Aeroelastic vibrations of a straight wing of high aspect ratio with symmetric cross-sectional profiles in subsonic flow under the action of vertical wind gusts varying according to a harmonic law are considered. The wing profiles are assumed to be non-deformable. Displacements and twist angles of the wing cross-sections are represented using the Ritz method in the form of expansions in given functions with unknown coefficients, which are taken as generalized coordinates. The aerodynamic loads acting on the elastic wing are calculated based on quasi-steady and unsteady theories of plane-parallel separated flow around an oscillating profile in subsonic flow. The vibration equations in generalized coordinates are written as Lagrange equations. The reduction of the system of differential equations is considered using a two-degree-of-freedom model, for which the first generalized coordinate characterizes bending vibrations and the second characterizes torsional vibrations. The vibration equations are presented in dimensionless form. The critical values of the dimensionless parameter characterizing the velocity of the incoming flow at the boundary of static and dynamic stability of aeroelastic vibrations are determined. Neglecting the inertial and damping forces caused by wing torsion, as well as the inertial forces of the added air masses, simplified vibration equations were obtained. Analytical solutions of the differential equations were obtained for two variants of the reduced equations of harmonic vibrations. As an example, a wing with a symmetric profile and a rectangular structural cross-section is considered. Graphs of calculation results obtained by solving the full and reduced systems of differential equations using unsteady and quasi-steady theories are presented. The values of the reduced frequency of harmonic vibrations at which the calculation results for the reduced and full systems of differential equations are close to each other are determined.

The article considers computer models of three-dimensional composites with an epoxy binder reinforced with fabrics with a three-dimensional “interlock with layer-by-layer binding” weave made of carbon fiber for a typical composite of this class. A parametric analysis of the geometric characteristics of reinforcement and the elastic properties of the composite depending on the weft density and fabric shear angle is carried out at the meso-level. Calculations were performed using the WiseTex and TexComp software for practically achievable ranges of changes in weft density and shear angle. Quantitative estimates of the fabric structure parameters and mechanical properties of the composites are obtained. It is shown that an increase in the density of the three-dimensional structure in the weft direction predictably leads to a significant increase in Young’s modulus in the weft direction, a slight increase in the direction perpendicular to the main fabric surface, but at the same time, there is a decrease in the warp direction. The shear moduli and Poisson’s ratios do not undergo large changes with an increase in the fiber volume fraction in the composite, while the Poisson’s ratio in the fabric plane is significantly lower than the other two. The assessment of changes in elastic characteristics during reinforcement shear can be used to calculate the local properties of composites during fabric draping on a mold.

The previously considered composition of the powder mixture in the ZrSi2-MoSi2-ZrB2-Si system was adjusted towards reducing the content of relatively low-melting phases ZrSi2 and MoSi2 and increasing the proportion of the high-melting phase ZrB2. A heat-resistant coating was formed on a C/C-SiC composite by the slurry-fusion method of the powder mixture at a temperature of 1750°C and an argon vacuum pressure of 150-200 Pa. The phase composition of the coating includes, mol.%: 23.2 ZrSi2, 16.8 MoSi2, 46.0 ZrB2, and 14.0 ZrC. The synthesis of the secondary phase ZrC is carried out in situ as a result of the reaction interaction in the ZrSi2-C system. Tests for oxidation and ablation resistance under conditions of flow and surface heating in the range of 1300-2350°C by an air plasma flow at a speed of 4.7-4.8 km/s and a stagnation enthalpy of 48-50 MJ/kg were carried out. It is shown that the performed composition adjustment increased the protective ability of the coating at 2200°C by 2.5 times — up to 170 s, and also increased the maximum permissible operating temperature level from 2200 to 2350°C. At the same time, the average values of the specific mass loss and mass loss rate of the coating decreased by 23 and 14% and amounted to 3.9 mg/cm² and 13.1 mg/(cm²·h), respectively. Estimates were obtained for the values of the heterogeneous recombination rate constant of atoms and ions of the air plasma on the coating surface: 2±1, 5±2, 9±3, 14±3, and 19±2 m/s at 1300-1450, 1500-1750, 1800-1950, 2000-2150, and 2200-2350°C, respectively. A decrease in the spectral emissivity of the coating ελ from 0.69±0.02 in the initial state to 0.41±0.02 after fire tests in the wavelength range λ=600-900 nm at room temperature was established. It is shown that the main factors limiting the service life of the protective action of the coating are through oxidation of the ZrSi2 matrix and evaporation of the zirconium-modified borosilicate glass, leading to an increase in the oxide film of the proportion of the ZrO2 phase with high anionic conductivity and catalytic activity.

