Scattering of Rayleigh and Stoneley waves by two adhering elastic wedges

The method of Sommerfeld integrals is used to study propagation of Rayleigh and Stoneley waves in a system of two bonded solid wedges with a common vertex. Numerical results are obtained for configurations with a wide range of angles of steel and aluminum wedges.     

Diffraction of an antiplane shear wave by two coplanar griffith cracks in an infinite elastic medium

The scattering of a time-harmonic antiplane shear wave by two parallel and coplanar Griffith cracks embedded in an infinite elastic medium is considered. The input wave normally impinges on the cracks. Fourier transformations are utilized to reduce the problem to two simultaneous integral equations which can be solved by the series expansion method. The dynamic stress intensity factors are numerically computed.     

Diffraction of acoustic waves by two nonparallel circular cylinders

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Frikladnaya Mekhanika, Vol. 25, No. 1, pp. 43–51, January, 1989.     

Diffraction of an elastic wave by an embedded quarter-space

A method of matching asymptotic fields has recently been applied to the problem of the diffraction of a plane time-harmonic acoustic wave by an embedded quarter-space with different acoustic properties from the rest of space. The method is here applied to the equivalent problem of elastic waves. The normal to the incident wavefront is perpendicular to the apex of the quarter-space and so the problem is two-dimensional in plane strain.Exact expressions are found for the far-field on the boundary of the quarter-space, neglecting those terms which decay faster than the inverse half power of the distance. The main case of interest is where the incident wave propagates parallel to one of the interfaces.The method, unfortunately, does not lead to any information about the amplitude of any interface (Stoneley or Rayleigh) wave which may exist.     

Study on Mach stems induced by interaction of planar shock waves on two intersecting wedges

The properties of Mach stems in hypersonic corner flow induced by Mach interaction over 3D inter-secting wedges were studied theoretically and numerically. A new method called “spatial dimension reduction” was used to analyze theoretically the location and Mach num-ber behind Mach stems. By using this approach, the problem of 3D steady shock/shock interaction over 3D intersecting wedges was transformed into a 2D moving one on cross sec-tions, which can be solved by shock-polar theory and shock dynamics theory. The properties of Mach interaction over 3D intersecting wedges can be analyzed with the new method, including pressure, temperature, density in the vicinity of triple points, location, and Mach number behind Mach stems. Theoretical results were compared with numerical results, and good agreement was obtained. Also, the influence of Mach number and wedge angle on the properties of a 3D Mach stem was studied.     

Diffraction of a plane electromagnetic wave by a slit in a thick screen placed between two different media

The diffraction pattern due to a plane H-polarized electromagnetic wave is investigated, when this wave is incident upon an infinitely long slit of finite width in an opaque screen of non-vanishing thickness. The screen is located between the plane boundaries of two media with different electromagnetic properties. A Green's function formulation of the problem is employed, leading to a system of four coupled integral equations in which the field distributions in the slit occur as unknowns. Numerical results are presented for the field just below the screen as well as for the far field pattern.     

Three-dimensional shock wave reflection over a corner of two intersecting wedges

This paper presents an experimental and numerical investigation of three-dimensional shock wave reflections over a corner of two wedges intersecting perpendicularly in a shock tube. Experiments were conducted in a diaphragmless shock tube equipped with double-exposure diffuse holographic interferometry in which the time interval between the first and second exposure was set to be . This arrangement clearly visualized complex configurations of three-dimensional shock wave reflections. A numerical study was also carried out for interpreting these holographic interferometric observations by using the Weighted Average Flux (WAF) method to solve the three-dimensional unsteady compressible Euler equations. It was found that along the line of the intersection of these two wedges, two Mach stems intersected each other resulting in the formation of a Mach stem which leaned forward. Received 30 June 1996 / Accepted 6 October 1996     

Numerical investigation on three-dimensional shock wave reflection over two perpendicularly intersecting wedges

The three-dimensional (3D) shock wave reflections over two perpendicularly intersecting wedges are numerically studied in this paper, using the finite volume method which is based on the MUSCL-Hancock interpolation technique and self-adaptive unstructured mesh. Two kinds of 3D Mach stem structures are demonstrated by the numerical simulations for different shock Mach numbers and wedge angles. A four-shock or three-shock wave configuration appears in the vicinity of the corner of the wedges.     

