Search

A problem of diffraction by an elongated body of revolution is studied. The incident wave falls along the axis. The wavelength is small comparatively to the dimensions of the body. The parabolic equation of the diffraction theory is used to describe the diffraction process. A boundary integral equation is derived. The integral equation is solved analytically and by iterations for diffraction by a cone.

The interaction of oblique incident waves with a floating porous plate has been investigated using the matched eigenfunction expansion method (MEEM). The porous boundary condition based on Darcy’s law is applied at a floating porous plate (Zhao et al. (2009)). Depending on the presence of a vertical rear wall, the wave energy dissipation by a floating porous plate is evaluated with two analytical models: wave barrier and wave absorber. The nonlinear dispersion equation, derived from the porous boundary condition, is solved numerically by using Muller’s method to obtain the complex-number eigenvalues in the porous-plate covering region. Notably, it is confirmed that the real part of the first-mode eigenvalue is closely related to the energy dissipation due to the generation of vortices when waves propagate past a floating porous plate, and the porosity parameter b = 5 . 0 (plate porosity P = 0 . 1 ) is found to be the optimal value for the maximum energy dissipation. The analytical solutions are validated by means of the model test with a floating porous wave barrier.

Complete analytical solutions are obtained here for normally incident water wave scattering by vertical porous barriers of various configurations. By allowing incident waves from either direction separately, two quarter-plane problems are posed for porous potentials associated with the physical problem as well as for solid potentials associated with the scattering problem that involves the vertical solid barrier of same configuration. Then, two integral relations are introduced to establish a link between the porous and the solid wave potentials. They involve auxiliary wave potentials that describe radiation of bi-directional waves by the solid barrier. Moreover, they aid to decompose the original problem into four analytically solvable problems in a quarter-plane and to determine the porous potentials explicitly.

The scattering of obliquely incident waves by straight features in a plate is solved analytically. The reflection matrix of a free straight edge and the scattering matrix of a straight thickness step are obtained respectively by modal decomposition based on a real orthogonal relation. The formulas are illustrated through numerical examples. The matrices are found to be Hermitian for the propagating modes; thus, the mode conversions are reciprocal in terms of energy. The matrices can be used to determine the scattering from more complicated straight features if the cross sections are approximated as sequences of stairs and steps.

In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a finite number of Helmholtz resonators in a unit cell and that unit cell is repeated periodically. To solve the scattering problem, the mathematical framework elaborated in Ammari et al. (2019) is used. The main result is an approximate formula for the scattered wave in terms of the lengths of the openings. Our framework provides analytic expressions for the scattering wave vector and angle and the phase-shift. It justifies the apparent absorption. Moreover, it shows that at specific lengths for the openings and a specific frequency there is an abrupt shift of the phase of the scattered wave due to the subwavelength resonances of the Helmholtz resonators. A numerically fast implementation is given to identify a region of those specific values of the openings and the frequencies., Wave Motion, 97, ISSN:0165-2125

In this paper we consider an inverse scattering problem from an open arc with impedance boundary conditions on both sides of the crack. Our aim is to recover both the impedance function and the unknown crack simultaneously from the far-field pattern with only one incident wave. Making the most out of the direct problem, a straightforward method of iterative nature is developed for the inverse problem. The ill-posedness of this problem is considered by incorporating the Tikhonov regularization. Numerical examples are provided at the end of the paper to show the feasibility of our method.

We have considered a semi-infinite crack embedded in a transversely isotropic medium and studied two special cases, one, in which the axis of symmetry is normal to the crack face and the wave incidence is arbitrary and another, in which the axis lies in the crack plane normal to the edge and the incident wave vector is also normal to the edge. The problem is of interest in Non-Destructive Evaluation, because austenitic steels that are found in claddings and other welds in the nuclear reactors are often modeled as transversely isotropic. In both cases, we have expressed the scattered field in a closed form and computed the corresponding diffraction coefficients. An extended version of the article, which contains representative plots of the magnitudes of some such coefficients, can be found on http://arxiv.org/pdf/0802.0460 .

In this paper we consider an inverse scattering problem whose aim is to recover the impedance function for an arbitrary crack from the far field pattern. Because of the ill-posedness of this problem, regularization method for example, Tikhonov regularization, is incorporated in our solution scheme. Several numerical examples with only one incident wave are given at the end of the paper to show the feasibility of our method.

The linear theory of two-dimensional reflection and transmission of time-harmonic, elastic waves by the spatially periodic interface between two perfectly elastic media is developed. A given phase progression of the incident wave in the direction of periodicity induces a modal structure in the elastodynamic field and leads to the introduction of the so-called spectral orders. The main tools in the analysis are the elastodynamic Green-type integral relations. They follow from the two-dimensional form of the elastodynamic field reciprocity theorem, where in the latter a Green state adjusted to the periodicity of the structure at hand is used. One of these relations is a vectorial integral equation from which the elastodynamic field quantities can be determined. The consequences of field reciprocity in the structure and of the conservation of energy are developed in view of their serving as a check on numercal results to be obtained from the relevant integral equations. The formalism thus developed applies to profiles, if periodic, of arbitrary shape and size and can without too serious difficulties be implemented on a computer. The major difficulty in this respect is the relevant Green function, the series representation of it being slowly convergent. Its evaluation becomes tractable after an appropriate technique for accelerating the convergence. The only practical limitations are then put by the speed of the computer and its storage capacity.