Statement of the Second Law of Thermodynamics on the Basis of the Postulate of Nonequilibrium

Research in the field of unsteady interaction of shock waves propagating in continuous media with various deformable barriers are of considerable scientific interest, since so far there are only a few scientific works dealing with solving problems of this class only for the simplest special cases. In this work, on the basis of analytical solution, we study the inverse non-stationary boundary-value problem of diffraction of plain pressure wave on convex surface in form of parabolic cylinder immersed in liquid and exposed to plane acoustic pressure wave. The purpose of the work is to construct approximate models for the interaction of an acoustic wave in an ideal fluid with an undeformable obstacle, which may allow obtaining fundamental solutions in a closed form, formulating initial-boundary value problems of the motion of elastic shells taking into account the influence of external environment in form of integral relationships based on the constructed fundamental solutions, and developing methods for their solutions. The inverse boundary problem for determining the pressure jump (amplitude pressure) was also solved. In the inverse problem, the amplitude pressure is determined from the measured pressure in reflected and incident waves on the surface of the body using the least squares method. The experimental technique described in this work can be used to study diffraction by complex obstacles. Such measurements can be beneficial, for example, for monitoring the results of numerical simulations.

Solution of inverse non-stationary boundary value problems of diffraction of plane pressure wave on convex surfaces based on analytical solution

Egorova¹,

Kyaw²

2020

The inverse problem of recovering an unsteady linear load for an elastic rod of finite length

Vahterova¹,

Fedotenkov²

2020

The main purpose of the paper is to obtain solutions for new non-stationary inverse problems for elastic rods. The objective of this study is to develop and implement new methods, approaches and algorithms for solving non-stationary inverse problems of rod mechanics. The direct non-stationary problem for an elastic rod consists in determining elastic displacements, which satisfies a given equation of non-stationary oscillations in partial derivatives and some given initial and boundary conditions. The solution of inverse retrospective problems with a completely unknown space-time law of load distribution is based on the method of influence functions. With its application, the inverse retrospective problem is reduced to solving a system of integral equations of the Volterra type of the first kind in time with respect to the sought external axial load of the elastic rod. To solve it, the method of mechanical quadratures is used in combination with the Tikhonov regularisation method.

Mathematical modelling of the effect of heat fluxes from external sources on the surface of spacecraft

Kyaw¹,

Pronina²,

Polyakov³

2020

Modelling the extraneous heat exchange of spacecraft using solar radiation simulation facility and simulators of the planetary radiation field in a number of cases is an intractable problem not only in technical, but also in methodological terms. For a number of technical reasons, the solar radiation simulator is stationary. Consequently, in order to reproduce a possible change in the orientation of the test object relative to the solar radiation flux, it is necessary to equip the thermal vacuum unit with devices that allow the test object to be rotated at least about two axes. In this paper, a mathematical model and a method for solving the problem of heat transfer in a multilayer structure of screen-vacuum thermal insulation under the influence of solar radiation is proposed. A method is proposed for the numerical solution of a normal system of nonlinear differential equations using the linearisation of nonlinear terms. Various results of numerical modelling were obtained, which indicate the adequacy of the proposed mathematical model. It has been revealed that high-inertia thermal insulation of sufficient thickness is required to stabilise the thermal state inside the spacecraft.