Unsteady flow of a fourth-grade fluid due to an oscillating plate

The governing non-linear high-order, sixth-order in space and third-order in time, differential equation is constructed for the unsteady flow of an incompressible conducting fourth-grade fluid in a semi-infinite domain. The unsteady flow is induced by a periodically oscillating two-dimensional infinite porous plate with suction/blowing, located in a uniform magnetic field. It is shown that by augmenting additional boundary conditions at infinity based on asymptotic structures and transforming the semi-infinite physical space to a bounded computational domain by means of a coordinate transformation, it is possible to obtain numerical solutions of the non-linear magnetohydrodynamic equation. In particular, due to the unsymmetry of the boundary conditions, in numerical simulations non-central difference schemes are constructed and employed to approximate the emerging higher-order spatial derivatives. Effects of material parameters, uniform suction or blowing past the porous plate, exerted magnetic field and oscillation frequency of the plate on the time-dependent flow, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviour of the fourth-grade non-Newtonian fluid is also compared with those of the Newtonian fluid.     

Gravitational and acoustic waves due to the motion of an oscillating thin plate beneath the surface of a heavy weakly-compressible fluid

The three-dimensional problem of the motion of a thin plate in an inviscid, heavy, weakly-compressible fluid is solved. The surface tension is disregarded. The plate moves rectilinearly at a constant velocity under the surface of an infinite-depth fluid and oscillates at a given frequency. The fluctuating dipole potential is obtained from the Euler and continuity equations with account for the conditions on the free surface (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions imposed on the plate surface. Formulas for calculating the far acoustic field are derived. The calculations for a square plate are carried out.     

Wave motions of a fluid due to a moving system of pressures on an inclined bottom

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 38–44, November–December, 1991.     

Flexural-gravity wave resistances due to a surface-moving line source on a fluid covered by a thin elastic plate

Analytical solutions for the flexural-gravity wave resistances due to a line source steadily moving on the surface of an infinitely deep fluid are investigated within the framework of the linear potential theory. The homogenous fluid, covered by a thin elastic plate, is assumed to be incompressible and inviscid, and the motion to be irrotational. The solution in integral form for the wave resistance is obtained by means of the Fourier transform and the explicitly analytical solutions are derived with the aid of the residue theorem. The dispersion relation shows that there is a minimal phase speed c_min, a threshold for the existence of the wave resistance. No wave is generated when the moving speed of the source V is less than c_min while the wave resistances firstly increase to their peak values and then decrease when V ? c_min. The effects of the flexural rigidity and the inertia of the plate are studied.     

Visco-elastic flow due to a plate which starts oscillating in the presence of a parallel stationary plate

In this paper, the flow of a visco-elastic liquid between two parallel plates has been studied when one plate is stationary and the other plate suddenly starts oscillating. Both finite Fourier sine transform and Laplace transform technique have been employed to solve the basic differential equations. The flow phenomenon has been characterized by the parameters, and and the effects of these on the flow characteristics have been studied through several graphs.Late professor of the department, who died in an accident on 7th July 1978.     

Dynamics of thin periodic plates resting on a periodically inhomogeneous Winkler foundation

Summary The aim of the paper is to investigate the dynamic response of thin elastic plates having periodic substructure in planes parallel to the plates midplane and interacting with a Winkler foundation. The main goal of the analysis is to describe the effect of substructure size on the plates dynamics. For this purpose, the method proposed in [4, 5] is used. Two special cases are analysed: a plate band with a constant thickness interacting with a periodically inhomogeneous Winkler foundation, and a plate band with a periodically variable thickness interacting with a homogeneous Winkler foundation. The physical correctness conditions of the model are also discussed. Received 14 July 1998; accepted for publication 7 January 1999     

Waves due to an oscillatory pressure on a stratifield fluid: A uniformly valid asymptotic solution

The three-dimensional axisymmetrical initial-value problem of waves in a two-layered fluid of finite depth by an oscillatory surface pressure is solved. The exact integral solutions for velocity potentials of each layer and wave elevations at the surface and interface are obtained. The uniform asymptotic analysis of the unsteady state of waves is carried out when lower fluid is of infinite depth.     

SH waves due to a point source in an inhomogeneous medium

The propagation of SH waves due to a point source in an homogeneous medium lying over an inhomogeneous substratum has been investigated in this paper. The Green's function technique developed by Ghosh has been used to solve the problem.     

Waves in an inhomogeneous plasma with Hall dispersion

The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 139–144, September–October, 1976.The author is grateful to V. B. Baranov for constant interest in the work and valuable comments.     

Motion of gas due to a point explosion in an inhomogeneous atmosphere

The problem of a strong point explosion in an atmosphere with exponential dependence of the density on the altitude was considered in detail in the monograph [1]. As the blast wave becomes weaker, it is necessary to take into account the counterpressure and the gravitational force. Then in the central hot region of the explosion the gas-dynamic processes are intensified, and the method of calculating the flow parameters in the neighborhood of the point of energy release becomes important. The singularity at this point can be eliminated by including dissipative factors in the treatment; it is then possible to use standard difference methods in the hot central region. In the present paper, the qualitative and quantitative effects of the counterpressure and gravitation are analyzed. A model of the explosion with a simple mechanism of energy dissipation — heat transfer by radiation — is considered. The calculations of the explosion are continued until the formation of the mushroom cloud. The results are compared with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zfaidkosti i Gaza, No. 6, pp. 144–151, October–December, 1981.     

Problem of heavy fluid flow above a plate in the presence of a vortex

The free-surface flow of a heavy incompressible inviscid ideal fluid along a semi-infinite plate with the formation of a vortex near its edge is investigated. Solitary wave type flows are considered. A unique solution with a free vortex is obtained.     

Three-dimensional problem of the stability of a plate in an inhomogeneous subcritical state

International Applied Mechanics -     

Two-dimensional problem of periodic loading of an elastic plate floating on the surface of an infinitely deep fluid

The action of external periodic pressure on an elastic plate floating on the surface of a fluid assumed to be ideal and incompressible is examined by the method of normal modes in the linear formulation. The behavior of the matrix of coefficients of the hydrodynamic load on the plate is considered in detail for different frequencies. The behavior of the plate under localized periodic loading is compared for the cases of a heavy fluid with a finite or infinite depth and for a weightless infinite-depth fluid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 61–72, May–June, 2005.     

Motion of a thin plate in an elastic medium

A solution to the problem of motion of a thin rigid plate in an elastic medium is obtained using the Smirnov-Sobolev method for solving a two-dimensional wave equation.