Unsteady motion of a source in a fluid under a floating plate

This paper studies the three-dimensional unsteady problem of the hydroelastic behavior of a floating infinite plate under the impact of waves generated by horizontal straight motion of a point source of mass in a fluid of infinite depth. The solution is carried out using known integral and asymptotic methods. The formulas obtained are used to numerically analyze the effect of plate thickness, depth of submergence of the source, and its acceleration, deceleration, and velocity of uniform motion on the deflection of the floating plate.     

Oblique entry of a slender body in an incompressible fluid

The plane problem of oblique penetration of a slender semiinfinite body in an ideal, weightless, and incompressible fluid is examined. Detailed numerical computations are performed for a wedge with rectilinear sides. The formulas obtained are applicable also for the calculation of the hydrodynamic reactions during emergence of a body from a fluid or during transverse motion of a half-blunt body with a low relative velocity. Moreover, the results of the present paper can be used to evaluate the hydrodynamic forces acting on underwater wings or propeller blades during intersection with a free surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 16–24, September–October, 1977.     

Scattering of Surface Waves by the Edge of a Floating Elastic Plate

The diffraction of plane surface waves by a semiinfinite floating plate in a fluid of finite depth is studied. An explicit analytical solution of the problem is obtained using the Wiener–Hopf technique. Simple exact formulas for reflection and transmission coefficients and their asymptotic expressions are derived. Results of numerical calculations using the obtained formulas are presented.     

The influence of a uniformly compressed floating elastic plate on the development of three-dimensional waves in a homogeneous fluid

A study is made in the linear formulation of the influence of a uniformly compressed floating elastic plate on the unsteady three-dimensional wave motion of a homogeneous fluid of finite depth. Waves are excited by a region of normal stresses which moves on the surface of the plate. Three-dimensional flexural-gravity waves were studied in [1, 2] without allowance for compressing forces. Plane waves under conditions of longitudinal compression were considered in [3, 4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 78–83, November–December, 1984.     

Linear theory of unsteady gas flow under the influence of nonpotential external forces

We determine in the linear formulation the velocity and pressure fields excited in a compressible medium by a lifting filament that displaces and deforms arbitrarily. For general unsteady motion of such a filament we give explicit formulas that express the velocity at a given point in terms of the intensity of the free vortices entering the audio signal audibility zone constructed for this point. We examine gas flow caused by an arbitrary external body force field.Studies devoted to the determination of gas velocity fields for flow past slender bodies relate primarily to translational motion of a body with a dominant constant velocity [1–3]. Gas velocities for helical motion of a rectilinear lifting filament within the gas have been examined in [4].     

Motion of a slender body near the free surface of a compressible fluid

An analytic solution to the problem of motion of a slender rigid body in a semi-infinite domain of a compressible fluid is obtained for the case when the body moves in parallel to the free surface at a constant velocity. This problem is similar to the problem of motion of a hydrofoil ship whose wing-like device allows it to lift its hull above the water surface and to decrease the friction and drag forces limiting the speed of usual ships. During its motion in water, a hydrofoil produces a lift force. The obtained analytic solution allows one to derive explicit expressions for the drag force and for the lift force in the limiting cases of relatively small and large depths. When depth is small, the drag force is greater than that in an infinite medium, since the wave drag is additionally evolved. When the velocity increases and approaches the sound velocity, the forces exerted on the body increase without limit, which is typical for a linear formulation of the problem.     

Motion of an External Load over a Semi-Infinite Ice Sheet in the Subcritical Regime

The three-dimensional problem of steady-state forced vibrations of fluid and semiinfinite ice sheet under the action of a local external load traveling along the rectilinear sheet edge at a constant velocity is considered. Two cases are analyzed. In the first case the fluid surface outside the ice sheet is free and in the second the fluid is confined by a rigid vertical wall and the ice sheet edge adjacent to the wall can be both clamped and free. The ice sheet is simulated by a thin elastic isotropic plate floating on the surface of fluid of finite depth. The load traveling velocity is assumed to be not higher than the minimum phase velocity of the flexural-gravity waves (subcritical regime). The solution to the linear problem is obtained by means of the integral Fourier transform and matching the expansions of the velocity potential in the vertical eigenfunctions. Examples of the numerical investigation of the ice sheet and fluid displacements are given.     