The increase in the reverse martensitic transformation temperatures in a number of shape memory alloys observed during the first heating after deformation of samples in the martensitic state, known as the martensite stabilization effect, must be taken into account when designing temperature-sensitive sensors and actuators whose activation must occur in a given temperature range. Several assumptions have been made in the literature regarding the reasons for this phenomenon, including the appearance of dislocations and vacancies that hinder the reverse martensitic transformation, as well as internal stresses arising from incompatible plastic deformation during martensite accommodation. However, the nature of the martensite stabilization effect is still not fully understood. This work adopts a recently proposed hypothesis about damage to the boundaries between martensite orientation domains during their reorientation under the action of stresses as the cause of the martensite stabilization effect. Based on this hypothesis, within the framework of a microstructural approach previously developed for modeling the functional-mechanical behavior of shape memory alloys, a model for the accumulation of damage to intermartensite boundaries during martensite reorientation is formulated, and the temperature dependence of strain during heating of Ti50Ni50 shape memory alloy after its tensile deformation in the martensitic state is modeled. It is shown that taking into account only internal stresses and without considering the influence of the damage factor on the reverse martensitic transformation condition, the modeling shows a decrease, rather than an increase, in the reverse martensitic transformation temperatures. At the same time, introducing this factor into the model makes it possible to logically describe the martensite stabilization effect, while the dependence of the shift in the start temperature of the reverse martensitic transformation, taking into account the scatter of experimental data, gives qualitatively correct values; in particular, at a deformation of 8-10%, the martensitic transformation temperatures shift by more than 50 K.

Based on the semi-momentless theory of thin orthotropic shells using nonlinear equilibrium equations for small deformations and displacements commensurate with the wall thickness, the stress-strain state of curved pipes under bending and internal pressure is determined. The pipe is represented as a thin-walled toroidal shell with variable wall thickness. Solving the nonlinear system of equilibrium equations makes it possible to account for nonlinear effects, in particular, the influence of normal pressure on the pipe deformation during bending. The initial system of equations is simplified by the assumptions of the semi-momentless shell theory and linearized by the small parameter method. The pipe material is orthotropic with layers symmetrically arranged relative to the middle surface and obeys Hooke’s law. The pipe wall thickness in the circumferential direction is variable. A parametric analysis of the stress-strain state of the shell is carried out by varying the length and curvature, and by installing flanges at the pipe ends. The dependence of the stress magnitude on the variability of the pipe cross-section wall thickness is shown. Experimental studies of the strength and stiffness of curved pipes of six standard sizes made of fiberglass under pure bending were carried out. A good correlation between theoretical and experimental results is shown. To assess the strength of fiberglass under a plane stress state, phenomenological strength criteria were used. It is shown that to assess the strength of curved pipes made of fiberglass, it is advisable to use a modified Mises-Hill strength criterion or the maximum stress criterion. The fracture nature of experimental samples under pure bending is analyzed.

The widespread use of composites in mechanical engineering, aerospace technology, construction, calculations of buildings and structures taking into account their interaction with foundation soils, as well as calculations of underground structures and mine workings together with the surrounding rock mass (soils and rocks are essentially naturally occurring composites) poses the task of a reliable, fast and convenient method for determining the mechanical characteristics of such composite materials. In geomechanics, determining mechanical properties is often time-consuming and very expensive, and sometimes it is impossible to determine them experimentally (the problem of determining the characteristics of rock masses). Thus, it can be stated that currently in engineering and scientific activities, the problem of determining the effective characteristics of composite materials is relevant. The aim of this work is to demonstrate the possibility of determining the stiffness tensor using theoretical methods by solving the problem on a periodicity cell, rather than on a representative volume element, under the condition of periodicity of the arrangement of inclusion centers. The paper presents five options for assessing the effective characteristics of the deformation properties of composite materials with a periodic arrangement of inclusion centers and random values of their sizes. The applicability of the proposed probabilistic approach to determining the effective stiffness tensor on a periodicity cell is shown. This approach allows obtaining not only the average values (effective stiffness tensor), but also the three main central moments — from the 2nd to the 4th order, characterizing the random nature of the effective stiffness tensor. The approaches developed in the article for assessing the effective deformation characteristics of composite materials with a periodic arrangement of inclusion centers, characterized by a random radius value, can be practically extended to the assessment of other physical and mechanical properties.

