The paper considers a developed mathematical model of adjusting multi-layer sound-absorbing structures in order to get the set absorption frequencies based on experimental frequency results of single-layer sound-absorbing structures. Mesh samples which are actually Helmholtz resonators are considered as sound-absorbing structures that have resonant sound absorption. Resonant frequency of a single-layer or mesh type with different geometrical parameters is defined by the acoustic device "Interferometer". Combining such one-layer sound-absorbing structures and piling it into a multilayer structure leads to the increase of sound absorbing spectral range and of sound absorption coefficient. Mathematical model of the acoustic system in multilayer resonance sound-absorbing structures is built based on acoustomechanical analogue with resonant system, where the number of freedom degrees complies with the number of sound absorbing structures. The model helps to find the characteristics of sound-absorbing structures adjusted to the set ratio of resonance frequencies. Resonant frequencies of multilayer sound-absorbing structures are analytically determined by means of resonance frequencies of single-layer cellular sound-absorbing structures on the basis of the mathematical model developed for the oscillatory system with several degrees of freedom. Experimental verification of the calculation results showed that the difference between the experimental and calculated resonance frequencies of sound-absorbing structures is not more than 3 %. Thus, the proposed computational and experimental technique is experimentally confirmed, and geometrical parameters of the resonant cellular aggregate to create multilayer cellular sound-absorbing structures which can be used in the construction of aircraft engines is created.

The proposed work is focused on polycrystalline materials with cubic symmetry of the lattice, subjected to thermomechanical treatment and having a crystallographic texture. As a subject of study the link of physical and mechanical properties anisotropy with integral characteristics of texture was examined. As integral texture characteristics (texture parameters) the authors selectedaverage values of certain combinations of the direction cosines defining the provisions of the crystallographic axes grain polycrystalline, in the laboratory system of axes. On the basis of the published data analysis a problem of findingborders of distribution of texture parameters that determine the anisotropy of the elastic properties of textured polycrystals was formulated. A vector-matrix algorithm for constructing the required piecewise smooth enclosed surface was proposed. The initial data for the area construction was used as restrictions imposed on the textural parameters, which derived from the condition of positivity of the weight coefficients in the corresponding problem of averaging - determining the weighted average degree of eigenvalues of a textured polycrystal elasticity operator. It was established that the distribution area of textural parameters has a fold symmetry axis and is limited by flat and conical elements. In the analytical form the equations of boundary surface elements and the lines of their intersection were obtained. Validation of the mathematical model for constructing the distribution area of texture parameters was performed by comparison with the empirical data. The empirical data on the evolution of the texture was obtained earlier, by an independent research in rolling of sheets of aluminum alloys at a multistand camp. It was established that the experimentally determined values of texture parameters belong to the trajectory lying inside the found analytical field. This will lead to a targeted control of technological processes in manufacturing items and semi-finished products of metal materials.

This article considers an innovative idea of decreasing the aerodynamic drag of missile by an inflight forming of an aft fairing of preferable geometry on the basis of plastic deformation of corrugated thin-walled shell by gasdynamic influence. The mathematical description of the interfaced impulse gas-dynamic and deformation processes of forming aft fairing in flight is given with the thermal effects. The algorithm for the numerical simulation of these co-occurring processes is presented. In the numerical experiment the authors proved preferred technical solutions that realize the principle of the flight transformation. The adequacy of the results obtained by the developed research instruments confirmed by comparing the numerical simulation data with the data of natural experiments. The numerical experiment preferred variants of the technical solutions implementing the principle of flight transformation are justified. In particular, it is shown that a membrane with a coaxial arrangement of the corrugations is more preferable than the radial arrangement. In this case we have managed to present the version of the mounting membrane with the best streamlined form during deployment of the membrane. The paper proposed two ways to improve the fairing: by changing the geometric parameters of the original thin-walled diaphragm; and due to variation of the deforming impacts. The best form is obtained when creating a combined force, which first of all transforms the central part and then the peripheral region of the corrugated shell. Also, the work shows a perspective direction based on the formation of the shell by a special gas jet. In general, on the basis of the research it became possible to prove the principal possibility of obtaining the specified geometrical form on board the missile by pulsed deformation of corrugated shell of the aft fairing, which is optimal from the viewpoint of reducing aerodynamic drag.

The processes occurring in the metallic samples under the impact of electrical current of high density are considered. The processes occurring in the vicinity of microdefects in the form of flat cracks under the action of electric current are studied. The dynamic problem is solved numerically for a representative element of the material with crack. The problem is solved in two stages using finite elements method. At the first stage, we have studied the thermal electrodynamic problem in order to obtain the temperature distribution and the regions of phase transformations in the material. Regions of the phase transformations (melting and evaporation of the material) are cross-calculated without the explicit allocation of the phase boundaries. At the second stage, we have solved a coupled unsteady thermomechanical problem of deformation of the heated elastoplastic sample taking account of the initial temperature field distribution in the material obtained at the first stage at different moments of time. Additionally, quasistatic thermomechanical problem was solved in order to obtain the displacement field (residual strain) after temperature equalization in the material. The influence of the size and orientation of microcracks on the localization of the electromagnetic field in the region of the defect is examined. The calculations on the base of the proposed model show that the current density at the tips of the microcracks may by an order exceed the current density applied to the sample. Numerical modelling has shown, that large gradients of electromagnetic field and current arise in the vicinity of the microdefects,, which leads to intensive heating, melting and evaporation of the metal in the tips of the microcracks. The melted material flows into the microcrack under the action of thermal stresses. At the same time the metal starts to evaporate. The shores of the microcracks converge. All these processes lead to a "healing" of defects.

For the calculation of residual stresses and plastic strains in hollow and solid surface-hardened cylindrical specimens we suggest the mathematical models, which take into account both the cases of hardening leading to the isotropy (hydraulic shot blasting procedure) and to the anisotropy (roller burnishing process) of plastic strains in the surface layer. The introduced mathematical model has a hardening anisotropy parameter which ties the axial and circumferential components of the residual plastic strains tensor. We use the determined axial and/or circumferential components of the residual stresses tensor as the input information. Also we use the following assumptions: smallness of the off-diagonal elements of the residual plastic strains tensor and residual stresses tensor, plastic incompressibility of material, absence of the secondary plastic strains of the material in the compression area of the surface layer. The boundary value problems of the hardened layer stress-strain state estimation after the hardening for the hollow and solid cylindrical specimens are solved and the solution is given in the paper. We give the method for the mathematical model parameter identification under the condition of self-equilibrated residual stresses and the method for the experimental determination of residual stresses by the circles and strips approach. Also, the cycle of the hardening experiments for the hollow and solid specimens from the 40Kh steel (having different proportions of internal and outer diameters) in the roller burnishing process and hydraulic shot blasting modes was performed with the determination of the residual stresses. The mathematical model adequacy is verified through the comparisons with experimental data; good agreement of the calculated and experimental data is demonstrated. The calculated numerical values of the hardening anisotropy parameter are given. The fact that the procedure of surface anisotropic hardening (roller burnishing process) leads to the strong layering of the epures of axial and circumferential residual stresses in depth of the hardened layer is established. Contrastingly, the case of the isotropic hardening (hydraulic shot blasting) leads to almost coinciding epures. Using the experimental and calculated data we have shown that the hardening of tool roller type leads to the larger absolute values of the compressing stresses, which by more than 30% exceeds the stresses after the hardening of hydraulic shot blasting type for the specimens of the same geometry. For the main results of the research we have given the necessary data in the table and also we have presented the epures for the residual stresses distribution.