves caused by a line heat source moving with a uniform velocity inside isotropic homogeneous thermoelastic half-space are studied under the GL model of generalized thermoelasticity. The problem is reduced to the solution of three differential equations by introducing the elastic vector potential and the thermoelastic scalar potential. Using Laplace and Fourier transforms solutions are obtained in transforms domain. Applying inverse transforms approximate solutions of the displacement at the boundary valid in the small time range are given. Also the approximate region valid for the solutions is given and two special cases, (i) the source is motionless and (ii) the relaxation times vanish, are studied. Numerical evaluations are presented for the medium of copper.     

基于一致性几何绕射理论的曲面表面绕射声场解

提出了一种基于一致性几何绕射理论的理想刚性光滑曲面表面绕射声场高频近似计算方法。分别以圆球和无限长圆柱为例,计算了其表面绕射声场,并将计算结果与解析解进行了比较。结果表明,该方法具有计算简单明确,物理概念清晰,计算结果精确的特点。     

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: Formulation and validation

This paper proposes a simple, efficient algorithm to trace a moving delamination front with an arbitrary and changing shape so that delamination growth can be analyzed by using stationary meshes. Based on the algorithm, a delamination front can be defined by two vectors that pass through any point on the front. The normal vector and the tangent vector for the local coordinate system can then be obtained based on the two delamination front vectors. An important feature of this approach is that it does not require the use of meshes that are orthogonal to the delaminations front. Therefore, the approach avoids adaptive re-meshing techniques that may create a large computational burden in delamination growth analysis. An interface element that can trace the instantaneous delamination front, determine the local coordinate system, approximate strain energy release rate components and apply fracture mechanics criteria has been developed and implemented into ABAQUS^® with its user-defined element (UEL) feature. In this Part I of a two-part paper, the approach and its implementation are described and validated by comparison to results from existing cases having analytical solutions or other established FEA predictions.     

Shear-horizontal waves in a rotated Y-cut quartz plate with an imperfectly bonded mass layer

We study shear-horizontal (SH) waves in an unbounded plate of rotated Y-cut quartz carrying a thin mass layer imperfectly or nonrigidly bonded to the surface of the quartz plate. The imperfect interface is described by the socalled shear-lag model that allows the displacement to be discontinuous across the interface. A transcendental frequency equation that determines the dispersion relations of the waves is obtained. Exact and approximate solutions to the frequency equation are presented. The effects of the mass layer and the imperfect interface on the dispersion relations are examined. A quantitative criterion is given which distinguishes whether the combined effect of the mass layer and the imperfect interface raises or lowers the wave frequencies.     

Scalar diffraction field calculation from curved surfaces via Gaussian beam decomposition

We introduce a local signal decomposition method for the analysis of three-dimensional (3D) diffraction fields involving curved surfaces. We decompose a given field on a two-dimensional curved surface into a sum of properly shifted and modulated Gaussian-shaped elementary signals. Then we write the 3D diffraction field as a sum of Gaussian beams, each of which corresponds to a modulated Gaussian window function on the curved surface. The Gaussian beams are propagated according to a derived approximate expression that is based on the Rayleigh-Sommerfeld diffraction model. We assume that the given curved surface is smooth enough that the Gaussian window functions on it can be treated as written on planar patches. For the surfaces that satisfy this assumption, the simulation results show that the proposed method produces quite accurate 3D field solutions.     

Two-to-one internal resonances in a shallow curved beam resting on an elastic foundation

Summary Vibrations of shallow curved beams are investigated. The rise function of the beam is assumed to be small. Sinusoidal and parabolic curvature functions are examined. The immovable end conditions result in mid-plane stretching of the beam which leads to nonlinearities. The beam is resting on an elastic foundation. The method of multiple scales, a perturbation technique, is used in search of approximate solutions of the problem. Two-to-one internal resonances between any two modes of vibration are studied. Amplitude and phase modulation equations are obtained. Steady state solutions and stability are discussed, and a bifurcation analysis of the amplitude and phase modulation equations are given. Conditions for internal resonance to occur are discussed, and it is found that internal resonance is possible for the case of parabolic curvature but not for that of sinusoidal curvature.     

