On the solutions of a class of dual integral equations occurring in diffraction problems

Designing the antenna systems for space vehicles employing electrojet thrusters has to be based on a strict solution of the problem of electromagnetic wave diffraction on two bodies. Here, the problem of diffraction on two spherical surfaces is strictly solved in terms of the scalar field potentials. A method for the transformation of wave amplitudes upon a shift of the spherical coordinate system is proposed. The results of numerical calculations are presented.

We consider the problem of diffraction of an arbitrary electromagnetic wave by a thin disk made from different materials and located in free space. Here we imply a zero- thickness perfectly electrically conducting (PEC) disk, and also thin electrically resistive (ER) and dielectric disks whose thickness is much smaller than the disk radius and the free space wavelength, and also much smaller than the skin-layer depth in the ER disk case. The method used for the modeling is based on the integral equation (IE) technique and analytical regularization. Starting with Maxwell's equations, boundary conditions and the radiation condition at infinity we obtain a set of coupled dual IEs (DIEs) for the unknowns and then reduce this set of equations to the coupled IEs of the Fredholm second kind. To verify our results we calculate the far field characteristics in the case of the PEC disk with the incident field being the field of horizontal electrical dipole located on the disk axis. (5 pages)

The propagation of an anti-plane moving crack in a functionally graded piezoelectric strip (FGPS) is studied in this paper. The governing equations for the proposed analysis are solved using Fourier cosine transform. The mixed boundary value problems of the anti-plane moving crack, which is assumed to be either impermeable or permeable, are formulated as dual integral equations. By appropriate transformations, the dual integral equations are reduced to Fredholm integral equations of the second kind. For the impermeable crack, the stress intensity factor (SIF) of the crack in the FGPS depends on both the mechanical and electric loading, whereas, the SIF for the permeable crack depends only on the mechanical loading. The results obtained show that the gradient parameter of the FGPS and the velocity of the crack have significant influence on the dynamic SIF.

In the present paper the problem of plane electromagnetic wave diffraction by a thin metal plate is considered. A numerical algorithm is developed using method of moments with NVIDIA CUDA technology implementation. The results of numerical modeling of a plane wave diffraction by the square thin metallic plate is shown. Comparative analysis of the performance for CPU and GPU is carried out. It is shown that the method of moments implementation by graphical processor provides a sufficient gain in the performance.

Diffraction of elastic waves by two coplanar and parallel rigid strips

Diffraction of SH waves by Griffith cracks or rigid strips lying in a laterally and vertically non-homogeneous infinite medium

The problem on the diffraction of the electromagnetic plane wave on the impedance interface between two media is investigated. The impedance is assumed to be different from a constant on a segment of the interface, where the impedance is described by piecewise-linear, quadratic, or step functions. Bibliography: 4 titles.

The processes of propagation, interaction and diffraction of electromagnetic waves in periodic mediums with sinusoidally modulated coupling coefficient, which is provided by biharmonic multiple (pi) -phase shifted Bragg grating, are investigated theoretically. The applicability of biharmonic grating for improving the transmission characteristics of narrowband wavelength-selective optical filters is discussed.

The radiation and diffraction of steady-state elastic waves in a periodically perforated orthotropic plane

Since the radio-transmissivity method of high frequency electrical exploration presents difficulties for mathematical analysis of the data, Dayev resorts to models in continuous media subject to the following criteria: ∊1f1 2l1 2 = ∊2f2 2l2 2and p2f1l1 2=p1f2l2 2, where f = field frequency, 1 = linear dimensions, e = dielectric constant, and p = resistivity of the medium; indices 1 and 2 refer to the parameters of the natural conditions and of the model respectively. In the experiments described the model was made to correspond to p= 3,000 ohms, ∊ = 8, and f = 5 megacycles as in natural conditions. Diffraction of electromagnetic waves on vertical metal plates was studied for waves perpendicularly incident to the plate and for waves with different angles of incidence. Similar experiments were conducted with square conducting plates and linear conductors. The results of the study are presented in graphs which provide data on the location and size of conducting deposits.–Courtesy of Geophysical Abstracts, 17...

