Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Radaev Y. N. Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields. Izv. Sarat. Univ. Math. Mech. Inform., 2020, vol. 20, iss. 4, pp. 468-477. DOI: 10.18500/1816-9791-2020-20-4-468-477

Published online: 
30.11.2020
Full text:
(downloads: 42)
Language: 
English
Heading: 
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2020-20-4-468-477

Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields

Autors: 
Radaev Yurii Nickolaevich, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Abstract: 

The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.

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Received: 
11.05.2020
Accepted: 
28.06.2020
Published: 
30.11.2020