Mechanics

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.