Plane problem of hydrodynamic rocking of a body submerged in a two-layer fluid without forward speed

The results of numerically solving the linear problem of the rocking of a submerged body in an inviscid incompressible fluid bounded either by a rigid top or by a free surface are presented. In each case the equivalence relations connecting the solutions of the radiation and diffraction problems are derived. The apparent mass and damping coefficients are calculated and a comparison with an approximate solution is given.Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 144–155, May–June, 1994.     

Plane problem of wave motions occurring in a continuously stratified fluid during the flow around a submerged body

The plane stationary problem of wave motions occuring in the flow of a uniform inviscid incompressible gravity fluid with an arbitrary continuous (stable) change in density with depth around submerged sources and sinks of equal intensity is investigated in a linear formulation. An analysis of the structure of the wave motion in a flow with an arbitrary density change is performed in [1].Paper presented at the First Soviet-American Symposium on Internal Waves in the Ocean, Novosibirsk, December 3–8, 1976.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 148–152, July–August, 1978.     

Self motion of a body in a fluid

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 111–118, March–April, 1990.     

Oscillations of a cylindrical body submerged in a fluid with ice cover

The linear plane problem of oscillations of an elliptic cylinder in an ideal incompressible fluid of finite depth in the presence of an ice cover of finite length is solved. The ice cover is modeled by an elastic plate of constant thickness. The hydrodynamic loads acting on the body are determined as functions of the oscillation frequency and the positions of the cylinder and plate.     

Planar contact problem for a body of rectangular cross section in a prestressed state

Scientific Engineering Institute of Mechanics and Applied Mathematics, Rostov State University, Rostov-on-Don. Translated from Prikladnaya Mekhanika, Vol. 26, No. 12, pp. 81–89, December, 1990.     

On the formulation of the problem of the motion of a body in water

The selection of solutions describing steady irrotational flow of an ideal incompressible fluid over bodies is considered. The selection is based on restrictions that follow from the physical properties of a real fluid and from the presence of a boundary layer on the body. In particular, for any body one can specify a minimal Euler number below which flow without cavitation becomes physically impossible. In the limiting case of an Euler number equal to zero, only the Kirchhoff scheme is physical admissible, and the cavity section tends to a circle. An equation is derived for the limiting shapes of cavities at small cavitation numbers, and a comparison is made with known results.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 19–26, September–October, 1980.     

Formulation of the problem of the motion of a small body in a perturbed flow

The classical problem of the hydrodynamic reactions on a body of arbitrary shape moving in a fluid at rest [1] was generalized by Sedov to the case of an accelerated translational flow [2]. In the expressions for the hydrodynamic reactions, the shape of the body is represented only by the coefficients λ_ij of the added masses and the volume Ω of the body. In the general case of motion of a body in a nontranslational flow the shape of the body cannot be represented by a finite set of coefficients in the determination of the hydrodynamic reactions. An important simplification occurs in the small-body formulation, which again leads to expressions for the force and torque similar to the classical expressions. The problem of the motion of a small body in a perturbed nontranslational flow was posed by Grigoryan and Yakimov [3], and with allowance for deformation of the body by Yakimov [4]. Later studies containing this formulation have been reviewed by Vil'khovchenko and Yakimov [5]. The aim of the present paper is to formulate the small-body problem more precisely. The order of smallness of the terms in the earlier studies was estimated solely as a function of the power of a small parameter — the size of the body. In the present paper it is shown that if it is additionally required that the final expression for the reactions should contain only principal terms containing the components ν_i and ω_i of the translational and angular velocities, and also terms describing the flow structure, then the expression found by Grigoryan and Yakimov [3] for the hydrodynamic reaction is valid. The terms are estimated on the basis of dimensional analysis. Such arguments have already been used by the author for special examples [6, 7].     

Behavior of a pulsating rigid body in a viscous fluid in the presence of gravity

The paper considers the motion of a rigid sphere due to specified pulsations of the sphere and gravity in a viscous fluid which is at rest away from the sphere.     

