Diffraction by an acoustically penetrable or an electromagnetically dielectric half plane II

The present work gives a mathematical model for an acoustically penetrable or electromagnetically dielectric half plane. An approximate boundary condition is derived which depends on the thickness of, and the material constants which constitutes, the half plane. A solution is obtained, using the approximate boundary condition, for the problem of a line source field diffracted by a semi-infinite penetrable/dielectric half plane. The asymmetry of the approximate boundary condition results in a matrix Wiener-Hopf problem, which is solved explicitly

Efficient techniques for scattering from planar and cylindrical structures with edges

In this work, we present rigorous and efficient methods for analyzing scattering from the following structures • Tandem Slit loaded with homogeneous material • Eccentrically loaded cylinder with multiple slits • Semicircular cylinder and slit • Dielectric loaded Wedge shaped cylinder • Circular cylinder with resonant cavities and resonant cavities on circular arc. For analyzing the material loaded tandem slit configuration, the boundary value problem is formulated into a pair of simultaneous Wiener-Hopf equations via Fourier transformation. After decoupling these equations by elementary transformation, each modified Wiener-Hopf equation is reduced to a Fredholm integral equation of the second kind. The integral equations are then solved approximately to yield the Fourier transform of the diffracted fields. The inverse transform is evaluated asymptotically to obtain the far field expressions. Measurements and numerical simulations are also performed for several different geometric and material configurations. The analytic solutions compare well with measured and simulated results. The possibility of reducing beamwidth and increasing power coupled through the loaded tandem slit is explored. The analysis of the eccentrically loaded cylindrical cavity with multiple slits under plane wave illumination is formulated using two distinct approaches: (1) an integral equation/combined boundary condition (IE/CBC) formulation and (2) an integral equation/Neumann series expansion (IE/NS) formulation. The IE/NS formulation is shown to converge faster than the IE/CBC formulation based on the proper edge behavior exhibited by the Neumann series current expansion functions. Results for the backscattered radar cross section (RCS) of several geometries are presented, and the relationships between the RCS and the scatterer characteristics are explored. The applicability of the Neumann series method to find a fast method for evaluating scattering from a metallic strip and semicircular cylinder is presented. The Neumann series of different periodicity is used for studying scattering from wedge shaped cylinder. The Neumann series is also applied to study scattering from a circular cylinder with resonant cavities and resonant cavities on a circular arc. These resonant cavities on a circular arc have superdirective properties, which are useful for high gain antenna design

Edge waves and resonance on elastic structures: An overview

Copyright @ 2011 SAGE PublicationsOver 50 years have elapsed since the first experimental observations of dynamic edge phenomena on elastic structures, yet the topic remains a diverse and vibrant source of research activity. This article provides a focused history and overview of such phenomena with a particular emphasis on structures such as strips, rods, plates and shells. Within this context, some of the recent research highlights are discussed and the contents of this special issue of Mathematics and Mechanics of Solids on dynamical edge phenomena are introduced

Okvirno rješenje za difrakciju ravnog vala impedacijskom trakom: slučaj H-polarizacije

In this study, the diffraction of H-polarized plane wave by an infinitely long strip which has the same impedance on both faces with a width of 2a is investigated by using an analytical-numerical method. The diffracted field is obtained by an integral equation in terms of the electric and magnetic currents induced by the incident field. This integral equation is reduced to two uncoupled integral equations that include only induced electric and magnetic currents separately. Both of the currents are defined as a sum of infinite series of Gegenbauer polynomials with unknown coefficients satisfying the edge conditions. The integral equations are transformed to linear algebraic equations by using analytical methods and the unknown coefficients are determined by solving numerically obtained matrix equations. Numerical examples on the RCS (radar cross section) are presented, and the far field scattering characteristics of the strip are discussed in detail. Some of the obtained results are compared with the other existing method.U ovom radu istražuje se difrakcija H-polariziranog ravnog vala od beskonačno duge trake koja ima jednak otpor na obje strane i širinu 2a korištenjem analitičkog-numeričke metode. Difraktirano polje dobiveno je putem integralne jednadžbe u smislu električnih i magnetskih struja induciranih upadnim poljem. Ova integralna jednadžba svedena je na dvije odvojene integralne jednadžbe koje zasebno uključuju samo inducirane električne i magnetske struje. Obje struje definirane su kao zbroj beskonačnog niza Gegenbauerovih polinoma s nepoznatim koeficijentima koji zadovoljavaju rubne uvjete. Integralne jednadžbe pretvorene su u linearne algebarske jednadžbe pomoću analitičkih metoda i nepoznati su koeficijenti utvrđeni rješavanjem numerički dobivenih matričnih jednadžbi. Predstavljeni su numerički primjeri na PRP-u (površina radarskog presjeka), a karakteristike rasipanja na dalekom polju kod traka detaljno su raspravljeni. Neki od dobivenih rezultata uspoređeni su s drugom postojećom metodom

