Izvestiâ Akademii nauk. Rossijskaâ akademiâ nauk. Mehanika tverdogo tela.

An electromechanical mathematical model of a piezoelectric fibre-optic FibrCD actuator has been developed, which is a circular coil of a piezoelectric cable with radial polarization of a polymer piezoelectric layer between a core and a shielding electrode; coil turns are connected to each other with a polymer binder. Found are numerical values of effective characteristics of transversal-isotropic elastic and piezoelectric properties of composite fibre structure of disk FibrCD-actuator as a result of numerical solution by finite element method of coupled boundary value problems of electroelasticity for fragment of ideal periodic hexagonal laying of piezoelectric cable turns in polymer epoxy matrix taking into account applied control voltage to cable electrodes. An exact analytical solution of the boundary value problem of the elasticity theory for deformation fields of a homogenized extremely thin disc (ring) of a FibrCD actuator with cylindrical anisotropy of transversal-isotropic effective properties, axis of symmetry of which along circular coordinate, was obtained as part of a thermo analogy approach. Calculation and numerical analysis of deformation fields and performance characteristics of the circular FibrCD actuator with its various geometric parameters were performed.

A mathematical model of dynamic processes in a bimorph plate composed of inhomogeneous pre-stressed piezoelectric and piezomagnetic layers is proposed. The model is based, on one hand, on the use of linearized constitutive relations and equations of motion for a pre-stressed magneto-electro-elastic (MEE) medium. On the other hand, it utilizes a numerical-analytical approach for solving dynamic problems for inhomogeneous pre-stressed MEE media. This approach involves reducing the boundary value problem formulated with partial differential equations to a system of initial-boundary Cauchy problems for the components of the extended stress tensor and displacement vector, combined with the application of efficient high-precision numerical solution schemes. The inhomogeneous piezoelectric and piezomagnetic layers of the plate are assumed to be made of functionally graded materials. A two-component model was used to simulate the inhomogeneity, wherein the parameters of the layer’s base material vary through the thickness until they match the parameters of the inclusion material. The initial strain state (ISS) within the plate’s constituents is homogeneous and is induced by initial mechanical stresses. Within the framework of the model and under the quasi-static approximation, the features of shear horizontal (SH) wave propagation in a plate made of pre-stressed functionally graded materials based on PZT-5H and CoFe₂O₄ are investigated. Wave propagation is initiated by a remote source of harmonic oscillations, assumed to be in a steady state. Perfectly bonded conditions are satisfied at the interface between the layers; the external surfaces are free from mechanical loads, electrically shorted, and magnetically open. The specific influences of the type and magnitude of the initial deformations in each layer on SH-wave velocities for different localizations of the plate’s inhomogeneity are investigated. The frequency ranges of the maximum and minimum influence of the layers ISS on the velocities of various SAW modes over a wide frequency range are determined. It is shown that in the case of an ISS with equal deformations in the layers, the influence of each layer’s ISS complements and reinforces the other. For the case of an ISS with different patterns of deformation in the layers, frequency ranges with partial compensation of the influence of each individual layer’s ISS are identified. The obtained results are presented in dimensionless parameters and may be of particular interest for the development, design, and optimization of new materials used in modern devices and instruments based on SH-SAWs.

Using a model of large strains, a solution of a nonisothermal boundary-value problem on deformation of a material in a rigid circular pipe under the influence of a variable pressure drop is obtained. Between the material and the pipe is a lubricant layer that can slide along the pipe wall. When the lubricant rubs against the pipe, it heats up and the heat is then transferred to the base material. The temperature of the materials also changes due to irreversible deformation. The base material and the lubricant have different elastic moduli, yield strengths and viscosity coefficients. The entire deformation process is considered, from reversible deformation and the occurrence of viscoplastic flow to flow deceleration, unloading and cooling.

