Vol 7, No 1-3 (2013)

The technique of data processing for thermogravimetry of calcite with use of MathCad 11 is developed. There are designed basic kinetic parameters of processes of calcite powder thermal decomposition with use of the equation of first order reaction: size of critical increment of energy, a kinetic constant of decomposition process. Decomposition point of calcite is experimentally determined.

The paper proposes analytical method of solving the contact problem for a two-layer elastic coating of solid cylinder applicable for circular layers of arbitrary thickness, simultaneously in case of compressible and incompressible materials. The law of contact pressure change is expressed in a form of an infinite series, containing an infinite number of unknown constants that are defined by the decomposition of known function of the built orthogonal functions.

The equations of the loading process in terms of rectangular shallow shells with bilateral compression when calculating the variational methods are derived. The problem is solved in view of geometrical non-linearity.

The paper refers to the opinion that the system of Navier-Stokes equations, which is one of the basics in the theory of continuous media and serves as a mathematical model of motion in fluid mechanics, does not describe some practically important movements. In particular, they do not describe the possible torsion of the current lines, i.e. do not describe the torsion of the continuum in small neighborhoods of points. Therefore, it is principally important to identify the degree of conformity of theoretical and experimental data of liquids flows. The flow at the entrance of the tube may be both observable and analytically described movement.

The exact solution of the problem of the dynamic response of a three-layer spherical shell immersed in a fluid under the action of external hydrodynamic pressure is built in the acoustic approximation. The system of differential equations of motion of the shell of the 14th order, taking into account the transverse shear and normal strains and stresses in the core, is integrated by the method of double integral transformations. The authors evaluated the response of envelope for different values of hydrodynamic pressure.

The authors consider the problem of bifurcation of a thin-walled circular cylindrical shell taking into account the complex nature of the deformation at the time of loss of stability under complex loading by sub-critical axial compressive force and torque in the deviatoric A. Ilyushin plane of strains .

The author studies the best approximation of classes of periodic functions of several real variables with a given majorant of the mixed moduli of continuity by analogues of “own” and “alien” hyperbolic crosses. The majorant has the power factors in different degrees and logarithmic factors in different degrees.

The article considers the possibility of using dynamic inertial dampers. A method for dynamic damping body under the action of two disturbing forces varying harmonically is described. differential equations of perturbed motion for a system with three degrees of freedom are studied, compiled on the basis of exact solutions of the Lagrange equations of the second order.

The adsorptive abilities of waste of aluminosilicate production in relation to molybdate ions are investigated. The acid way of activation of red mud and the aluminosilicate component (ASC) is offered, allowing to increase their adsorptive properties.

The results of the study of vibration sensitivity of a rotor of stationary gas-turbine unit (GTU) on slide bearings to the change of the main settings of the system are described in the paper. The authors used a beam model of the rotor which takes into account the non-linear stiffness and damping characteristics of an oil film in radial bearings, and a multi-disciplinary model of rotor dynamics including the model of the shaft, rotating discs and radial bearings. Numerical calculations for calculating the orbits of GTU rotor at different operating conditions are performed. The paper also demonstrates the sensitivity of the “rotor-bearing” system to a change of system parameters such as a disbalance of the rotor, constructive damping and viscosity of the oil in bearings.