規範形状をもつ2次元物体による波動散乱に関する解析的研究

【学位授与の要件】中央大学学位規則第4条第1項【論文審査委員主査】小林　一哉　（中央大学理工学部教授）【論文審査委員副査】庄司　一郎（中央大学理工学部教授）、白井　宏（中央大学理工学部教授）、山﨑　恆樹（日本大学理工学部教授）博士（工学）中央大

Acoustic diffraction from a semi-infinite elastic plate under arbitrary fluid loading with application to scattering from Arctic ice leads

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution May 1989The problem of a low-frequency acoustic plane wave incident upon a free surface coupled to a semi-infinite elastic plate surface, is solved using an analytic approach based on the Wiener-Hopf method. By low-frequency it is meant that the elastic properties of the plate are adequately described by the thin plate equation (kH ≲ 1). The diffraction problem relates to issues in long range sound propagation through partially ice-covered Arctic waters, where open leads or polynya on the surface represent features from which acoustic energy can be diffracted or scattered. This work focusses on ice as the material for the elastic plate surface, and, though the solution methods presented here have applicability to general edge diffraction problems, the results and conclusions are directed toward the ice lead diffraction process. The work begins with the derivation of an exact solution to a canonical problem: a plane wave incident upon a free surface (Dirichlet boundary condition) coupled to a perfectly rigid surface (Neumann boundary condition). Important features of the general edge diffraction problem are included here, with the solution serving as a guideline to the more complicated solutions presented later involving material properties of the boundary. The ice material properties are first addressed using the locally reacting approximation for the input impedance of an ice plate, wherein the effects of elasticity are ignored. This is followed by use of the thin plate equation to describe the input impedance, which incorporates elements of elastic wave propagation. An important issue in working with the thin plate equation is the fluid loading pertaining to sea ice and low-frequency acoustics, which cannot be characterized by simplifying heavy or light fluid loading limits. An approximation to the exact kernel of the Wiener-Hopf functional equation is used here, which is valid in this mid-range fluid loading regime. Use of this approximate kernel allows one to proceed to a complete and readily interpretable solution for the far field diffracted pressure, which includes a subsonic flexural wave in the ice plate. By using Green's theorem, in conjunction with the behavior of the diffracted field along the two-part planar boundary, the functional dependence of ∏D (total diffracted power) in terms of k (wavenumber), H (ice thickness), α (grazing angle) and the combined elastic properties of the ice sheet and ambient medium, is determined. A means to convert ∏D into an estimate of dB loss per bounce is developed using ray theoretical methods, in order to demonstrate a mechanism for acoustic propagation loss attributed directly to ice lead diffraction effects. Data from the 1984 MIZEX (Marginal Ice Zone Experiments) narrow-band acoustic transmission experiments are presented and discussed in this context.I also gratefully acknowledge financial support provided by the WHOI Education Office and the Office of Naval Research

High-contrast approximation for penetrable wedge diffraction

Abstract The important open canonical problem of wave diffraction by a penetrable wedge is considered in the high-contrast limit. Mathematically, this means that the contrast parameter, the ratio of a specific material property of the host and the wedge scatterer, is assumed small. The relevant material property depends on the physical context and is different for acoustic and electromagnetic waves for example. Based on this assumption, a new asymptotic iterative scheme is constructed. The solution to the penetrable wedge is written in terms of infinitely many solutions to (possibly inhomogeneous) impenetrable wedge problems. Each impenetrable problem is solved using a combination of the Sommerfeld–Malyuzhinets and Wiener–Hopf techniques. The resulting approximated solution to the penetrable wedge involves a large number of nested complex integrals and is hence difficult to evaluate numerically. In order to address this issue, a subtle method (combining asymptotics, interpolation and complex analysis) is developed and implemented, leading to a fast and efficient numerical evaluation. This asymptotic scheme is shown to have excellent convergent properties and leads to a clear improvement on extant approaches.</jats:p

A uniform GTD analysis of the EM diffraction by a thin dielectric/ferrite half-plane and related configurations

A uniform geometrical theory of diffraction (UTD) solution is developed for the problem of the diffraction by a thin dielectric/ferrite half plane when it is excited by a plane, cylindrical, or surface wave field. Both transverse electric and transverse magnetic cases are considered. The solution of this problem is synthesized from the solutions to the related problems of EM diffraction by configurations involving perfectly conducting electric and magnetic walls covered by a dielectric/ferrite half-plane of one half the thickness of the original half-plane

Wave transmission across surface interfaces in lattice structures

Within the lattice dynamics formulation, we present an exact solution for anti-plane surface waves in a square lattice strip with a surface row of material particles of two types separated by a linear interface. The considered problem is a discrete analog of an elastic half-space with surface stresses modelled through the simplified Gurtin–Murdoch model, where we have an interfacial line separating areas with different surface elastic properties. The main attention is paid to the transmittance and the reflectance of a wave across the interface. The presented results shed a light on the influence on surface waves of surface inhomogeneity in surface elastic properties such as grain and subgrain boundaries