Rigorous accounting diffraction on non-plane gratings irradiated by non-planar waves

The modified boundary integral equation method (MIM) is considered a rigorous theoretical application for the diffraction of cylindrical waves by arbitrary profiled plane gratings, as well as for the diffraction of plane/non-planar waves by concave/convex gratings. This study investigates two-dimensional (2D) diffraction problems of the filiform source electromagnetic field scattered by a plane lamellar grating and of plane waves scattered by a similar cylindrical-shaped grating. Unlike the problem of plane wave diffraction by a plane grating, the field of a localised source does not satisfy the quasi-periodicity requirement. Fourier transform is used to reduce the solution of the problem of localised source diffraction by the grating in the whole region to the solution of the problem of diffraction inside one Floquet channel. By considering the periodicity of the geometry structure, the problem of Floquet terms for the image can be formulated so that it enables the application of the MIM developed for plane wave diffraction problems. Accounting of the local structure of an incident field enables both the prediction of the corresponding efficiencies and the specification of the bounds within which the approximation of the incident field with plane waves is correct. For 2D diffraction problems of the high-conductive plane grating irradiated by cylindrical waves and the cylindrical high-conductive grating irradiated by plane waves, decompositions in sets of plane waves/sections are investigated. The application of such decomposition, including the dependence on the number of plane waves/sections and radii of the grating and wave front shape, was demonstrated for lamellar, sinusoidal and saw-tooth grating examples in the 0th & –1st orders as well as in the transverse electric and transverse magnetic polarisations. The primary effects of plane wave/section partitions of non-planar wave fronts and curved grating shapes on the exact solutions for 2D and three-dimensional (conical) diffraction problems are discussed.

Mathematical models of the evolution of classical and solitary cylindrical waves

The evolution of nonlinear elastic cylindrical displacement waves for initial profiles in the form of a Hankel and Macdonald functions is analyzed theoretically and numerically. The difference between the two waves is that the MacDonald function has no hump, decreases monotonically and has a concave downward profile, and the Hankel function is a harmonic attenuating wave. The main novelty is that the evolution of cylindrical waves is studied for two different approaches to the solution of a nonlinear equation. Some significant differences of these waves are shown. First, the features of the Hankel wave, a harmonic wave (symmetrical profile), are briefly described. Then, theoretically and numerically, a single wave with an initial profile in the form of a MacDonald function is analyzed in more detail. Distortion of the initial profile due to the nonlinear interaction of the wave itself and the increase in the maximum amplitude during wave propagation is common to these profiles. Significant features of the McDonald wave are shown - an uncharacteristic initial profile (a profile without a classical hump) evolves in an uncharacteristic way - the profile becomes much steeper and remains convex downwards. Keywords: classical and solitary cylindrical waves; five-constant Murnaghan potential; approximate methods; Hankel and Macdonald initial wave profiles; evolution.

Diffraction of Transient Cylindrical Waves by a Rigid Oscillating Strip

This investigation portrays the transient cylindrical wave diffraction by an oscillating strip. Mathematical analysis of the problem is carried out with the help of an integral transforms and the Wiener–Hopf technique. Using far zone approximation, the scattered field is evaluated by the method of steepest descent. This study takes into consideration the transient cylindrical source and an oscillating strip such that both the source and a scatterer have different oscillating frequencies ω 1 ′ and ω 0 ′ , respectively. The situation under consideration is well supported by graphical results showing the effects of emerging parameters.

On the question of cylindrical waves in elastic media

Рассматривается задача о распространении цилиндрической волны сжатия в упругой среде. Получены значения радиальных смещений точек среды и радиальных напряжений. Указаны асимптотические оценки полученных решений для поля смещений в среде на больших расстояниях от источников волны, а также статистическое распределение смещений среды. The problem of propagation of a cylindrical compression wave in an elastic medium is considered. The values of radial displacements of medium points and radial stresses are obtained. Asymptotic estimates of the obtained solutions for the displacement field in the medium at large distances from the wave sources are given, as well as the statistical distribution of the displacement of the medium.

Нагружение, деформирование и разрушение цилиндрических образцов из полиметилметакрилата и фторопласта с использованием электрического взрыва проводников

The paper presents outcomes of the experimental study of mechanical loading, deformation and fracture of the cylindrical specimens of poly(methyl methacrylate) and fluoropolymer performed with the electric explosion of conductors with various rates of loading. Propagation of the cylindrical waves of mechanical loading through the sample analyzed and correlated with generation and evolution of the fractures. Comparison of main mechanisms of fracture based on the fractographic analysis performed. Leading features of the distortion processes revealed.