Narrow Results

This paper is concerned with the numerical investigation of hydroelastic stability of stationary or rotating coaxial cylindrical shells, interacting with compressible fluid flows having the axial and tangential velocity components. The behavior of a flowing and rotating compressible fluid is considered in the framework of the potential theory. Elastic shells are described using the model of the classical shell theory. Numerical implementation was accomplished based on the semi-analytical variant of the finite element method. The paper presents the results of numerical experiments on the stability of shells interacting with different flow patterns for a variety of boundary conditions, geometrical dimensions, width of the annular gap between the outer and inner shell under the constraint of the outer shell rigidity. It has been shown that the elasticity of the outer shells has the greatest effect on the dynamic behavior of coaxial shells interacting with fluid flows having different combinations of velocity components.

The paper deals with a three-dimensional problem on natural vibrations and stability of thin-walled cylindrical shells with arbitrary cross sections, containing a quiescent or flowing ideal compressible fluid. The motion of compressible non-viscous fluid is described by a wave equation, which together with the impermeability condition and corresponding boundary conditions is transformed using the Bubnov–Galerkin method. A mathematical formulation of the problem of thin-walled structure dynamics has been developed based on the variational principle of virtual displacements. Simulation of shells with arbitrary cross sections is performed under the assumption that a curvilinear surface is approximated to sufficient accuracy by a set of plane rectangular elements. The strains are calculated using the relations of the theory of thin shells based on the Kirchhoff–Love hypothesis. The developed finite element algorithm has been employed to investigate the influence of the fluid level, the ratio of the ellipse semi-axes and types of boundary conditions on the eigenfrequencies, vibration modes and the boundary of hydroelastic stability of thin-walled circular and elliptical cylindrical shells interacting with a quiescent or flowing fluid.

This paper presents the results of studies on natural vibrations of circular cylindrical shells containing liquid and resting on an elastic foundation, which is described by the Pasternak two-parameter model. In the meridional direction, the elastic medium is nonuniform and represents an alternation of sections in which the foundation is present or absent. The behavior of the elastic structure and the compressible fluid is described in the framework of classical shell theory based on the Kirchhoff–Love hypothesis and the Euler equations. The equations of motion of the shell are reduced to a system of ordinary differential equations with respect to new unknowns. The wave equation written for pressure in the fluid also reduces to a system of ordinary differential equations using the straight line method. The solution of the formulated boundary value problem is found by the Godunov orthogonal sweep method. The validity of the results obtained is confirmed by comparison with the known numerical-analytical solutions. The dependences of the minimum vibration frequencies on the characteristics of elastic medium with variable nonuniformity along the length of the structure have been obtained for cylindrical shells with different boundary conditions. It has been found that the violation of smoothness of the derived dependences is caused by a change of the vibration mode with minimum frequency and is determined both by the ratio of the size of the elastic foundation to the entire length of the shell and its stiffness, and also by a combination of boundary conditions set at the edges of the thin-walled structure.

The paper investigates the dynamic behavior of thin-walled reservoirs containing an ideal liquid taking into account the effects of hydroelastic interaction and sloshing. A mathematical statement of the problem is based on the principle of virtual displacements, which accounts for the pre-stressed non-deformed state of the shell caused by various force factors. The behavior of compressible liquid is described by linearized Euler equations, which are transformed by the Bubnov–Galerkin method. The dynamics of partially filled circular and elliptical cylindrical reservoirs are investigated numerically using a finite element procedure. It has been shown that allowing for sloshing considerably reduces eigenfrequencies of vibrations of the examined systems but has inessential effect on the displacements of the structure under non-stationary loads. Based on the modal analysis we present a classification of eigenmodes of free surface oscillations of a liquid in vertical tanks. It has been found that due to consideration of the sloshing effect, the frequency spectrum of the system can split into two parts in the case when the vibration frequencies of liquid differ from the vibration frequencies of an empty shell. Moreover, under harmonic excitation consideration of liquid sloshing leads to a more complicated amplitude-frequency curve characterized by displacement jumps.

This paper presents the results of investigation of the natural vibrations and stability of circular vertical multilayered cylindrical shells, fully or partially filled with a quiescent compressible fluid subjected to hydrostatic and external static loads. The behavior of the elastic structure and fluid medium is described based on the classical shell theory and Euler’s equations. The linearized equations of motion of the shell, together with the corresponding geometrical and physical relations are reduced to a system of ordinary differential equations with respect to new unknowns. The acoustic wave equation is transformed to a system of differential equations using the method of generalized differential quadrature. The solution of the formulated boundary value problem is developed using Godunov’s orthogonal sweep method. The dependences of the lowest vibration frequencies and critical external pressure on the ply angle and the filling level of two-layer and three-layer cylindrical shells are analyzed in detail. It is demonstrated that, in contrast to the ply angle and a given combination of boundary conditions, the lay-up scheme of composite materials plays different parts in the problems of maximizing the fundamental frequency of vibrations and extending the stability boundaries.