Summarising of the polyparametric functional sets according to own elements of the hybrid Fourier – legendre – eulerian operator in the polar axis segment [R0, R3]
Journal Title: Вісник Тернопільського національного технічного університету - Year 2015, Vol 77, Issue 1
Abstract
Efficient introduction of composites in modern technological processes requires to be aware of their physical-technological parameters, foremost in stationary operating regimes, in which they operate after sharp temperature or power load. It results in thermomechanic problems of the lump – homogenous media. In practice even in the simplest model problems the values, which characterise the stationary state, are expressed as polyparametric functional set, which can be adjacent conventionally in the condition, when it represents the analytical function. It follows, that the functional set is reasonable to be replaced by its adjacent result, which is of special importance for the engineering calculations. Solution of the separate system of the Fourier, Legendre and Eulerian differential equations is based on the three-component segment of the polar axis with the boundary conditions and conjugation conditions taking advantage of the Cauchy functions method. With this purpose at first the fundamental system of these equations solutions was obtained, and the boundary conditions the conjugation conditions result in heterogonous algebraic system, which consists of six equations, to find the values Aj, Bj, the determinant of which does not equal zero. The main solutions of the boundary problem, which are caused by the boundary conditions for the Green function and heterogeneity of the conjugation conditions, were found. The solution of this boundary problem is built by the method of the relative finite hybrid integral transformation. Polyparametric family of the functional sets has been summarised while comparing these solutions.
Authors and Affiliations
Andrii Kaplun
Keywords
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