Summarising of the polyparametric functional sets according to own elements of the hybrid Fourier – legendre – eulerian operator in the polar axis segment [R0, R3]

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

Related Articles

Decrease of surfaces roughness for parts processed with edge tool by improvement of the lathe working components uniform feed

The relative motion smoothness of the tool and processing workpiece has an essential influence on the quality of the edge tool processing. The analyses of the process of the surface roughness formation on the parts proce...

Experimental study of contact spot welding of the agricultural machines parts

In the article the results of experimental studies of contact spot welding process of the agricultural machines parts are presented. The subject of experimental studies was selected the compression force of electrodes, w...

Theoretical-probabilistic model for defining the gear grinding stock allowance

According to the stock allowance measurement results the theoretical-probabilistic model for determining the grinding stock allowance is determined. The model includes constant and variable components. The variable compo...

The procedure of the specimen loading parameters in fixing video frame of crack profile

Digital videography, which makes it possible to accomplish direct measurements of geometric parameters of the crack profile in real time, finds wide use in experimental fracture mechanics. Practical implementation of vid...

Imitation modeling for the investigation of the loaded lock of mobile versta - work

In this article the issues of dynamic analysis of the executive branch of the machine system are considered. The analysis of the design scheme consisting of the spatial system, suspended in space on the flexible elements...

Download PDF file
  • EP ID EP572097
  • DOI -
  • Views 79
  • Downloads 0

How To Cite

Andrii Kaplun (2015). Summarising of the polyparametric functional sets according to own elements of the hybrid Fourier – legendre – eulerian operator in the polar axis segment [R0, R3]. Вісник Тернопільського національного технічного університету, 77(1), 299-310. https://europub.co.uk/articles/-A-572097