Interaction of surface and flexural-gravity waves in ice cover with a vertical wall

The problem of the interaction of surface and flexural-gravity waves with a vertical barrier is solved in a two-dimensional formulation. It is assumed that the fluid is ideal and incompressible, has infinite depth, and is partially covered with ice. The ice cover is modeled by an elastic plate of constant thickness. The eigenfrequencies and eigenmodes of oscillation of the floating elastic ice plate, the deflection and deformation of ice, and the forces acting on the wall are determined.     

Unsteady Couette flow of a micropolar fluid with slip

The unsteady Couette flow of an isothermal incompressible micropolar fluid between two infinite parallel plates is investigated. The motion of the fluid is produced by a time-dependent impulsive motion of the lower plate while the upper plate is set at rest. A linear slip, of Basset type, boundary condition on both plates is used. Two particular cases are discussed; in the first case we have assumed that the plate moves with constant speed and in the second case we have supposed that the plate oscillates tangentially. The solution of the problem is obtained in the Laplace transform domain. The inversion of the Laplace transform is carried out numerically using a numerical method based on Fourier series expansion. Numerical results are represented graphically for the velocity, microrotation, and volume flux for various values of the time, slip and micropolar parameters.     

Numerical analysis of finite amplitude motion of waves and a moored floating body under severe storm conditions

The motion of a moored floating body under the action of wave forces, which is influenced by fluid forces, shape of the floating body and mooring forces, should be analysed as a complex coupled motion system. Especially under severe storm conditions or resonant motion of the floating body it is necessary to consider finite amplitude motions of the waves, the floating body and the mooring lines as well as non-linear interactions of these finite amplitude motions. The problem of a floating body has been studied on the basis of linear wave theory by many researchers. However, the finite amplitude motion under a correlated motion system has rarely been taken into account. This paper presents a numerical method for calculating the finite amplitude motion when a floating body is moored by non-linear mooring lines such as chains and cables under severe storm conditions.     

Unsteady Behavior of an Elastic Beam Floating on the Surface of an Infinitely Deep Fluid

The effect of initial disturbances and unsteady external loading on an elastic beam of finite length which floats freely on the surface of an ideal incompressible fluid is studied in a linear treatment. The fluid flow is considered potential. The beam deflection is sought in the form of an expansion in the eigenfunctions of beam vibrations in vacuum with time-dependent amplitudes. The problem reduces to solving an infinite system of integrodifferential equations for unknown amplitudes. The memory functions entering this system are determined by solving the radiation problem. The beam behavior is studied for various loads with and without allowance for the weight of the fluid. The effect of fluid depth on beam deformation was determined by comparing with the previously obtained solutions of the unsteady problem for a beam floating in shallow water. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 85–94, January–February, 2006.     

Nonlinear steady-state motion of an elastic plate floating on the surface of a liquid of infinite depth

The nonlinear problem of steady-state waves in an ideal fluid of infinite depth with a thin elastic plate floating on its surface is considered. The solution is found by a perturbation method. Three approximations are obtained. A case of branching of the solution is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 119–123, March–April, 1987.     

Transient motion of a floating body having a rectangular shape

The twodimensional transient problem of a floating body having a rectangular shape in a fluid layer of finite depth is considered. Vertical displacements of the body are specified. The problem is studied within the framework of the linear theory of potential ideal incompressible flow. The fluid flow equations reduce to an infinite system of Volterra integral equations of the second kind by the method of decomposition of the flow region. The system obtained is studied and solved numerically by the reduction method. A method of solving the problem for the flow velocity potential is proposed. The distribution of the hydrodynamic pressure and force acting on the body is determined.     

