On disturbances in a semi-infinite visco-elastic rod in a magnetic field

Summary The paper makes use of electromagnetic equations of Maxwell, the equations of mechanical motion together with stress and strain relation of a particular visco-elastic material, to determine the disturbances in it when excited by a magnetic field.     

Propagation of a spherical magnetogasdynamic shock in a self gravitating system

Summary This paper considers a spherical shock, in a conducting gas, produced on account of explosion into an inhomogeneous self gravitating system. Similarity principles have been used to reduce the equations governing the flow to ordinary differential equations under the assumption that the density varies as an inverse-power of distance from the explosion centre.     

Horizontal vibrations of a disk on a poroelastic half-space

This paper analytically examines the horizontal vibration of a rigid disk on a saturated poroelastic half-space. The pressure-solid displacement form of the harmonic equations of motion for asymmetric dynamic problem are developed from the form of the equations originally presented by Biot. Making use of a new method the solution of the above equations is obtained. According to the mixed boundary -value conditions, the dual integral equations of the horizontal vibration of a rigid disk on a saturated poroelastic half-space are established. By appropriate transforms, it is shown that the dual integral equations can be reduced to a pair of Fredholm integral equations of the second kind, whose solutions are then computed. Numerical results for the horizontal dynamic compliance coefficient are given at the end of this paper.     

On the electron dynamics in the field of a whistler wave propagating along a magnetic field in a weakly inhomogeneous plasma

The relativistic motion of electrons in the field of a finite amplitude circularly polarized whistler propagating along a constant magnetic field in a plasma with longitudinal inhomogeneity is considered. It is shown that the equations of the particle motion exhibit a constant of the motion despite the spatial dependence of the wave parameters. The existence of the constant allows one to reduce the equations of motion to a canonical form describing one-dimensional oscillations of a particle with the Hamiltonian slowly varying in the process of the oscillations.     

On disturbances in a viscoelastic solid rod of Burger's type subjected to a magnetic field

Summary The propagation of disturbances in a semi-infinite visco-elastic rod of Burger's type has been investigated, when the rod is subjected to an initially static magnetic field, making use of the electro-magnetic equations of Maxwell, equations of elasticity and the stress-strain relations of the material.     

Horizontal vibration of a rigid disk buried in a poroelastic half-space in contact with a fluid half-space

This paper addresses the horizontal vibration of a rigid disk embedded in a poroelastic half-space in contact with a fluid half-space using the poroelastic theory of potentials. The solution of this problem is expressed in terms of dual integral equations that are converted into Fredholm integral equations of the second kind and solved numerically. Selected numerical results for the horizontal dynamic impedance coefficient are examined based on different poroelastic materials, embedment depths, and excitation frequencies; furthermore, the results are analyzed for the cases in which there is and is no fluid overlying the poroelastic medium to examine the effect of fluid. The results of this study are helpful for designing a foundation embedded in the seabed due to dynamic horizontal forces.     

Magneto-elastic plane waves in a cosserat medium

Summary The propagation of plane waves in an electrically conducting cosserat medium placed in a magnetic field is investigated. The constitutive equations of cosserat elasticity developed recently byParia have been combined with the field equations of electromagnetism to obtain the basic equations for the problem. The results obtained in this investigation are in agreement with the corresponding results on magneto-elastic plane waves in Hookean solids when the cosserat constants are supposed to be absent.     

Numerical solution of micro-physical equations in a model of a convective cloud

Summary The procedure for computation and the numerical results of the first testing of the so-called Mi-operation, which is a construction unit of the model of a convective cloud[1] and represents the formulation of microphysical phenomena occurring in a convective cloud, are described. In this paper the Mi-operation is applied to the case of the liquid stage, restricted to condensation and drop evaporation. The solution of the corresponding system of kinetic equations serves the purpose of an initial test of the applicability of the integration method to the type of equations mentioned.     

