Mechanics

Micropolar Thermoelastic Continuum Models with Constrained Microstructural Parameters

Authors: Kovalev V. A., Radaev Y. N.

A new micropolar thermoelastic continuum model forrmulated by microstructural d-vectors and d-tensors of an arbitrary ranks is proposed. The microstructural vectorial and tensorial extra-field variables are restricted by holonomic or non-holonomic (differential) constraints. The study is carried out in the framework of the Lagrange field formalism as a 4covariant field theory.

The Geometrical Irregular Plates under the Influence of the Quick Changed on the Time Coordinate Forces and Temperature Effects

Authors: Belostochnyj G. N., Mylcina O. A.

On the basis of incoherent thermoelasticity, the dynamic behaviour of geometrically irregular plates under the influence of quick changed, on the time coordinate, forces and temperature effects on surfaces is considered. An approach allowing to obtain the analytical solution of the thermoelasticity dynamic problem for the plate under inhomogeneous boundary conditions at all four edges is suggested.

Nonlinear Wave on the Surface Layer of a Viscous Liquid

Authors: Basinsky K. Y.

The nonlinear problem of the propagation of waves on the free surface of the layer of viscous incompressible fluid of infinite depth in the plane case. Using small parameter method, this nonlinear problem is decomposed into problems in the first two approximations that consistently allowed. Nonlinear expressions for the components of the velocity vector, the dynamic pressure and the shape of the free surface. The motion of particles of the viscous fluid caused by the spread of the wave of the free surface.

The Problem of a Longitudinal Crack with a Filler in a Strip

Authors: Antonenko N. N.

The method of the solution the problem of the central longitudinal crack with a filler in a strip is proposed. It is assumed that the jumps of the components of displacement vector is proportional to the corresponding stresses at its upper edge. Fourier’s method of integral transformation is used. The problem is reduced to a system of integro-differential equations. The effects of influence of thickness, mechanical properties of a strip and a filler of the crack on Mode I and Mode II stresses intensity factors (SIFs) are examined.

Околорезонансные режимы в стационарной задаче о подвижной нагрузке в случае трансверсально изотропной упругой полуплоскости

Authors: Prikazchikov D. A.

A moving load problem on a transversely isotropic elastic half-plane is considered under steady-state assumption. The approach relies on the hyperbolic-elliptic asymptotic model for surface wave, allowing drastic simplifications. In particular, the formulation is reduced to a Dirichlet problem for a scaled Laplace equation having a straightforward solution in terms of elementary functions. The obtained approximate solutions are valid for loads travelling at speeds close to surface wave speed.

The Parametric Oscillations of Heterogeneous Round Cylindrical Shell of Variable Density on Different Boundary Conditions

Authors: Mochalin A. A.

We consider an isotropic cylindrical shell of varying thickness and density along the generatrix. Let the shell be under pressure, which is symmetric and also varying along the generatrix. We follow the polupostamenty theory by V. Z. Vlasov and consider the problem of the dynamical stability of the shell. We obtain the exact solution corresponding to the certain relation between thickness, pressure and density.

Impulsive Action on the Three-layered Circular Cylindrical Shells in Elastic Media

Authors: Leonenko D. V., Starovoitov E. I.

The paper considers oscillations of three-layered cylindrical shells filled by an elastic medium. External loads are impulsive. The Kirchhoff – Love’s hypotheses are assumed for thin isotropic bearing layers. The work of the transverse shear and thickness reduction in the thick filler is taken into account. Variations in displacements in the transverse coordinate are assumed to be linear. The conditions of continuous displacements are used on the contact boundary. The reaction of the inertia-free elastic filler is described in terms of the Winkler’s model.

Nonlinear Deformation Waves in a Geometrically and Physically Nonlinear Viscoelastic Cylindrical Shell Containing Viscous Incompressible Fluid and Surrounded by an Elastic Medium

Authors: Blinkova A. Y., Blinkov Y. A., Ivanov S. V., Mogilevich L. I.

The present study is devoted to analysis of nonlinear deformation of longitudinal waves in a cylindrical shell surrounded by an elastic medium and containing viscous incompressible fluid inside. The physical properties of the shell are defined by the equations of quadratic theory of viscoelasticity, which takes into account the linear elastic volume strain.

Edge Waves in Plates with Fixed Faces and Various Boundary Conditions on the Front Edge

Authors: Ardazishvili R. V., Wilde M. V., Kossovich L. Y.

This paper is concerned with the propagation of surface waves in plates subject to free or mixed boundary conditions on the front edge. Symmetric and antisymmetric waves in plates with fixed faces are considered. Asymptotic analysis is performed, which shows that there is an infinite spectrum of higher order edge waves in plates. Asymptotics of phase velocity are obtained for large values of wave number.

Solution of a Problem of Spacecraft’s Orbit Optimal Reorientation Using Quaternion Equations of Orbital System of Coordinates Orientation

Authors: Pankratov I. A., Sapunkov Y. G., Chelnokov Y. N.

The problemof optimal reorientation of the spacecraft’s orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited inmagnitude. Functional, which determines a quality of control process, is weighted sum of time and impulse (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft’s orbit. Optimal control laws, transversality conditions, not containing Lagrange multipliers, examples of numerical solution of the problem are given.

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