# Mechanics

## 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. The average lifetime of stents is 3–6 months.

## 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.

## Unsteady Electromagnetic Elasticity of Piezoelectrics Considering Diffusion

The paper considers a model of the linear theory of deformation of elastic continuum with diffusion and piezoelectric effect taken into account, which describes the relationship between mechanical deformations, mass transfer, and the internal electric field. A one-dimensional model of electromagnetic diffusion in a rectangular Cartesian coordinate system is used.

## 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.

## Biomechanics of Human Carotid Artery with Pathological Tortuosity

Pathological tortuosity of carotid artery ranks second among the causes of cerebro-vascular insufficiency. In their previous researches authors have described the influence of pathological tortuosity type on carotid artery behaviour. In this article we discuss the influence of different anatomic (bending angle, bulb size) and rheological factors on haemodynamics and stress-strain state of carotid artery with pathological tortuosity. Decreasing of the bending angle leads to blood volume reduction in brain and possible formation of septal stenosis in bending area.

## The Problem of a Hydroelasticity for a Tube Ring-type a Profile with Elastic, Geometrically Irregular Outer Shell at Pressure Influence

The mechanical model presented in the form of a tube of ring section, formed by two surfaces of coaxial cylindrical shells cooperating with viscous incompressible liquid is considered. The mathematical model of this system consisting of the differential equations in private derivatives of describing dynamics of viscous incompressible liquid and an elastic ridge shell together with boundary conditions is constructed.

## Stress-strain State of an Elliptical Cylinder with an Ellipsoidal Bottoms of Dissimilar Materials Based FEM

The algorithm of calculating the construction in the form of an elliptical cylinder with ellipsoidal bottom of different materials based on the finite element method with the use of scalar and vector fields interpolating movements is described. As part of the sampling using rectangular curved finite elements with eighteen degrees of freedom in the node. Calculations of a circular cylinder with an articulated ellipsoid of rotation the verification of the algorithm and shows its effectiveness.

## Finite Element Analysis of the Influence of the Orthodontic Appliance Design on the Maxillary Expansion

In present paper the results of the stress-strain state finite element analysis of the humanmaxillary complex after activating orthodontic appliance are performed. Skull and abutment teeth models are obtained on the basis of the tomographic data of the dry intact adult skull. Orthodontic appliance designs are differ in the arrangement of rods and screws relative to the sky. The equivalent stresses and displacements of the maxillary bones and supporting the teeth are evaluated.

## Synthesis of Asymptotically Stable Motion of a Robot Arm Manipulator

The paper is about an active control problem. It solves the inverse problem of dynamics and concerns with construction of program motions of non-autonomous mechanical systems. This study is important and necessary in software design of automated systems for control of mechanisms. In particular, it is used in various modeling problems of robot-manipulators. Here, we construct all possible asymptotically stable program motions for a model of robots arm-manipulator, which is simulated by a mechanical system with three degrees of freedom.