A Boussinesq-Type Model for Nonlinear Wave-Heaving Cylinder Interaction

In the present work, a Boussinesq-type numerical model is developed for the simulation of nonlinear wave-heaving cylinder interaction. The wave model is able to describe the propagation of fully dispersive and weakly nonlinear waves over any finite water depth. The wave-cylinder interaction is taken into account by solving simultaneously an elliptic equation that determines the pressure exerted by the fluid on the floating body. The heave motion for the partially immersed floating cylinder under the action of waves is obtained by solving numerically the body’s equation of motion in the z direction based on Newton’s law. The developed model is applied for the case of a fixed and a free-floating circular cylinder under the action of regular waves, as well as for a free-floating cylinder undergoing a forced motion in heave. Results (heave and surge exciting forces, heave motions, and wave elevation) are compared with those obtained using a frequency domain numerical model, which is based on the boundary integral equation method.

Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

Diagnostics of Polymer Composite Materials by Waveguide Method

This article considers the use of radio wave method for testing polymer composites used as structural material for manufacture of aircrafts. Measuring process, analysis and calculation by integral equation method are described.

Ray Optical Scattering from Uniform Reflective Cylindrical Metasurfaces using Surface Susceptibility Tensors

A ray optical methodology based on the uniform theory of diffraction is proposed to model electromagnetic field scattering from curved metasurfaces. The problem addressed is the illumination of a purely reflective uniform cylindrical metasurface by a line source, models the surface with susceptibilities and employs a methodology previously used for cylinders coated in thin dielectric layers [1]. The approach is fundamentally based on a representation of the metasurface using the General Sheet Transition Conditions (GSTCs) which characterizes the surface in terms of susceptibility dyadics. An eigenfunction description of the metasurface problem is derived considering both tangential and normal surface susceptibilities, and used to develop a ray optics (RO) description of the scattered fields; including the specular geometrical optical field, surface diffraction described by creeping waves and a transition region over the shadow boundary. The specification of the fields in the transition region is dependent on the evaluation of the Pekeris caret function integral and the method follows [1]. The proposed RO-GSTC model is then successfully demonstrated for a variety of cases and is independently verified using a rigorous eigenfunction solution (EF-GSTC) and full-wave Integral Equation method (IE-GSTC), over the entire domain from the deep lit to deep shadow.

A meshless local Galerkin integral equation method for solving a type of Darboux problems based on the radial basis functions

The main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ the Gauss–Legendre integration rule on the influence domains of shape functions to compute the local integrals appearing in the method. Since the scheme is constructed on a set of scattered points and does not require any background meshes, it is meshless. The error bound and the convergence rate of the presented method are provided. Some illustrative examples are included to show the validity and efficiency of the new technique. Furthermore, the results obtained demonstrate that this method uses much less computer memory than the method established using global radial basis functions. doi:10.1017/S1446181121000377

Modelling of the reflectance profile of axisymmetrical radiolocation objects using the integral equation method

Based on the first-kind integral equation method for the electric field, the procedure and software for calculating the radar cross-section of axisymmetrical objects, bodies of revolution, are developed. Algorithms are proposed for computation of the matrix of mutual impedances and Green's function of a ring source providing the computation accuracy required for obtaining a stable solution. The method of solution approximation accuracy evaluation by azimuthal harmonics is proposed. Comparison with test examples is carried out and the applicability for solving real-world problems is shown.

Analysis of Eigenfrequencies of a Circular Interface Delamination in Elastic Media Based on the Boundary Integral Equation Method

The widespread of composite structures demands efficient numerical methods for the simulation dynamic behaviour of elastic laminates with interface delaminations with interacting faces. An advanced boundary integral equation method employing the Hankel transform of Green’s matrices is proposed for modelling wave scattering and analysis of the eigenfrequencies of interface circular partially closed delaminations between dissimilar media. A more general case of partially closed circular delamination is introduced using the spring boundary conditions with non-uniform spring stiffness distribution. The unknown crack opening displacement is expanded as Fourier series with respect to the angular coordinate and in terms of associated Legendre polynomials of the first kind via the radial coordinate. The problem is decomposed into a system of boundary integral equations and solved using the Bubnov-Galerkin method. The boundary integral equation method is compared with the meshless method and the published works for a homogeneous space with a circular open crack. The results of the numerical analysis showing the efficiency and the convergence of the method are demonstrated. The proposed method might be useful for damage identification employing the information on the eigenfrequencies estimated experimentally. Also, it can be extended for multi-layered composites with imperfect contact between sub-layers and multiple circular delaminations.

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.

Development of the Approximating Functions Method for Problems in a Planar Waveguide with Constant Polarization

Article introduces an extension of the approximating functions method, a particular case of the finite element method (FEM) with interpolating functions in the form of Lagrange polynomials of a special form, to solve electrodynamics problems in a planar waveguide with constant polarization in the spatial-temporal domain using the Volterra integral equation method. The main goal of the article is to expand the area of ​​applicability of this method to three-dimensional problems in a planar waveguide with constant polarization, as well as to obtain general interpolation expressions in analytical form, which will be used to construct a system of nonlinear equations for solving specific problems.