Vol 52, No 1 (2017)

The control of an orbital tethered system (OTS) with an aerodynamic stabilizer (AS) is considered. The aerodynamic stabilizer is a light body of spherical shape with a relatively large ballistic coefficient. The system is deployed with the use of aerodynamic forces and with controlled braking by a special mechanism located on the main spacecraft (SC). A mathematical model describing the deployment and furthermotion of the OTS is constructed. The dynamic and kinematic control laws for the OTS deployment with and without feedback are analyzed. The influence of various disturbances on the stability of OTS deployment processes is estimated. An example where an aerodynamic stabilizer is used to ensure spacecraft descent from a low-earth orbit is given.

The simplest model of longitudinal vibrations of a bar with incipient transverse cracks is considered under the essential assumption that the crack size is small compared with the bar cross-section area and the difference between the mode shapes of the bar with incipient cracks and the undamaged bar is small. The different manifestation of cracks in the phases of extension and compression strains is taken into account. The natural vibration frequencies and the crack coordinates and dimensions are determined from experimental values of natural frequencies.

The Kirchhoff approximation in the theory of diffraction of acoustic and electromagnetic waves by plane screens assumes that the field and its normal derivative on the part of the plane outside the screen coincides with the incident wave field and its normal derivative, respectively. This assumption reduces the problem of wave diffraction by a plane screen to the Dirichlet or Neumann problems for the half-space (or the half-plane in the two-dimensional case) and permits immediately writing out an approximate analytical solution. The present paper is the first to generalize this approach to elastic wave diffraction. We use the problem of diffraction of a shear SH-wave by a half-plane to show that the Kirchhoff theory gives a good approximation to the exact solution. The discrepancies mainly arise near the screen, i.e., in the region where the influence of the boundary conditions is maximal.

The contact problem is considered for a system of bodies subject to wear on a common base. The deformation properties of the bodies and the base are described by the Winkler model. The problem is reduced to a system of ordinary differential equations and an integral equation of hereditary type with difference kernel. The solution of the problem is constructed with the use of the Laplace transform. The asymptotics of the solution at large times is studied. The continuity conditions for the contact of each of the bodies with the base are derived.

Methods for calculating the creep strain of beams or plates in compression were considered by several authors (e.g., see [1–3]).

The goal of calculations is to determine the function describing the deflection increase and the time in which the deflection attains the maximum admissible value.

In this paper, we consider the creep strain with regard to the common action of compression and bending stresses.

The constitutive equations of nonlinear mechanics of a prestressed electrothermoelastic continuum are linearized in the framework of the theory of small strains imposed on finite strains. Simple and convenient-to-operate formulas of linearized constitutive equations and equations of motion of the mediumare obtained. A model of electrothermoelastic half-space with inhomogeneous coating, which is a structure of functionally graded layers, is proposed. It is assumed that each of the medium components is under the action of initial mechanical strains and initial temperature, and the materials of the medium components are orthotropic pyroelectric materials of hexagonal crystal system of class 6 mm. The integral representation of the mediumwave field is constructed by a hybrid numerical-analytical method based on a combination of analytical solutions and numerical schemes used to reconstruct the Green function for the inhomogeneous components of the coating and the matrix approach used to satisfy the boundary conditions.