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A technique has been developed and a calculation has been made of the irradiance of the entrance pupil of a ground-based optoelectronic system (OES) from a cylindrical space object illuminated by the Sun at night. The results of calculating the minimum irradiance and corresponding stellar magnitude at the input pupil of the OES are presented with a signal-to-noise ratio at the output of the photodetector matrix with a current equal to 7 in the wavelength range of 0.45 ÷ 0.85 mm. The dependence of the signal-to-noise ratio on the distance to the space object for its three different sizes is constructed. The program ROSN-1 was developed and its control panel was presented for calculating the characteristics of ÷ 0.85 mm was presented, and the possibilities of this program were explained.

The features of high-power and high-contrast imaging in a bistatic laser active optics system (laser monitor) are considered. In the developed system, a brightness amplifier has a larger volume than an illumination source, which makes provides for high-power contrast images of micro objects. For the first time, the influence of the time shift between a superradiance pulse of the amplifier and the time of signal arrival at its input on the contrast and power of images formed by one pulse was was ascertained. It is shown that artifacts formed as a result of the superluminous radiation "parasitic" reflection and scattering from optical circuit elements significantly reduce the contrast and power of the generated signals. This effect can be eliminated by the generation of an amplifier input signal before the generation of amplified spontaneous emission. The optimal delay is 1 ns.

An improved Ritchie-Knott-Rice failure criterion, namely (4δ_t, σ_22c) criterion, for the A515-70 steel is studied with allowance for the specimen geometry, specimen temperature, and initial crack length. The results show that the (4δ_t, σ_22c) criterion can effectively predict the cleavage fracture. Results of studying the possibility of using a dimensionless function for determining the fracture toughness are reported.

The possibility of phase transitions (martensitic transformations) in shape-memory alloys is evaluated using the concept of eigenmoduli and eigenstates from the linear theory of elasticity. For alloys with cubic and hexagonal lattices, the matrices of elastic moduli and compl are given and expressions for their eigenmoduli and eigenstates are written. For cubic and hexagonal phases, the specific strain energy is presented as the sum of six independent terms corresponding to six orthogonal eigenstates. It is shown that depending on the ratio of eigenmoduli, there are six types of materials (alloys) with cubic and hexagonal symmetry. The specific strain energies in the cubic and hexagonal phases are compared. If the strain energy is greater in the hexagonal phase than in the cubic phase, the alloy can tend to return to its original state with lower energy. In addition, the strain energies in different phases can be compared using the formulas of the tensors closest in the Euclidean energy norm to cubic and hexagonal tensors. The energies are compared for some values of elastic constants.

For boundary-value problems, the Helmholtz equations in wedge-shaped domains, it is shown that in packed block elements corresponding to the same boundary-value problem can be combined taking into account the type of boundary conditions, also forming a packed block element. The result is verified using another method. It is shown that in the presence of corner points in the domain in which the boundary-value problem is considered, combining block elements does not involve additional complications. It is found that since the solutions of some boundary-value problems in continuum mechanics and physics can be represented as a combination of solutions of boundary-value problems of the Helmholtz equation, this approach can be used to study more complex boundary-value problems and design materials with mosaic structure.

Interaction between a thin viscoelastic layer and a rigid cylinder whose contacting end surface is nominally flat but has a microrelief is studied. The microrelief is modeled by a periodic system of axisymmetric indenters. Analytical expressions for the depth of indentation and the actual contact area are obtained using an approach based on consideration of micro- and macroscale levels. The effect of the surface microgeometry of the punch and mechanical properties of the layer on the time dependences of the indentation depth and the actual contact area.

A self-balanced stress field for an incompressible sphere is constructed based on a non-Euclidean model of a continuous medium. The total stress field is presented as the sum of the elastic and self-balanced fields. The requirement that there are no singular contributions to the stress field leads to the fact that the coefficients at the singularities of the elastic and self-balanced stress fields can be related by a linear transformation, ensuring the removal of singularities. The compensating role of self-balanced stress fields allows one to construct a nonsingular equilibrium stress field for a spherically symmetric state of a continuous medium.

A problem of damping vibrations of a smart structure consisting of elastic and viscoelastic materials and piezoelements with connected shunt circuits is considered. It is proposed to replace the classical resistor in the shunt circuit by an element made of an electroconducting material, in particular, a polymer material filled with graphene nanoparticles. This element plays the role of several resistors with different resistance values, which ensure multimodal damping of vibrations. A mathematical formulation of the problem of forced steady and natural vibrations of smart systems under consideration is provided, as well as results of numerical calculations, which show that graphene-based composites can be used for additional damping of vibrations of smart structures based on piezoelements.

Results of theoretical and experimental investigations of physical and mechanical properties of a heterogeneous material based on the TiB ceramics and VT-6 metallic alloy obtained by means of controlled laser processing are reported. Elastic properties of the heterogeneous structure under analysis are described by the method of conditional moments. Young's modulus of the created heterogeneous material cased on the titanium alloy and titanium boride is measured. The experimental data are found to be in good agreement with the numerical predictions.

Results of the analysis of elastoplastic deformation of a rotating solid cylinder with fixed end faces under monotonic loading by centrifugal forces are reported. The theory of small elastoplastic strains is used in formulating the problem. The general piecewise-linear condition of plasticity and the associated law of the flow are used for calculating the plastic component of the strain. The chosen plasticity condition depends on the parameter that can be considered as a material characteristic. An exact solution of the governing system of equations is derived. Regular features of plastic flow development are found. It is demonstrated that six plasticity domains are formed in the cylinder in the general case; these domains correspond to different ribs and faces of the surface defined by the general piecewise-linear condition. The dependence of the critical velocity of cylinder rotation on the parameter included into the plasticity condition is derived.