# Mechanics

## Features of complex vibrations of flexible micropolar mesh panels

In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent.

## On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder

The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables.

## The flexural strength of anisotropic composite plates with free edges

Modern technology shows increased demands on the strength properties of machines, their parts, as well as various structures, reducing their weight, volume and size, which leads to the need to use anisotropic composite materials. Finding criteria to determine the ultimate strength characteristics of structural elements, engineering structures is one of the urgent problems of solid mechanics. Strength problems in structures are often reduced to finding out the nature of the local stress state at the vertices of the joints of the constituent parts.

## Dynamic Bending of an Infinite Electromagnetoelastic Rod

The problem of non-stationary bending of an infinite electromagnetoelastic rod is considered. It is assumed that the material of the rod is a homogeneous isotropic conductor. The closed-form system of process equations is constructed under the assumption that the desired functions depend only on the longitudinal coordinate and time using the corresponding relations for shells which take into account the initial electromagnetic field, the Lorentz force, Maxwell’s equations, and the generalized Ohm’s law.

## The Method of Reconstruction of Residual Stresses in a Prismatic Specimen with a Notch of a Semicircular Profile after Advanced Surface Plastic Deformation

The stress-strain state in a surface-hardened bar (beam) with a stress concentrator of the semicircular notch type is investigated. A numerical method for calculating the residual stresses in the notch region after an advanced surface plastic deformation is proposed. The problem is reduced to the boundary-value problem of fictitious thermoelasticity, where the initial (plastic) deformations of the model are simulated by temperature deformations in an inhomogeneous temperature field. The solution is constructed using the finite element method.

## Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields

The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out.

## Hydroelastic Response of a Sandwich Plate Possessing a Compressible Core and Interacting with a Rigid Die Via a Viscous Fluid Layer

The three-layered plate interaction with a rigid die through a layer of viscous fluid was investigated. The plate and rigid die formed a narrow channel with rectangular parallel walls. The channel was completely filled with a viscous incompressible fluid. The fluid movement in the channel was studied as a creeping one. The motion law of the rigid die was considered to be given as a harmonic one and the forced steady-state oscillations problem of the sandwich plate was considered.

## Mathematical Modeling of Deposits Accumulation on the Plastic Biliary Stent Surface for Predicting Its Occlusion

Endoprosthetics with plastic stents has been used to restore bile drainage through the percutaneous or endoscopic method since the late 1970s. The long-term results cannot be considered satisfactory due to the high incidence of jaundice recurrence which is caused by the occlusion of plastic stents with a biliary sludge (accumulation of cholesterol crystals, pigment crystals, bacteria and calcium salts). Cholesterol is considered to be the main component of biliary sludge that stimulates the reduction of the stent lumen.

## Single Waves in a Gas-Liquid Bubble Mixture

Nonlinear wave processes in a two-phase medium (bubbly liquid) do not lose their relevance asan object of study due to their wide use in various fields of physics, engineering, chemical and petroleum industries. Last decades the jump in the development of computing has expanded the possibilities for the study of significantly nonlinear problems. The aim of this work was to obtain a stationary solution of equations describing the motion of a solitary wave in a gas-liquid mixture without taking into account dissipative processes.

## Influence of Convolution Kernel and Beam-Hardening Effect on the Assessment of Trabecular Bone Mineral Density Using Quantitative Computed Tomography

Quantitative computed tomography along with densitometry is used to assess mineral density and strength of bone tissue. Raw data obtained by computed tomography are converted by software using convolution kernels. It is known that the use of convolution kernels can significantly change tissue density, which is measured in Hounsfield units. The beam-hardening effect is described in literature: when x-ray passes through an object, the absorption of lower-energy x-ray photons occurs.