One-Dimensional Models in Turbine Blades Dynamics

Turbine blades are considered as straight naturally twisted rods. Two models are discussed: BernoulliEuler beam and Cosserat rod. Linear theories with small displacements, rotations and loads are used. The equations of dynamics taking into account bending, twisting, axial and shear deformations and cross links between them are derived. The stiffness coefficients in elasticity relations are defined. In the case of harmonic oscillations, we have for amplitudes the ordinary differential equations solved by means of computer mathematics (Mathcad). As a result the normal modes, the natural frequencies and also the amplitudes of forced oscillations are obtained. For the BernoulliEuler beam the LagrangeRitzKantorovich variational approach with approximations of deflections is proposed. The unknown coefficients of approximation depending on time are found by the numerical integration of the Lagrange system of equations. Proposed methods are applied to calculation of the real turbine blade.(VLID)484893

Special Features Symmetry of the Space of Liquid State

В статье представлены результаты анализа связи геометрии пространства жидкого состояния вещества для случая плоской пятигранной сетки с его свободной энергией. Показано, что в растворе димеров с изменением температуры может иметь место фазовый переход первого рода.In the article the results of the analysis of the connection of the geometry of the space of the liquid state of substance for the case of flat pentahedral grid with its free energy are represented. It is shown that in the solution of dimers with a change in the temperature the first-order transition can occur

Special Features Symmetry of the Space of Liquid State

В статье представлены результаты анализа связи геометрии пространства жидкого состояния вещества для случая плоской пятигранной сетки с его свободной энергией. Показано, что в растворе димеров с изменением температуры может иметь место фазовый переход первого рода.In the article the results of the analysis of the connection of the geometry of the space of the liquid state of substance for the case of flat pentahedral grid with its free energy are represented. It is shown that in the solution of dimers with a change in the temperature the first-order transition can occur

The Thermal Transformations of Foundry High-Temperature Oxidation-Resistant Steels During the Melting and the Crystallization

In the article the results of study with the aid of the thermal analysis, microradiography and the scanning electron microscopy of thermal transformations in the models of hightemperature oxidationresistant steels with the heating and the cooling are represented.В статье представлены результаты изучения с помощью термического, микрорентгеноспектрального анализов и растровой электронной микроскопии термических превращений в образцах жаростойких сталей при нагревании и охлаждении

The Thermal Transformations of Foundry High-Temperature Oxidation-Resistant Steels During the Melting and the Crystallization

In the article the results of study with the aid of the thermal analysis, microradiography and the scanning electron microscopy of thermal transformations in the models of hightemperature oxidationresistant steels with the heating and the cooling are represented.В статье представлены результаты изучения с помощью термического, микрорентгеноспектрального анализов и растровой электронной микроскопии термических превращений в образцах жаростойких сталей при нагревании и охлаждении

Characteristic Features of Ultrafine-Grained Ti-45 wt.% Nb Alloy under High Cycle Fatigue

The paper presents the results of fatigue-testing ultrafine-grained and coarse-grained Ti-45 wt.% Nb alloy samples under very high cycle fatigue (gigacycle regime), with the stress ratio R = −1. The ultrafine-grained (UFG) structure in the investigated alloy was formed by the two-stage SPD method, which included multidirectional forging (abc–forging) and multipass rolling in grooved rollers, with further recrystallization annealing. The UFG structure of the Ti-45 wt.% Nb alloy samples increased the fatigue limit under the high-cycle fatigue conditions up to 1.5 times compared with that of the coarse-grained (CG) samples. The infrared thermography method was applied to investigate the evolution of temperature fields in the samples under cyclic loading. Based on numerical morphology analysis, the scale invariance (the Hurst exponent) and qualitative differences for UFG and CG structures were determined. The latter resulted from the initiation and propagation of fatigue cracks in both ultra-fine grained and coarse-grained alloy samples under very high-cycle fatigue loading