Open AccessRepresentation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields
Author(s) -
Yuri Nikolaevich Radayev
Publication year - 2020
Publication title -
izvestiâ saratovskogo universiteta. novaâ seriâ. seriâ matematika. mehanika. informatika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.255
H-Index - 4
eISSN - 2541-9005
pISSN - 1816-9791
DOI - 10.18500/1816-9791-2020-20-4-468-477
Subject(s) - elasticity (physics) , mathematical analysis , vortex , mathematics , differential equation , classical mechanics , vector field , physics , mechanics , geometry , thermodynamics
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.