Numerical investigation of flow past a system of two sweptback compression wedges

Supersonic flow past a three-dimensional configuration consisting of two neighboring wedges with sweptback leading edges mounted on a preliminary compression surface is numerically investigated. The case of sweptback wedges is considered, when their beveled surfaces deflect the compressed flows to opposite directions. The calculations are carried out on the basis of the averaged Navier-Stokes equations, together with the SST k-? turbulence model, at the freestream Mach number M = 6. The results obtained are compared with the data for inviscid flow calculated using the Euler equations. The flow pattern features, due to the interaction in the plane of symmetry between the shocks formed by the wedges and the shock-induced three-dimensional quasiconical separations of the turbulent boundary layer on the preliminary compression surface along the swept leading edges, are established. Within these separation zones the flow is directed away from the plane of symmetry of the configuration and is characterized by considerably greater values of the transverse velocity component, as compared with the flow outside of the separation zone.     

Diffraction of SH-Waves by an elliptic elastic cylinder

Diffraction of SH-waves by an elliptic elastic cylinder has been discussed. Results are derived also for the case of an elliptical cavity. Numerical results are presented for the shear stress on the cylinder.     

Diffraction of an evanscent plane wave by a half plane

A proper analytic continuation of Sommerfeld's solution is shown to provide the solution to the problem of diffraction of an evanescent plane wave. This is done by a correct extension of a parameter (detour parameter) from real to complex values. Some peculiarities of this solution are discussed. A few representative three-dimensional graphs show the field magnitude in the vicinity of the edge.     

Diffraction by a grating of cylinders with an arbitrary cross-section

The diffraction of a monochromatic plane electromagnetic wave by a grating consisting of parallel, electrically perfectly conducting cylinders is investigated. Two separate two-dimensional scalar problems are dealt with viz. the case ofE-polarization and the case ofH-polarization. A new Green's function formulation of the problem is employed leading to integral equations for the unknown field distributions on an elementary scatterer of the grating. Numerical results are presented for a grating of cylinders with either square or circular cross-section.     

Diffraction of an arbitrary acoustic wave by a strip of finite width

The problem of the diffraction of an arbitrary acoustic wave by a strip of finite width is solved. The solution is constructed by means of a generalization of the previously obtained integral for the problem of the diffraction of acoustic waves by a half-plane [5]. The problem of the diffraction of an arbitrary acoustic wave by the Riemannian manifold corresponding to the strip of finite width is first found. After this, by substitution of the values of the polar angle a solution is obtained for the reflected wave associated with diffraction on the Riemannian manifold, and then the boundary conditions on the surface of the strip are satisfied by means of a linear combination of these solutions. The problem of the diffraction of an arbitrary acoustic wave by a slit of finite width could be constructed in exactly the same way.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–175, March–April, 1991.     

Diffraction of P-wave by crack in an elastic strip at asymmetric position

Scattering of P-wave by a Griffith Crack in a long elastic strip situated at an asymmetric position has been studied in this paper. Using Fourier transform, the mixed boundary value problem has been reduced to the solution of dual integral equations which finally has been reduced to the solution of a Fredholm integral equation of second kind. Solving this integral equation numerically, stress intensity factors have been calculated and illustrated graphically to show the effect of asymmetry of position of the crack.     

Diffraction of antiplane shear waves by two cracks in the presence of a magnetic field

The problem of scattering of horizontal polarized shear waves by the two cracks in a uniform magnetostatic field is considered. The magnetic field is assumed to be parallel to the crack surfaces as well as perpendicular to the crack surfaces. The elastic medium under consideration is a homogeneous, isotropic and infinitely conducting one. The solution of the problem is reduced into a pair of triple integral equations having trigonometrical kernels. Using the finite Hilbert transform technique, solution of the pair of triple integral equations is obtained for the low frequencies. Finally, approximate formulae are derived for the stress intensity factors.