A class of boundary value problems in the theory of surface waves

Boundary value problems are formulated concerning characteristic oscillations relative to capillary-sound equilibrium forms and theorems are established concerning properties of spectra of these problems; theorems are also presented concerning stability of the indicated forms of equilibrium.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 359–364, March, 1991.     

One version of the Linearized theory of nonstationary boundary-value problems with free boundary

We analyze the principle of linearization and linear boundary-value problems obtained by using this principle in the nonlinear theory of motion for a bounded volume of liquid with free surface subjected to the action of a nonstationary oscillating load. We formulate and study the problem of vibrocapillary equilibrium state, spectral problems in the theory of linear waves, and problems of stability of equilibrium states, including the problem of bifurcation of equilibrium states.     

A Review of the Research into the Mathematical Problems of Mechanics and Control Theory at the Institute of Mathematics of the National Academy of Sciences of Ukraine

Ukrainian Mathematical Journal - We present a review of the research into the mathematical problems of mechanics and control theory carried out at Institute of Mathematics of the National Academy...     

Eigenoscillations of three- and two-element flexible systems

Eigenfrequencies and eigenmodes of composite mechanical systems consisting of a thin-walled cylindrical shell and elastic beams [beam–shell–beam (BSB), beam–beam–beam (BBB), etc. systems] are described by using semi-analytical methods. The methods are less universal comparing with the Finite Element Method, but they are very accurate and CPU-efficient, and they could have advantages in studying multicomponent structures. A comparative analysis of eigenfrequencies and eigenmodes of the considered composite systems versus characteristic geometric dimensions is presented.     

Linear and nonlinear sloshing in a circular conical tank

Linear and nonlinear fluid sloshing problems in a circular conical tank are studied in a curvilinear coordinate system. The linear sloshing modes are approximated by a series of the solid spheric harmonics. These modes are used to derive a new nonlinear modal theory based on the Moiseyev asymptotics. The theory makes it possible to both classify steady-state waves occurring due to horizontal resonant excitation and visualise nonlinear wave patterns. Secondary (internal) resonances and shallow fluid sloshing (predicted for the semi-apex angles >60) are extensively discussed.     

Natural sloshing frequencies and modes in a rectangular tank with a slat-type screen

Being installed in tanks, screens play the role of slosh-suppressing devices which may strongly change resonant sloshing frequencies and yield an extra nonlinear damping due to cross-flow resulting in either flow separation or jet flow. Employing the linear sloshing theory and domain decomposition method, we construct an accurate analytical approximation of the natural sloshing modes in a rectangular tank with a slat-type screen at the tank middle. Two-dimensional irrotational flow of an ideal incompressible liquid is assumed. Because the considered flow model does not account for flow separation and jet flow at the screen, the velocity field is locally singular at the sharp edges. The constructed solution captures this singularity. Analyzing this solution establishes a complex dependence of the natural sloshing frequencies on the solidity ratio, the number of submerged screen gaps, the liquid depth, and the position of perforated openings relative to the mean free surface. Results are compared with experimental data. Natural surface wave profiles are discussed in the context of a jump of the velocity potential at the screen and the local inflow component to the screen.     

A Note on the Variational Formalism for Sloshing with Rotational Flows in a Rigid Tank with Unprescribed Motion

Ukrainian Mathematical Journal - The Bateman–Luke-type variational formulation of the free-boundary “sloshing” problem is generalized to the case of irrotational flows and...     

Stabilization of liquid-gas interface in the presence of interaction with acoustic fields in the gas

It is shown that in the framework of the assumptions in [8] it is possible not only to describe surface stabilization in the presence of supercritical negative loads but also to determine more accurately the frequency range on which such stabilization is possible.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 80–86, May–June, 1991.