Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. Saratov Univ. Math. Mech. Inform.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Saratov Univ. Math. Mech. Inform., 2020, Volume 20, Issue 4, Pages 468–477 (Mi isu863)  

Scientific Part
Mechanics

Representation of waves of displacements and micro-rotations by systems of the screw vector fields

Yu. N. Radayev

Institute for Problems in Mechanics of RAS (IPMech RAS), 101 Vernadskogo Ave., Moscow 119526, Russia

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 micro-rotations 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.

Key words: micropolar elasticity, displacement vector, micro-rotation vector, coupled, vector potential, vortex part, screw equation, screw field, Helmholtz equation, waveguide.

Funding Agency Grant Number
Ministry of Science and Higher Education of the Russian Federation AAAA-A20-120011690132-4
Russian Foundation for Basic Research 18-01-00844_а
This work was in part financially supported by the Ministry of Science and Higher Education of the Russian Federation (State Registration Number AAAA-A20-120011690132-4) and by the Russian Foundation for Basic Research (project No. 18-01-00844).


DOI: https://doi.org/10.18500/1816-9791-2020-20-4-468-477

Full text: PDF file (239 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 539.3
Received: 11.05.2020
Accepted:28.06.2020
Language:

Citation: Yu. N. Radayev, “Representation of waves of displacements and micro-rotations by systems of the screw vector fields”, Izv. Saratov Univ. Math. Mech. Inform., 20:4 (2020), 468–477

Citation in format AMSBIB
\Bibitem{Rad20}
\by Yu.~N.~Radayev
\paper Representation of waves of displacements and micro-rotations by systems of the screw vector fields
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2020
\vol 20
\issue 4
\pages 468--477
\mathnet{http://mi.mathnet.ru/isu863}
\crossref{https://doi.org/10.18500/1816-9791-2020-20-4-468-477}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000605260300006}
\elib{https://elibrary.ru/item.asp?id=44287620}


Linking options:
  • http://mi.mathnet.ru/eng/isu863
  • http://mi.mathnet.ru/eng/isu/v20/i4/p468

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
    Number of views:
    This page:27
    Full text:16
    References:3

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021