Mechanics

Analytical Solution of Linear Differential Error Equations of Strapdown Inertial Navigation System, Functioning in the Normal Geographic Reference Frame, for the Case of an Object, Following the Geographical Equator

Authors: Loginov M. Y., Tkachenko M. G., Chelnokov Y. N.

Analytical solution of linear differential error equations of the strapdown inertial navigation system, functioning in the normal geographic reference frame, for the object, following the Earth equator with constant speed and on the constant height, is derived. The solution is represented in the form, which is convenient for the analysis. The roots of the auxiliary equation are derived in the explicit form. Obtained results can be used, for example, for analysis of the accuracy of strapdown inertial navigation system.

Explicit Models for Flexural Edge Waves in Thin Orthotropic Plates

Authors: Kossovich E. L.

Analysis of flexural edge wave propagation in thin plates is presented. Several problems of semi-infinite plates vibrations are solved. These plates are assumed to be orthotropic. Some basic features of flexural edge wave propagation are found using the constructed explicit parabolic-ellipticmodels. They extract the localized wave contribution into the overall solution.

Explicit Models for Flexural Edge and Interfacial Waves in Thin Isotropic Plates

Authors: Kaplunov J. D., Kossovich E. L., Mukhomodyarov R. R., Sorokina O. V.

Exact solutions for problems of vibrations of isotropic thin elastic plates are presented in the work. Some basic principles of explicit dual parabolic-elliptic models for flexural edge and interfacial waves propagation are revealed. The obtained explicit models extract the contribution of the flexural wave into the full dynamic response. Also, these models reveal a dual parabolic-elliptic nature of the flexural edge and interfacial waves.

Antisymmetric Higher Order Edge Waves in Plates

Authors: Wilde M. V., Kossovich L. Y.

This paper is concerned with the propagation of surface waves localized near the edge of plate (edge waves). Antisymmetric waves in a plate subject to traction free boundary conditions are considered. To study higher order edge waves three-dimensional equations of theory of elasticity are used. Asymptotic analysis is performed, which shows that there are an infinite spectrum of higher order edge waves. For the large values of wave number asymptotics of phase velocities are obtained.

Analytical Solution of Equations of Near-circular Spacecraft’s Orbit Orientation

Authors: Pankratov I. A.

The problem of optimal reorientation of spacecraft’s orbit with a limited control, orthogonal to the plane of spacecraft’s orbit, is considered. An approximate analytical solution of differential equations of near-circular spacecraft’s orbit orientation by control, that is permanent on adjacent parts of the active spacecraft’s motion, is obtained.

Modelling of Cracking in Circular Disk Loaded by Concentrated Forces

Authors: Mirsalimov V. M., Kalantarly N. M.

An isotropic disk of radius R, loaded on the contour by two concentrated forces P, apllied to the points z1 = R and z2 = −R, is considered. A model of cracking in a circular disk, based on consideration of fracture process zone, is proposed. It is assumed that the fracture process zone is a finite length layer, containing material with partially broken bonds between individual structural elements. Equations for determination of the external load critical value at which the crack is observed are obtained.

ON WEAK DISCONTINUITIES AND JUMP EQUATIONS ON WAVE SURFACES IN MICROPOLAR THERMOELASTIC CONTINUA

Authors: Kovalev V. A., Murashkin E. V., Radaev Y. N.

The present study is devoted to problem of propagating surfaces of weak and strong discontinuities of translational displacements, microrotations and temperature in micropolar (MP) thermoelastic (TE) continua. Problems of propagation of weak discontinuities in type-I MPTE continua are discussed. Geometrical and kinematical compatibility conditions due to Hadamard and Thomas are used to study possible wave surfaces of weak discontinuities. Weak discontinuities are discriminated according to spatial orientations of the discontinuities polarization vectors (DPVs).

Numerical Implementation of Method of Subsequent Perturbation of Parameters for Computation of Stress-Strain State of a Shell Rigidly Fixed on the Boundaries

Authors: Bessonov L. V.

The Karman model for a shell rectangular in the plan with rigid fixation of the boundaries is considered. An orthonormalized system of basis functions satisfying the boundary conditions of the problem is obtained. Linearization of the problem is given and the solution
is obtained by the method of subsequent perturbation of parameters due to Vladlen V. Petrov. The solutions including supporting intermediate results for the shell made of rolled duralumin are discussed.

On Control of Motion of a Parametric Pendulum

Authors: Bezglasnyi S. P.

The paper is devoted to a passive control problem. The problem of control of plane motions of a two-mass parametric pendulum in a uniform gravitational field is considered. The problem is important for and necessary in software design of automated systems for control of mechanisms. In particular, it can be applied to various modeling problems of pendulum motions of mechanical systems. The pendulum is modeled by two equivalent weightless rods with two equivalent point masses moving along the circle centered at the pivot.

Flow a Round Cylinder by Waves Extending on the Viscous Liquid Surface

Authors: Sycheva E. M.
Some marine hydro technical constructions have such support elements as piles in the form of vertical round cylinders. Questions about the incident wave’s interaction with such barriers and identification of wave regime on the fenced water areas has as the theoretical as the practical concern.We shall consider the motion of liquid, caused by the interaction of incoming gravitational wave, spreading on the surface of the viscous incompressible liquid coat with an infinitely long round cylinder. The problem was solved for the case of small oscillations.

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