Izvestiya of Saratov University.
ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


On the identification problem of the thermomechanical characteristics of the finite functionally graded cylinder

The problem of axisymmetric vibrations of a functionally graded finite hollow cylinder is considered. The ends of the cylinder are thermally insulated and are in a sliding fit. Zero temperature is maintained on the inner surface of the cylinder, free from stress, and a combined thermal and power load acts on the outer surface. The direct problem after applying the Laplace transform is solved based on the method of separation of variables.

Automata on algebraic structures

A survey of results obtained in investigations of automata determined over finite algebraic structures. The objects of research are automata over some finite ring, automata determined in terms of ideals, automata over varieties, and families of hash-functions determined by automata without output function. Computational security, complexity of simulation and homomorphisms of investigated automata are characterized. 

Identification of Properties of Inhomogeneous Plate in the Framework of the Timoshenko Model

We consider an inverse problem on identification of properties of an inhomogeneous circular plate for the Timoshenko model. The identification procedure is based on the analysis of acoustical response at some point of the plate in the given set of frequencies. The vibrations are caused by a uniformly distributed load applied to the upper face of the plate. We have derived the oscillation equations for a symmetric circular plate and formulated the boundary conditions in the dimensionless form.

On the Peculiarities of Solving the Coefficient Inverse Problem of Heat Conduction for a Two-Part Layer

The coefficient inverse problem of thermal conductivity about the determination of the thermophysical characteristics of the functional-gradient part of a two-component layer is posed. The input information is the temperature measurement data on the top face of the layer. After the Laplace transform and dimensioning, the direct problem of heat conduction is solved on the basis of Galerkin projection method. Conversion of transformant on the basis of the theory of residues is carried out.