The bending of an elastic three-layer circular plate connected to a two-parameter Pasternak foundation under the action of an arbitrary axisymmetric load is investigated. The problem formulation and its solution are carried out in a cylindrical coordinate system associated with the middle plane of the core. To describe the kinematics of the thickness-asymmetric three-layer package, simplifying hypotheses are introduced. For the thin load-bearing layers of the plate, Kirchhoff’s hypotheses are used, according to which the normal remains straight, perpendicular to the coordinate plane, and does not change its length. In the lightweight, relatively thick core, which does not bear load in the tangential direction, the Timoshenko hypothesis of incompressibility and straightness of the deformed normal, which rotates by some additional angle, is valid. The absence of relative shear of the layers at the plate contour is ensured by a rigid diaphragm. The boundary value problem is reduced to determining the plate deflection, the relative shear in the core, and the radial displacement of the coordinate plane. The inhomogeneous system of ordinary linear differential equilibrium equations is obtained using the Lagrange variational principle. The boundary conditions of hinged support of the plate contour are adopted. A fourth-order differential equation is obtained for the deflection, the solution of which is expressed in terms of Bessel functions. The relative shear in the core and the radial displacement are expressed through the plate deflection. A particular analytical solution of the system of equilibrium equations under an arbitrary axisymmetric load is obtained using the Cauchy kernel. The integration constants corresponding to the boundary conditions under an arbitrary axisymmetric load are determined. A numerical parametric analysis of the stress-strain state of a hinged-supported thickness-asymmetric three-layer circular plate is carried out. The dependence of the solution on the compression and shear parameters of the elastic foundation is investigated. A comparative analysis of the results using the Winkler and Pasternak models is performed, showing a significant influence of the shear properties of the foundation on the deformation of the structure.

The application of the nth-order plate theory to solving the problem of normal wave dispersion in a transversely inhomogeneous waveguide is considered. The nth-order plate model within the framework of the variational formalism of hierarchical theory is a Lagrangian continuum system defined on a reference plane by a configuration space that is a linear span of a set of field variables and a Lagrangian functional. The first-kind field variables are the coefficients of expansion of the components of the spatial displacement vector field in a certain biorthogonal system of functions of the dimensionless coordinate normal to the reference plane, forming a basis in the space of square-integrable functions. The surface and contour densities of the Lagrangian functional are generated by reducing the spatial dimension of the volume and boundary densities of the Lagrangian functional corresponding to the three-dimensional variational formulation of the dynamics problem of an elastic inhomogeneous body. The equations of motion of the nth-order theory are the generalized Lagrange equations of the second kind for a two-dimensional continuum system. Based on the nth-order plate theory, the problem of normal wave dispersion in a plane transversely inhomogeneous functionally graded elastic layer with a power-law distribution of the volume fractions of the structural components of the material and a local deviation from the power-law distribution (a structural defect model) given by a function with a discontinuity in the first derivative is formulated. The problem of wave dispersion is reduced to an eigenvalue problem for a pair of symmetric matrices. The solution to the problem is constructed using both orthogonal polynomials and piecewise linear finite functions of the “partition of unity” type as a basis. The dependence of the dispersion curves of propagating normal wave modes on the presence of a defect is shown. The convergence of the solution with respect to the cut-off frequencies of normal modes is investigated, and it is shown that the use of orthogonal polynomials leads to a higher convergence rate of the spectral problem solution in problems of waveguides with local inhomogeneity.

This article investigates thermal and wave effects in a composite material. For this purpose, a microwave electromagnetic field is applied to a model cell consisting of an outer layer of epoxy resin with an inner core made of carbon or glass fibers. The microwave exposure was carried out using a horn-type setup. The samples were processed alternately, and the placement of both cylinders relative to the horn was carried out in a similar manner and at the same distance from it. The result of the experimental part of the work was thermograms obtained using a thermal imager during the entire period of exposure to the samples. To characterize the distribution of thermal fields, the data obtained from the thermograms were compiled into a table, which made it possible to empirically estimate the heating intensity at different radii on the end surfaces of the samples. It is shown that microwave heating of the samples occurs from the center. It was noted that the model cell with a carbon fiber core heats up faster and to a higher temperature. To account for possible situations of changes in the structure of the experimental samples near the heat source, which was a rod of fibers of different nature (inner rod), it is necessary to consider a three-layer structure of the composite material. This model of its structure allows setting and investigating various conditions of thermal exposure, including exposure to part of the model sample. Based on the experimental results, a theoretical mathematical model is formulated, which is an uncoupled thermoelasticity problem. Calculations of the proposed mathematical model were carried out. A qualitative agreement with the experimental results was obtained.