Diffraction of a plane electromagnetic wave by a perfectly conducting elliptic cylinder

The scattering of a plane electromagnetic wave by a perfectly conducting elliptic cylinder is investigated theoretically. The calculations are based upon the expansion of the scattered wave functions in terms of Mathieu functions. Both E- and H-polarized waves are considered. Numerical results, in particular for the scattering cross-section, are presented for cylinders the cross-sectional dimensions of which are up to many wavelengths (e.g. distance between the focal lines up to 20 wavelengths).     

Diffraction of a sound wave by a slit

The diffraction of a sound wave by a slit in an unbounded plane is analyzed as an initial-boundary-value problem with a moving boundary for the two-dimensional wave equation. The initial-boundary-value problem is solved by the formation and inversion of Volterra integral equations. A solution is obtained in closed form in quadratures for an arbitrary angle of inclination of the incident wave front relative to the plane. The solution is presented in the form of recursion formulas, which take into account the influence of diffraction waves occurring in succession at the boundaries of the slit.     

Pulsed electromagnetic radiation from a line source in the presence of a semi-infinite screen in the plane interface of two different media

The two-dimensional diffraction of a pulsed electromagnetic wave by a semi-infinite screen located in the interface of two different media is investigated theoretically. The incident electromagnetic field is taken to be generated by a line source. With the aid of the Wiener-Hopf technique and the Cagniard-De Hoop technique closed-form expressions for the field components anywhere in the configuration are obtained. Numerical results are presented in the case of E-polarization.     

Electromagnetic diffraction by a thin conducting circular disk placed at the plane interface of two different media

In this paper, the problem of diffraction of time harmonic, electromagnetic waves by a thin ideally conducting disk lying at the plane interface of two different media is considered. In this analysis, the incident wave is a plane wave travelling in a direction perpendicular to the plane interface of the two media. A Hertz vector formulation is applied to reduce our electromagnetic diffraction problem to a system of two scalar problems which are solved by the help of two pairs of Fredholm integral equations of the second kind. Low frequency approximations to the tangential components of the magnetic intensity associated with the diffracted field at the surfaces of the disk, the induced surface current density on the disk and the scattering cross section are obtained.     

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 of a plane wave by a reinforced circular cavity in a massif

State University, Donetsk. Translated from Prikladnaya Mekhanika, Vol. 28, No. 3, pp. 19–22, March, 1992.     

Diffraction by a nonplanar screen

This paper is concerned with diffraction of short waves by a nonplanar screen (two-dimensional case, Dirichlet boundary condition). The high-frequency asymptotic approximation to the solution is obtained. First the wave field of the primary wave is found in a neighbourhood of the screen edge and then this field is continued along the boundary. Secondary waves arise here as the consequence of interaction between the edge and the primary wave. The secondary wave is diffracted by another edge of the screen, and a third order wave arises, and so on. This process gives the formulas for the wave field in a neighbourhood of the screen. Green's formula is used to continue the solution outside of this neighbourhood.     

Experimental study of mutual interference between two spheres placed on a plane boundary

This paper describes an experimental study of the mutual interference between two spheres placed on a plane boundary. The experiment was carried out in an N. P. L. type wind-tunnel having a working section of 500×500×2000 mm³ in size at a Reynolds number of 4.74×10⁴. The surface-pressure distributions of two spheres were measured for the various relative positions of two spheres and the drag, side-force, and lift coefficients were determined from surface-pressure distributions. The separation of the flow and the formation of vortices were observed by the method of visualization. The distributions of velocities, and turbulent intensities of the flow past two spheres were measured. The experimental results for two spheres were compared with those of a single sphere.List of symbols C _D drag coefficient - C _L lift coefficient - C _p surface-pressure coefficient of sphere=(P-P )(qU ² ) - C _s coefficients of side force - D diameter of sphere [mm] - P static pressure [Pa] - P static pressure in free stream [Pa] - Re Reynolds number= DU/v - S spacing between the centers of two adjoining spheres in plane view [mm] - U time-mean velocity in X-direction [m/s] - [m/s] free stream velocity [m/s] - u, v, w X, Y and Z-components of velocity fluctuation [m/s] - X, Y, Z coordinate axes with origin at the bottom center of test sphere, X, Y, Z axis being taken in the streamwise, lateral and vertical directions respectively [mm] (Fig. 1) - latitude angle [°] - longitude angle [°] - angle between the line connected with the centers of two spheres and wind direction [°] (Fig. 2) - kinematic viscosity of air [m²/s] - density of air [N/m³] This paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986     

