S. A. Bochkarev

Bio: S. A. Bochkarev is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Finite element method & Boundary value problem. The author has an hindex of 7, co-authored 35 publications receiving 167 citations.

Parametric investigation of the stability of coaxial cylindrical shells containing flowing fluid

Abstract: The dynamic behavior of elastic coaxial cylindrical shells interacting with two flows of a perfect compressible fluid is investigated by application of the finite element method. The fluid behavior is described by the potential theory, the equations of which are reduced to the integral expressions using the Bubnov–Galerkin method. The pressure exerted by the fluid on the deformable body is determined through the use of the Bernoulli equation. The treatment of elastic shells is accomplished in the framework of the classical shell theory. A mathematical formulation of the problem is based on the principle of virtual displacements. With all things considered, the stated problem reduces to simultaneous solution of 4 sets of equations. For shells with different boundary conditions the numerical investigations have been carried out to explore the effects of the annular gap, the flowing fluid density and physicomechanical properties of the shells on the stability boundary.

Hydroelastic stability of a rectangular plate interacting with a layer of ideal flowing fluid

Abstract: The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges.

Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

Abstract: The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.

Numerical modelling of the stability of loaded shells of revolution containing fluid flows

Abstract: A mixed finite-element algorithm is proposed to study the dynamic behavior of loaded shells of revolution containing a stationary or moving compressible fluid. The behavior of the fluid is described by potential theory, whose equations are reduced to integral form using the Galerkin method. The dynamics of the shell is analyzed with the use of the variational principle of possible displacements, which includes the linearized Bernoulli equation for calculating the hydrodynamic pressure exerted on the shell by the fluid. The solution of the problem reduces to the calculation and analysis of the eigenvalues of the coupled system of equations. As an example, the effect of hydrostatic pressure on the dynamic behavior of shells of revolution containing a moving fluid is studied under various boundary conditions.

Specific Features of Dynamic Behavior of Stationary and Rotating Single/Coaxial Cylindrical Shells Interacting With the Axial and Rotational Fluid Flows

Abstract: The paper is concerned with the finite element analysis of hydroelastic stability of stationary or rotating elastic single and coaxial cylindrical shells subjected to compressible fluid flows having axial and tangential velocity components. The behavior of the flowing and rotating fluid is described in the framework of the potential theory. Consideration of elastic shells is based on the classical shell model. The results of the numerical analysis of shell stability for various boundary conditions, geometrical dimensions and different sizes of the annular gap between the outer and inner shells are discussed. It has been found that single and coaxial shells interacting with the combined fluid flows show qualitative differences in the dynamic behavior.

Stability analysis of multi-span viscoelastic functionally graded material pipes conveying fluid using a hybrid method

Abstract: In this paper, a hybrid method which combines reverberation-ray matrix method and wave propagation method is developed to investigate the stability of multi-span viscoelastic functionally graded material (FGM) pipes conveying fluid. The material properties of FGM pipes are considered as graded distribution along thickness direction according to a power-law. A parametric study is conducted to verify the effectiveness of present method and investigate effects of volume fraction exponent, fluid velocity, internal pressure and internal damping on stability of the FGM pipes conveying fluid. The numerical results demonstrate that the present method provides accurate results by using only a small number of elements and the viscoelastic FGM pipes exhibit some special dynamic behaviors. Moreover, the results also reveal that the natural frequencies of FGM piping system could be adjusted by devising the volume fraction exponent. This particular feature of FGM pipes can be tailored to fulfill the special applications in engineering.

Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment

Abstract: The divergence and flutter instabilities of the thin-walled spinning pipes reinforced by single-walled carbon nanotubes in thermal environment are investigated. The material properties of carbon nanotube-reinforced composites are assumed to be uniform distribution as well as two types of functionally graded distribution patterns. The thermal effects are also considered and the material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent. The cantilever pipe conveying fluid is spinning along its longitudinal axis and subjected to an axial force at the free end. Based on the thin-walled Timoshenko beam theory, the governing equations of motion are derived using the extended Hamilton's principle and discretized via the Galerkin method. The resulting thermal-structural-fluid eigenvalue problem is solved and the frequency and the critical fluid velocities are calculated. The effects of carbon nanotubes distributions, volume fraction of carbon nanotubes, compressive axial force, spinning speed, gravity and fluid mass ratio on the critical divergence and flutter velocities of the thin-walled spinning pipe conveying fluid are studied.