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Detailed chemical and structural studies were carried out for Li-Na-Fe-amphibole from cryolite rocks of the Katugin deposit, Transbaikalia. The rocks contain 30-70 vol.% cryolite, mafic minerals as Fe-silicates (Li-Na-Fe-amphibole, Li-containing fluorannite, and bafertisite), oxides (magnetite, ilmenite, pyrochlore, cassiterite, and others), and sulfides (sphalerite, pyrite, and chalcopyrite). Quartz, K-feldspar, polylithionite, REE-fluorides, and albite occur as minor or accessory phases. The chemical composition of amphibole (wt.%) varies as follows: SiO₂, 48.5-48.9; TiO₂, 0.4-0.8; Al₂O₃, 1.6-2.2; Fe₂O₃, 15.9-17.1; FeO, 17.6-18.4; MnO, 0.8-0.9; ZnO, 0.3-1.1; MgO, 0.2-0.3; CaO, <0.1; Na₂O, 8.4-8.7; K₂O, 1.4-1.5; Li₂O, 0.6-0.8; H₂O, 0.7-0.8; and F, 2.2-2.5. The amphibole has a specific composition intermediate among the F-Fe members of the Na-amphibole subgroup: 40-45 mol.% ferro-ferri-fluoro-nybøite, 40-45 mol.% ferro-ferri-fluoro-leakeite, and 10-20 mol.% fluoro-riebeckite ± fluoro-arfvedsonite. The mineral is monoclinic, space group C 2/ m , a = 9.7978(2), b = 17.9993(3), c = 5.33232(13) Å, b = 103.748(2)º, V = 913.43(3) ų, and Z = 2. The structural formula of Li-Na-Fe-amphibole is (Na_0.46K_0.24□_0.30)Na_2.00(Fe²⁺_0.95Mg_0.05)₂(Fe³⁺_0.95Ti_0.025Mg_0.025)₂(Li_0.37Fe²⁺_0.48Mn_0.10Zn_0.05)[(Si_0.91Al_0.09)₄Si₄O₂₂](F_0.58(OH)_0.42)₂. Raman and Mössbauer spectroscopy data are given for this amphibole.

The dynamic behavior of a magma melt filling a slotted channel (crack) in a closed explosive hydrodynamic structure is considered. The explosive hydrodynamic structure includes the volcano focal point with a connected vertical channel (conduit) closed by a plug and a system of internal cracks (dikes) near the dome, as well as a crater open to the atmosphere. A two-dimensional model of a slotted eruption is constructed with the use of the Iordanskii-Kogarko-van Wijngaarden mathematical model of two-phase media and the kinetics that describes the basic physical processes in a heavy magma saturated by the gas behind the decompression wave front. A numerical scheme is developed for analyzing the influence of the boundary conditions on the conduit walls and scale factors on the melt flow structure, the role of viscosity in static modes, and dynamic formulations with allowance for diffusion processes and increasing (by several orders of magnitude) viscosity. Results of the numerical analysis of the initial stage of cavitation process evolution are discussed.

Static and free vibration analyses of plates with circular holes are performed based on the three-dimensional theory of elasticity. The plates are made of a functionally graded material (FGM), and the volume fraction of the material varies continuously over the plate thickness. The effective properties of the FGM plate are estimated by using the Mori-Tanaka homogenization method. A graded finite element method based on the Rayleigh-Ritz energy formulation is used to solve the problem. The effects of different volume fractions of the material and hole sizes on the behavior of FGM plates under uniaxial tension are investigated. Natural frequencies of a fully clamped FGM plate with a circular cutout are derived. The results obtained are compared with available experimental data.

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wavefronts in an elastic material with different tensile and compressive strength is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The mode of impact on the boundary of the heteromodular sphere is determined in which a transition zone in the form of a spherical layer of constant density can occur between the compression and tension regions.

This paper presents the results of determining the free oscillation frequency of a structurally anisotropic, cylindrical fiberglass shell reinforced by annular ribs and containing fluid flow. Boundary Navier conditions are imposed on the ends of the shell. Natural oscillation frequencies are calculated as functions of the frequency on the fiberglass winding angle and liquid flow rate for different valuesof of wave parameters and the parameters characterizing the geometric dimensions of the shell.

This paper describes the influence of the intensity of the external additive white noise on the nonlinear dynamics of rectangular plates as mechanical systems with an infinite number of degrees of freedom. A new scenario is discovered, which is a combination of the classic Feigenbaum and Pomeau-Manneville scenarios. The classical methods of nonlinear dynamics and wavelet transforms were used to reveal the peculiarities of a modified scenario. The noise-induced transitions are investigated, and it is shown that the noise exposure is accompanied with the transition to chaotic oscillations with a lower amplitude of the driving load. It is found that the presence of external fluctuations does not affect the scenario of transition from harmonic to chaotic oscillations.

A theoretical-experimental method for determining the elastic and damping characteristics of materials based on analysis of vibrograms of damped flexural vibrations of test specimens with different structures is proposed. It is shown that during tension-compression and shear of a carbon plastic reinforced with Porcher 3692 carbon fabric, with EDT-69NM polymer binder, the dynamic elastic modulus decreases considerably with increasing frequency of its deformation in the range of 0-120 Hz. The amplitude dependences of the logarithmic vibration decrements of the carbon fiber reinforced plastic are determined Bb minimizing the discrepancy between the experimental and calculated internal-damping parameters of the test specimens in tension-compression and shear.

Wave processes in an isotropic hollow cylinder located in an inhomogeneous prestress field are studied. The dispersion equation of the problem is investigated, and some features of the structure of the dispersion curves in relation to the type of pre-stressed state are identified. Formulas describing the behavior of the dispersion curves in the neighborhood of radial resonances are derived using the perturbation method.

This paper describes the derivation of extremality conditions of each elasticity coefficient (Young's modulus, shear modulus, et al.,) for the general case of linear-elastic anisotropic materials. The stationarity conditions are obtained, and they determine the orthogonal coordinate systems being the main anisotropy axes, where the number of independent elasticity constants decreases from 21 to 18 and, in some cases of anisotropy, to 15 or lower. An example of a material with cubic symmetry is given.

It is shown that for corrugated, in particular multilayer, plates, the tree-dimensional cell-averaging problem can be reduced to the two-dimensional problem on the cross section of the plate periodicity cell. This significantly increases the accuracy of numerical calculation of the effective stiffness of corrugated plates. Numerical calculations of the stiffness of a plate with sinusoidal corrugation were performed, and the results were compared with available data.