不同拉压特性结构振动分析的双线性近似方法

对拉压特性不同的双模量结构的非线性自由振动进行了研究。给出了恢复力-位移曲线由三段斜率不 同的直线构成的单自由度系统自由振动频率的精确解。应用双线性近似方法讨论了有间隙双模量结构和无间隙双模量 结构非线性自由振动频率的近似求解问题。结果表明,不管恢复力-位移表达式多么复杂,应用双线性近似方法都可以 方便地求得结构的等效线性刚度,进而获得结构固有频率的近似解。通过近似计算结果与精确解之间的比较,验证了双 线性近似方法对于工程中大量存在的一类具有不同拉压特性的结构进行振动分析的实用性。     

Current displacement of a solid cylindrical conductor placed in a semiclosed slot, taking into account the leakage field in the gap

The field problem is solved assuming a constant magnetic field strength in the middle of the slot opening. Adapting the vector potential in gap and conductor, which has been expanded into Fourier series and described in different coordinate systems, one obtains a system of linear complex equations for the Fourier coefficients. The calculation of surface current density and surface field strength is checked by measuring the bar current and comparing it with a value deduced from the measurement of the voltage drop at the surface of the bar. This comparison becomes significant due to the fact that these quantities converge badly and determine the bar impedance by means of Poyntings's vector. Finally a comparison is made with the normal approach, which has high practical importance, and which takes the magnetic field strength on the surface of the conductor as a given boundary condition. This comparison shows the advantages of the analysis presented over the conventional approximation. At last a finite element (FE) solution for this problem is given.     

Anisotropic parametric plate discrete elements

A limitation of most plate and shell discrete elements now in use is the shape of their undeformed geometry. Typically, the plan form of these elements is a straight-sided triangle or quadrilateral that linearly approximates the undeformed geometry while often using higher-order polynomials to approximate the deformed geometry. This modelling difference leads to inefficiencies that can be eliminated, as demonstrated by a new parametric discrete element based entirely on bicubic Hermite polynomials. This representation of element geometry corresponds to the bicubic Coon's surface patch widely used in design, which allows a common mathematical model for design and analysis. Consideration is given to automating the generation of these patches. Solutions are presented for several plate bending and plate stretching problems. The solutions are in good agreement with closed-form solutions and photoelastic results in the case of a stress-concentration problem. These data demonstrate that the new parametric discrete element maintains solution accuracy for plates with curved boundaries.     

Optimum rigid motion with one perspective view

One of the central problems in dynamic computer vision is the determination of motion from correspondence of points on the visible surface of a moving object obtained at two different times. In the problem we consider, the initial position of several feature points on some object is assumed to be known. Then at some later time instant the corresponding perspective projection of those points is given. The moving body may be nonrigid or the measurements may be corrupted with noise. In either case, we determine the multiplicity of possible solution for the best-fitting rigid motion. We show that whenever at least three point correspondences are given, there are at most two possible solutions for the best-fitting rigid motion if the object space is two-dimensional, while there are at most forty possible solutions if the object space is three-dimensional. In the latter case the number of possible solutions drops to four if three point correspondence are known, the body is rigid, and the measurements are noise-free. Several examples are worked out to illustrate our results.©1994 John Wiley & Sons Inc     

Computation of 3-D magnetostatic fields using a reduced scalarpotential

Some improvements to the finite element computation of static magnetic fields in three dimensions using a reduced magnetic scalar potential are presented. Methods are described for obtaining an edge element representation of the rotational part of the magnetic field from a given source current distribution. When the current distribution is not known in advance, a boundary value problem is set up in terms of a current vector potential. An edge element representation of the solution can be directly used in the subsequent magnetostatic calculation. The magnetic field in a DC arc furnace is calculated by first determining the current distribution in terms of a current vector potential. A 3-D problem involving a permanent magnet as well as a coil is solved, and the magnetic field in some points is compared with measurement results     

Error estimation using hypersingular integrals in boundary element methods for linear elasticity

A natural measure of the error in the boundary element method rests on the use of both the standard boundary integral equation (BIE) and the hypersingular BIE (HBIE). An approximate (numerical) solution can be obtained using either one of the BIEs. One expects that the residual, obtained when such an approximate solution is substituted to the other BIE is related to the error in the solution. The present work is developed for vector field problems of linear elasticity. In this context, suitable ‘hypersingular residuals’ are shown, under certain special circumstances, to be globally related to the error. Further, heuristic arguments are given for general mixed boundary value problems. The calculated residuals are used to compute element error indicators, and these error indicators are shown to compare well with actual errors in several numerical examples, for which exact errors are known. Conclusions are drawn and potential extensions of the present error estimation method are discussed.     

Transmission of an inhomogeneous plane wave through an electrically small aperture in a perfectly conducting plane screen

Most solutions for electromagnetic diffraction by a circular aperture in a perfectly conducting plane screen are for an incident homogeneous (propagating) plane wave. When the aperture is electrically small (dimensions small compared to the wavelength), the well-known transmission coefficient behaves as the fourth power of the diameter/wavelength. We consider the case in which the incident field is an inhomogeneous (evanescent) plane wave. Numerical calculations for the electrically small circular aperture show that the transmission coefficient for an inhomogeneous plane wave can be substantially greater than for a homogeneous plane wave at the same frequency. This observation may be helpful in explaining the increased transmission recently reported for electrically small apertures in plane screens with modifications. The numerical calculations for the electrically small aperture are in agreement with results from approximate analytical expressions that are based on the equivalent electric and magnetic dipole moments for the electrically small complementary disk.