In the field of diffraction of acoustic, electro-magnetic and elastic waves the ray method has proven to be a powerful tool to obtain reliable results for the behaviour of short waves. In ship hydrodynamics where the generation of short waves by a slowly sailing vessel and the diffraction of short surface waves by these vessels is of importance recently the ray method is applied successfully. In this presentation we present two cases, each with its own free surface condition, treated with this method.

The boundary element method is a numerical method that can be advantageously used for a wide range of engineering problems, including the stress concentration problems encountered in fracture mechanics. In linear elastic fracture mechanics (LEFM), the stress intensity factor is an important parameter. Cracks, if present in the region experiencing the modes of deformation, increase the stress amplitude significantly and this high stress may lead to premature failure of the engineering components. If the value of the SIF is known, it is possible to predict whether the crack will propagate or not. As the conventional boundary integral equation (CBIE) degenerates when a mathematical crack is modelled, a previously developed dual boundary integral equation approach has been adopted in the current work. It utilizes the hypersingular boundary integral equation (HBIE) along with the CBIE. A weakly singular form of HBIE is utilized in the current work to eliminate the hypersingularity analytically. Stress intensity factors are evaluated using the crack opening displacement (COD), displacement extrapolation (DE), and the J-integral approaches. A stand-alone code has been developed for calculating the stress intensity factors of general two-dimensional domains with cracks. The code has been validated by evaluating the stress intensity factors for the standard components, for which the stress intensity factor values are available in the literature. Accurate and well-converged results are obtained proving the robustness of the code. A linear combination of the CBIE and HBIE was applied at the crack and a significant (87–97 per cent) reduction in the condition numbers for the system of equations was observed for the examples studied. Again, the results obtained are accurate and well converged.

This paper discusses the two-dimensional problem of the diffraction of magnetoelastic shear waves by a rigid strip in an infinite elastic perfect conductor. This problem is reduced to a system of dual integral equations of which the solution provides the diffracted field. The method of steepest descent has been used in the determination of the diffracted fields at a large distance from the strip. Diffraction patterns for displacement and stress fields have been computed and the effect of the magnetic field is distinctly marked.

Non destructive examination of industrial structures requires the modeling of specimen geometry echoes generated by the surfaces (entry, back-wall, etc.) of inspected blocks. For that purpose, the study of plane elastic wave diffraction by a wedge is of great interest since surfaces of complex industrial specimen often include dihedral corners. These inspections often deal with high frequency (f = 2–5 MHz) ultrasonic waves. Simulation of realistic inspections by finite elements and finite differences can therefore be time consuming because such methods require a small mesh step for a better description of the scattered wave. Semi-analytical methods are therefore preferred for high frequency problems. There exist various approaches for semi-analytical modeling of plane elastic wave diffraction by a wedge but the theoretical and numerical aspects of these methods have so far only been developed for wedge angles lower than π. Croisille and Lebeau [1] have introduced a resolution method called the Spectral Functions method in the different case of an immersed elastic wedge of angle less than π. Kamotski and Lebeau [2] have then proven existence and uniqueness of the solution derived from this method to the diffraction problem of stress-free wedges embedded in an elastic medium. The advantages of this method are its validity for wedge angles greater than π and its adaptability to more complex cases. The methodology of Croisille and Lebeau [1] has been first extended by the authors to the simpler case of an immersed soft wedge [3] (submitted). It has then been developed here for the 2D scattering problem of an elastic longitudinal wave and a numerical validation of the method for all wedge angles is proposed.

In the free field, making full use of scalar and vector information of acoustic field can bring many advantages for acoustic measurement, but under the conditions of the existence of sound baffle, the sound field should be distorted due to the superposition of diffraction wave. Taking the soft spherical baffle as background, the sphere scattering model is established, the diffraction pressure field and particle velocity field under the condition of different frequency, distance and incident angle is analyzed. The effect of diffraction wave on sound pressure and particle velocity is determined by the amplitude of diffraction wave and the phase difference between the diffraction wave and the incident wave, which is related with the frequency, distance and incident angle. The effect of diffraction wave on sound pressure and the particle velocity components in y axis is strong only on near field and high frequency, but for particle velocity component in x axis, on near field, the effect is always strong both at high and low frequency. The effect of diffraction wave can be ignored only in the far field for particle velocity component in x axis. The description of reference for influences on the directivity of vector sensor by soft ball boundary is not consistent with us.