三相驱动下含两质量块刚体的平面运动

本文研究了一类含两个质量块的振动驱动系统在粘性摩擦下的平面运动,其中两个内部质量在相互垂直的水平槽道上作三相运动。利用第二类拉格朗日方程,建立了系统的动力学方程;其次,利用系统直线运动时的理论解,验证速度Verlet积分法的可靠性;利用这种算法分析了系统的平面运动,得到了内部驱动参数与系统运动轨迹、运动速度的关系;然后,基于数值分析结果,通过调节内部驱动参数,得到了系统在不同轨迹间的六种转换形式;最后,通过组合不同的转换形式,得到了曲率连续变化的平面运动路径。     

Planar problem of penetration of thin elastic cylindrical shells into a compressible fluid

Institute of Mechanics, Academy of Sciences of the UkrSSR, Kiev. Kiev Automobile-Highways Institute, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 9, pp. 66–75, September, 1990.     

Inertial motion of a body in an ideal fluid from the state at rest

The motion of a body in an ideal incompressible fluid flow without vortices in the absence of external forces is considered. It is demonstrated that the body can move inertially from the state at rest if its shape satisfies certain conditions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 214–219, July–August, 2008.     

Internal waves arising in the presence of the unsteady motion of a source in a continuously stratified fluid

A general approach to the investigation of linear internal and surface waves in a stably stratified fluid, arising from different types of perturbations, is presented in [1]. The methods of calculation of the internal waves generated by the motion of a mass source are developed for particular cases of steady horizontal motion in a continuously stratified fluid in [2] and arbitrary motion in an unbounded exponentially stratified fluid in [3]. Internal waves generated by other types of perturbations have also been investigated but only for particular cases of motion (see, for example, [4]). This paper presents a method for the calculation of unsteady, linear, internal gravity waves arising in an inviscid incompressible fluid with continuous stable stratification.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 122–130, July–August, 1985.     

Viscous fluid flow created by the helical motion of a body of revolution

An investigation is made into the flow created by the helical, exponentially damped motion of a body of revolution in a viscous incompressible fluid stationary at points remote from the body. The forces exerted by the fluid on a body moving in this way are studied. It is shown that the induced flow is uniformly helical. The exposition is illustrated with reference to the example of the motion of a spherical surface. The exact and approximate (in the Stokes sense) solutions are compared. The classical results for the steady-state slow motions of a sphere (both translational and rotational) follow as particular cases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 47–52, March–April, 1985.     

A numerical method for studying the interaction between a partially submerged body and the surrounding fluid

Summary A numerical method has been developed to compute the solution of a mathematical model of the problem known in Naval Hydrodynamics as seakeeping. The solution is written as a potential of a single layer. Unsteady boundary conditions are used both on the free boundary and on the body. The latter take into account the reciprocal interaction between the body and the fluid.The numerical solution of the fluid flow has been obtained by means of the boundary element method, and a suitable difference method has been used to compute the time evolution. A few relevant prototype problems have been solved and compared with experimental data. The method can be directly extended to the nonlinear case, and can be effectively implemented on a parallel computer.

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Sommario Viene presentato un metodo numerico per la soluzione di un modello matematico del problema noto in Idrodinamica Navale con il nome di seakeeping. Si cerca la soluzione sotto forma di potenziale di strato semplice utilizzando condizioni al contorno non stazionarie sia sulla superficie libera che sul corpo; quest'ultima condizione tiene conto dell'interazione reciproca tra il corpo ed il fluido.Il metodo é basato su un'opportuna formulazione integrale delle equazioni nel campo fluidodinamico e su una discretizzazione alle differenze finite per quanto riguarda l'evoluzione temporale. Sono stati risolti alcuni problemi significativi ed i risultati ottenuti sono confrontati con i dati sperimentali disponibili in letteratura. Il metodo proposto é direttamente estendibile al caso non lineare e puó essere efficientemente implementato su un calcolatore parallelo.

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Presented at the II Convegno Italiano di Meccanica Computazionale, Roma, June 2–5, 1987.