No 1 (2025)

The problem of gyroscopic stabilization of the equilibrium position of nonlinear potential systems with a potential of a special kind is considered. The conditions of stabilization of the equilibrium position by attaching gyroscopic forces are obtained. Estimates from below for large parameters with matrices of gyroscopic forces guaranteeing stability of equilibrium in a closed system are given.

The premixed subsonic turbulent combustion of methane-air mixture in channel with backward step is considered. (Magre P. et al., ONERA, 1975-1989). These experiments represent basic physical mechanisms, which are common for combustion processes in gas turbine units. The brief review of previous works on numerical modeling of these experiments is presented. The new results of numerical investigation of stable flame regime for this experimental setup are presented. The choice of turbulence model and its influence on flow structure are described. Various approaches for turbulent combustion description, based on PaSR (Partially Stirred Reactor) are compared with quasi-laminar approach. The recommendations are given for choice between global and multistage chemical kinetics in combination with different models for turbulence combustion interaction. The influence of variable turbulent Prandtl and Schmidt number model on this flow representation. The ideas for further research are formulated.

Using the system of equations corresponding to the classical theory of orthotropic cylindrical shells, the free vibrations of a thin elastic orthotropic cylindrical panel with hinge-mounted edge generator are investigated. To calculate the natural frequencies and to identify the respective natural modes, the generalized Kantorovich-Vlasov method of reduction to ordinary differential equations is used. Dispersion equations for finding the natural frequencies of possible types of vibrations are derived. An asymptotic relation between the dispersion equations of the problems at hand and the analogous problem for a rectangular plate is established. A mechanism is given by which possible types of edge oscillations are distinguished. As examples, the values of dimensionless characteristics of natural frequencies are derived for an orthotropic cylindrical panels.

The problem of maximizing the value of the first natural frequency for a functionally graded material depending on the variation law of Young's modulus is considered. It is assumed that there is a limitation on the average integral value of Young's modulus. The effect of variable material properties on the value of the first natural frequency is shown using the finite element method for the numerical solution of a two-dimensional axisymmetric problem of free oscillations of a cylinder. The optimality condition is obtained using the methods of variational calculus based on the general formulation of the problem for an inhomogeneous elastic isotropic body. It is noted that the left-hand side of this condition has a quadratic form. The problem of finding the optimal variation law of Young's modulus is essentially nonlinear in the general case and special numerical methods must be used to solve it. Three special cases are considered using the obtained optimality condition: bending vibrations of a circular solid plate, longitudinal vibrations of a rod and radial vibrations of a solid thin disk, taking into account the corresponding hypotheses. The optimal variation laws of Young's modulus and the displacement function are obtained in analytical form for all problems. Particularly, in the problem for the disk, a representation is proposed for the radial component of the displacement field, which is described by a linear law. It is shown that in this case the corresponding radial and tangential components of the stress tensor are equal. The sought-for function of the change in Young's modulus along the radial coordinate is found in analytical form from the equation of motion and the boundary condition on the outer boundary. An analytical expression is obtained for determining the value of the natural frequency, corresponding to the found solution. The accuracy of this formula is estimated by comparing it with the numerical solution obtained using the finite element method in the FlexPDE package. A comparison of the values of the natural frequency for homogeneous and inhomogeneous disks is made.

When solving engineering problems, it is often necessary to know the physical properties of porous media with complex internal structure. In this paper we propose a technique for numerical modeling of heat conduction of this kind of bodies including non-conducting circular inclusions. This technique allows to calculate temperature fields and heat fluxes, as well as other parameters necessary for applications. One of such parameters demanded by practice is the effective thermal conductivity, which depends on the volume content of thermally insulated pores and their mutual location. The basis of the above studies is the indirect boundary element method proposed in this paper, based on pre-calculated analytical solutions, on which the decomposition is performed. In order to verify the developed methods, a comparison with the results of other authors is given in the paper. It showed a fairly good agreement.