Diffraction of a plane stress wave by a semi-infinite crack in a general anisotropic elastic material

The problem of a semi-infinite crack subjected to an incident stress wave in a general anisotropic elastic solid is considered. The plane wave impinges the crack at a general oblique angle and is of any of the three types propagating in that direction. A related problem of a semi-infinite crack loaded by a pair of concentrated forces moving along the crack surfaces is also considered. In contrast to the conventional approach by Laplace transforms, a Stroh-like formalism is employed to construct the solution directly in the time domain. The solution is shown to depend on a Wiener–Hopf factorization of a symmetric matrix. Closed-form solution of the stress intensity factors is derived. A remarkably simple expression for the energy release rate is obtained for normal incidence.     

Diffraction of a plane acoustic wave by a rigid sphere in a cylindrical cavity: An axisymmetric problem

The paper studies the interaction of a rigid spherical body and a cylindrical cavity filled with an ideal compressible fluid in which a plane acoustic wave of unit amplitude propagates. The solution is based on the possibility of transforming partial solutions of the Helmholtz equation between cylindrical and spherical coordinates. Satisfying the interface conditions between the cavity and the acoustic medium and the boundary conditions on the spherical surface yields an infinite system of algebraic equations with indefinite integrals of cylindrical functions as coefficients. This system of equations is solved by reduction. The behavior of the system is studied depending on the frequency of the plane wave     

Diffraction of a plane shock wave by a disk that enters a compressible liquid at an inclination

A study is made of the three-dimensional problem of the interaction between a disk that enters water asymmetrically and a shock wave that is moving toward the disk. The water is assumed to be a perfect compressible liquid and the flow adiabatic. The changes in the flow parameters and the state are determined by numerical integration of the equations that describe the flow. A three-dimensional version of the finite-difference scheme of [1] is used in accordance with the method of [2]. The influence of the intensity of the shock wave on the drag coefficient of the disk and the shape of the free surface is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 185–187, January–February, 1990.     

Diffraction by an aperture between two wedges

An asymptotic solution for large spacing is obtained in the problem of diffraction by an aperture between two conducting wedges. The variation of the wedge angles is shown to have significant effect on the far field amplitude of the transmitted field in certain ranges of angle forE-polarization. The wedge angles are seen to have a greater effect than interaction corrections in some cases but a lesser effect in others. Numerical comparisons are carried out.     

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored. This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

Diffraction of a sound wave by a nonmoving plate

The problem of determining the velocity field excited by a sound wave impinging on a plate at rest is analyzed as an initial- and boundary-value problem with a movable boundary for the two-dimensional wave equation. The latter problem is solved by the formulation and inversion of integral equations of the Volterra type. The solution is obtained in closed form for any angle of inclination of the incident wave relative to the plate surface and is represented by recursion relations allowing for the influence of any number of diffracted waves generated in succession at the plate boundary.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 123–130, March–April, 1972.     

Propagation of electromagnetic wave in the three phases soil media

IntroductionItisofparamountimportancetogetgeotechnicalparameterssuchasmoisture ,compactness,andshearstrengthforgeotechnicalengineeringtransaction .Butthemethodtofetchthesoilsamplesforlaboratorytestcannotavoidbringingthedisturbance ,andmakethetestresultsinconsistenttotheactualstatusofsoil.Inrecentyears,theapplicationofEMwaveinthedetectinghiddentroublesindamsandundergroundfoundationsdevelopedrapidly .Buttherearestillsomefactorsthatrestricttheadvanceofapplication .Firstly ,thesoilconstitutesthr…     

Cylindrical plane strain wave propagation in elastic/viscoplastic media

This paper discusses the influence of strain-hardening and of viscosity on the cylindrical elastic/viscoplastic wave-propagation. Perzyna's model is used with linear viscosity dependence, bilinear quasi-static stressstrain curve and a radial stress is assumed to be suddenly applied on the surface of a cylindrical cavity and maintained constant. It is shown by computer analysis that work-hardening and viscosity affect the results considerably and that at a certain time after the impact load is applied an elastic region appears within the viscoplastically deforming medium.