Vertical dynamic response of a disk on a saturated poroelastic half-space

This paper considers the vertical dynamic response of a disk on a saturated poroelastic half-space. Firstly the pressure-solid displacement form of the harmonic equations of motion for a poroelastic solid are developed from the form of the equations originally presented by Biot. These equations are solved by a new method. Then the mixed boundary value problem for the vertical harmonic vibration of a disk on a poroelastic half-space is studied. The two types of drainage conditions at the surface of the poroelastic half-space are considered: (a) the surface of the poroelastic half-space is assumed to be completely pervious both within and exterior to the plate; (b) The interface between the plate and the poroelastic half-space is assumed to be impervious and the exterior region is assumed to be pervious. By using the Hankel transform techniques, the paper develops the governing dual integral equations. These governing integral equations are further reduced to systems of standard Fredholm integral equations of the second kind by Abel transform.     

On the magneto-elastic disturbances in a finite elastic bar of variable cross-section

Summary The electro-magnetic equations of Maxwell and the equations of elasticity have been used to investigate the disturbances in an elastic bar acted upon by a magnetic field.     

On longitudinal vibration of an elastic bar in a magnetic field

Summary The equations of elasticity, electromagnetic equations of Maxwell have been applied to investigate the longitudinal vibration of a partly homogenous, partly inhomogeneous elastic bar permeated by a magnetic field.     

On the problem of generalizing Gerstner's trochoidal waves in a three-dimensional case

Summary It is shown that functions, which determine the position of a particle and which represent the solution of Euler's equations of motion in Lagrange's form, can be determined quite accurately from the differential equations established in the paper.     

On axisymmetric vibration in a transversely isotropic finite cylindrical shell acted upon by a magnetic field

Summary The present note seeks to investigate the axisymmetric vibration in a transversely isotropic finite cylindrical shell in presence of axial magnetic field by making use of the electromagnetic equations of Maxwell and the equations of elasticity. The frequency with its minimum value is obtained.     

Elastic radiation from buried sources in a semi-infinite heterogeneous medium

Summary The wave equations of elasticity in the presence of body forces for a semi-infinite, isotropic, heterogeneous medium with exponentially varying material properties have been solved. Using double Fourier transform the equations are first transformed to linear second order differential equations. From the solution of these equations the displacements are obtained by the use of inversion theorem for double Fourier transform. The method followed resolves the disturbance into its constitutive parts—incident and reflectedP, SV andSH type waves. Surface displacements due to a single couple, double couple and various other sources have been calculated.     

Radial vibration of a composite cylindrical shell subjected to a magnetic field

Summary The radial vibration in a composite cylindrical shell under the effect of a magnetic field has been investigated by solving the equations of elasticity, taking into account electromagnetic equations of Maxwell. The frequency equation has been obtained at the final stage.     

Performance of methods for estimating the time of concentration in a watershed of a tropical region

The time of concentration (T_c) is a fundamental parameter in the design of hydrological projects for watersheds. In this study a graphical methodology is described for estimating T_c in a watershed, and this is applied to 17 rainfall–runoff events from a rural watershed located near the capital city of Mato Grosso do Sul State, in the Brazilian Cerrado. The T_c values obtained through the graphical method were compared to T_c values estimated using 20 equations from various references. The equations were selected by considering those that were not developed using data for urban watersheds, and the results of the graphical method were compared to those derived by applying the equations to sub-basin data. The graphical method was reliable in determining T_c, and Ventura’s equation was found to present the best performance for a rural watershed in a tropical climate region.     

Propagation of Rayleigh waves on visco-elastic cylindrical surfaces placed in a magnetic field

Summary This paper studies axial Rayleigh waves in visco-elastic cylinder surrounded by vacuum and for body of same material with a cylindrical cavity. Magneto-elastic equations of motion for wave propagation in the radial and axial direction have been solved to obtain frequency equations.     

On the vibration of a visco-elastic cylindrical shell and a composite visco-elastic cylinder with an isotropic core in an axial magnetic field

Summary The electrc-magnetic equations of Maxwell and the equations of mechanical motion have been used to investigate the vibrations of a cylindrical shell and also a cylinder with an isotropic core characterised by a visco-elasticity of Voigt tupe.     

Computation of a dam-break flood wave in channel transitions

Dam-break flow in channel transitions is simulated by numerically solving the system of governing two-dimensional equations. A simple algebraic coordinate transformation technique is adopted for converting the general physical domain of a transition into a rectangular computational domain. The MacCormack scheme is used for solving the transformed equations. Numerical results of the present study show satisfactory agreement with the experimental data available in the literature. They also match previous numerical results well. Effects of the contractions and expansions on the dam-break flow depth at the dam site is also studied.