Wave forces on a submerged horizontal plate - Part I: Theory and modelling

This paper is concerned with the propagation of nonlinear gravity waves over a thin horizontal plate submerged in water of shallow depth. An unsteady solution of the problem is obtained by use of the theory of directed fluid-sheets for the two-dimensional motion of an incompressible and inviscid fluid. Particular attention is paid to the calculation of the nonlinear wave-induced vertical and horizontal forces and overturning moment by solving the Level I Green–Naghdi equations. The theoretical formulation of the problem is given in this paper (Part I), while the results due to solitary and cnoidal waves, and comparisons with the available experimental data are given in a companion paper under the same title (Part II).     

Generation of unsteady waves by concentrated disturbances in an inviscid fluid with an inertial surface

The surface waves generated by unsteady concentrated disturbances in an initially quiescent fluid of infinite depth with an inertial surface are analytically investigated for two- and three-dimensional cases. The fluid is assumed to be inviscid, incompressible and homogenous. The inertial surface represents the effect of a thin uniform distribution of non-interacting floating matter. Four types of unsteady concentrated disturbances and two kinds of initial values are considered, namely an instantaneous/oscillating mass source immersed in the fluid, an instantaneous/oscillating impulse on the surface, an initial impulse on the surface of the fluid, and an initial displacement of the surface. The linearized initial-boundary-value problem is formulated within the framework of potential flow. The solutions in integral form for the surface elevation are obtained by means of a joint Laplace-Fourier transform. The asymptotic representations of the wave motion for large time with a fixed distance- to-time ratio are derived by using the method of stationary phase. The effect of the presence of an inertial surface on the wave motion is analyzed. It is found that the wavelengths of the transient dispersive waves increase while those of the steady-state progressive waves decrease. All the wave amplitudes decrease in comparison with those of conventional free-surface waves. The explicit expressions for the freesurface gravity waves can readily be recovered by the present results as the inertial surface disappears.     

Hydroelastic behavior of a complex structure floating on waves

A numerical method is developed to solve the plane problem of the hydroelastic behavior of a complex structure floating on the surface of an ideal incompressible fluid of finite depth. The motion of the structure described by a deflection function is considered steady-state under the action of incident waves. The hydrodynamic part of the problem is solved using the proposed approach based on the normal-mode method for homogeneous plates. The problem is reduced to a system of linear algebraic equations by means of a transition matrix between representations of the required deflection in the form of expansion in the vibration eigenfunctions of the structure and the plate. It is shown that the results of the calculation performed are in good agreement with available calculation results for a two-part hinged structure at wavelengths comparable to the length of the structure.     

Unsteady Couette flow in a rotating system

The unsteady Couette flow between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system under the boundary layer approximations is investigated. An exact solution of the governing equations has been obtained by using Laplace transform technique. It is shown that when the oscillating plate situated at an infinite distance from stationary plate then the problem reduces to the unsteady boundary layer problem in a rotating system with non-torsional oscillations of the free-stream velocity.     

Rotating flow of a second-order fluid on a porous plate

A study is made of the unsteady flow engendered in a second-order incompressible, rotating fluid by an infinite porous plate exhibiting non-torsional oscillation of a given frequency. The porous character of the plate and the non-Newtonian effect of the fluid increase the order of the partial differential equation (it increases up to third order). The solution of the initial value problem is obtained by the method of Laplace transform. The effect of material parameters on the flow is given explicitly and several limiting cases are deduced. It is found that a non-Newtonian effect is present in the velocity field for both the unsteady and steady-state cases. Once again for a second-order fluid, it is also found that except for the resonant case the asymptotic steady solution exists for blowing. Furthermore, the structure of the associated boundary layers is determined.     

Unsteady behavior of an elastic beam floating on shallow water under external loading

A solution is derived for the twodimensional unsteady problem of the behavior of an elastic beam of finite dimensions floating on the free surface of water under external loading. It is assumed that the fluid is ideal and incompressible and its depth is well below the beam length. The simultaneous motion of the beam and the fluid is considered within the framework of linear theory, and the fluid flow is assumed to be potential. The behavior of the beam under various loadings with and without allowance for the inertia of the load is studied.     

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.