The article is devoted to the construction of a pyramid-shaped tether system, which includes six spacecraft. At the base of the pyramid is a square with a central spacecraft. Tethers connect five spacecraft located in the base of the pyramid. First, during the formation of the system, the base of the pyramid unfolds. First, during the formation of the system, the base of the pyramid unfolds. The central spacecraft performs two functions. Firstly, provides geometric stability of the square configuration by means of tethers connecting it to the terminal satellites. Otherwise, under the influence of perturbations, the square tends to deform into a rhombus when the system is deployed. Secondly, a satellite on a tether is separated from the central apparatus perpendicular to the base of the pyramid, and after its deployment, the formation of the system is completed. Low-thrust jet engines and mechanisms regulating the release of tethers are used to control the deployment of the tether system. When forming the base of the pyramid, jet engines and control mechanisms for the release of cables are located on the end satellites, and the central spacecraft plays a passive role. The tension of the tethers connecting the central spacecraft and the end satellites is not regulated. These tethers come out of the central spacecraft freely or with little friction. At the final stage of pyramid formation, control is carried out using a jet engine located on the satellite (which moves to the top of the pyramid) and a mechanism that regulates the tension of the cable located on the central apparatus. Ultimately, the pyramid retains its geometric configuration by rotating around a line that coincides with its height, and using a low-thrust engine located on the satellite (in the top of the pyramid). After the formation, the pyramid retains its orientation in a geocentric fixed coordinate system, which is assumed to be inertial. Simplified models of system motion constructed using Lagrange equations are used to construct nominal control programs for tethers release and reactive forces. The feasibility of the obtained control programs is checked on more complex models that take into account the extensibility of tethers, the possibility of their sagging, the operation of tethers deployed mechanisms, and errors in separating spacecraft at all stages of system formation.

A method for determining the stress-strain state (VAT) of beams during bending is presented, based on the synthesis of solutions found using the formulas of resistance of materials and the relations of the theory of elasticity. The peculiarity of the method is that the beam is divided into sections and solutions are obtained for each of them separately according to the formulas of resistance of materials or according to the theory of elasticity. Then these solutions are combined. The expediency of this approach is related to the need to calculate core systems with local damage in the form of cracks, changes in cross-sectional dimensions, cavities and heterogeneities in the structural material, as well as areas with reduced strength characteristics. Examples of problem solving are given, illustrating the features of the implementation of the described method, the reliability and accuracy of the calculated data obtained.

This article examines the dynamic behavior of elastic rods with a constant cross-section, taking into account the presence of elastic waves within the rod. Precise mathematical models are presented that describe the motion of rod points over time, taking into account both conservative and non-conservative loads. The solutions are formulated in compliance with fundamental conservation laws – the law of conservation of energy and the law of momentum. These laws ensure the physical adequacy of the obtained results and their compliance with the basic principles of mechanics. It is established that the wavefront moves along the rod with a constant velocity, and the accelerations of all points on the rod remain zero throughout the motion. Thus, the motion occurs at a constant, albeit time-varying, velocity. Furthermore, it is shown that within the framework of unsteady dynamics, an infinite number of linearly independent vibration modes exist for the first natural frequency of oscillations. This significantly differs from classical theory, where each frequency typically corresponds to a single vibration mode.

The problem of calculating the thermoelastic-plastic state of a flat reinforced disk rotating at a constant angular velocity is formulated. The structure is rigidly fixed to the shaft or hub (possibly with tension); blades are attached to the outer edge of the disc blade. The materials of the components of the composition are homogeneous and isotropic and obey the hypothesis of a single curve; their thermomechanical state is described by the theory of small elastic-plastic strains. The reinforcement structures of the disc web has radial symmetry. A structural model of composite mechanics has been developed that takes into account the complex stress state in all materials of the components of the composition and allows one to describe the thermoelastic-plastic behavior of compositions even with spatial reinforcement structures. The formulated physically nonlinear problem is solved using the method of variable elastic parameters. Calculations of homogeneous and reinforced disks were carried out for three limit states: 1) for the limit elastic state; 2) for the limit state of autofrettage, when secondary plasticity first occurs during unloading; 3) for the limit state corresponding to the initial destruction of one of the components of the composition. The cases of reinforcement of the disk web along cross-criss rectilinear trajectories and logarithmic spirals, as well as along radial and/or circumferential directions, were investigated. The comparison was made for disks of the same mass. Discs made of magnesium or titanium alloys reinforced with steel wire or SiC-fibers are considered. It has been shown that at the temperature of the natural state, the highest load-bearing capacity is possessed by disks made of high-strength steel, and in the presence of thermal exposure, by reinforced Ti–SiC-disks, profiled so that the summary density of reinforcement in them is constant.

В связи с непредвиденными обстоятельствами произведена замена DOI статей с префиксом Российской академии наук за 2025 год. В первом выпуске журнала РАН за 2026 год размещена информация о замене цифрового идентификатора на действующий DOI.