Skip to main content
SpringerLink
Log in

Transient Waves in Cosserat Beams: Ray Expansion Approach

  • Living reference work entry
  • First Online:
Encyclopedia of Continuum Mechanics

  • 85 Accesses

Synonyms

Micropolar elasticity; Pseudo-continuum Cosserat; Thin-walled beams of open profile

Definitions

The theory of propagation of transient waves (surfaces of strong discontinuity) in thin-walled beams of open profiles with Cosserat-type microstructure is presented, resulting in the data comparable with those corresponding to transient wave propagation in the three-dimensional Cosserat continuum.

Backgrounds and Some Historical Remarks

It is well known that in order to generalize the Bernoulli-Euler beam model, Stephen Timoshenko in his Russian publication (Timoshenko, 1916), which is more known worldwide by its English publication (Timoshenko, 1921), introduced into consideration two independent functions, namely, the displacement of the center of gravity of the cross section and the rotation of the cross section with respect to the longitudinal central axis, i.e., he suggested to consider the angle of transverse shear as an independent variable. It was a starting point for...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Ambartsumyan SA (1967) Theory of anisotropic plates (in Russian). Fizmatlit, Moscow

    Google Scholar 

  • Grigoluk EI, Selezov IT (1973) Nonclassical theories of vibrations of rods, plates and shells (in Russian). Outputs in science and technology, series of mechanics of deformable solids, vol 5. VINITI, Moscow

    Google Scholar 

  • Korbut VA, Lazarev VI (1974) Equations of flexural-torsional waves in thin-walled bars of open cross section. Sov Appl Mech 10(6):640–644

    Article  Google Scholar 

  • Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates. J Appl Mech 18(1):31–38

    MATH  Google Scholar 

  • Nowacki W (1962) Theory of elasticity (in Polish). PaÅ„stwowe Wydawnictwo Naukowe, Warszawa

    Google Scholar 

  • Nowacki W (1986) Theory of asymmetric elasticity. Pergamon Press, Oxford

    MATH  Google Scholar 

  • Pal’mov VA (1964) Fundamental equations of the theory of asymmetric elasticity. J Appl Math Mech 28(3): 496–505

    Article  MathSciNet  Google Scholar 

  • Reissner E (1944) On the theory of bending of elastic plates. J Math Phys 23(4):184–191

    Article  MathSciNet  Google Scholar 

  • Rossikhin YA, Shitikova MV (1995) Ray method for solving dynamic problems connected with propagation of wave surfaces of strong and weak discontinuities. Appl Mech Rev 48(1):1–39

    Article  Google Scholar 

  • Rossikhin YA, Shitikova MV (2007) The method of ray expansions for investigating transient wave processes in thin elastic plates and shells. Acta Mech 189:87–121

    Article  Google Scholar 

  • Rossikhin YA, Shitikova MV (2011) Dynamic response of pre-stressed spatially curved thin-walled beams of open profile. Springer briefs in applied sciences and technology. Springer, Netherlands

    Book  Google Scholar 

  • Rossikhin YA, Shitikova MV (2012) Dynamic response of spatially curved thermoelastic thin-walled beams of generic open profile subjected to thermal shock. J Therm Stresses 35:205–234

    Article  Google Scholar 

  • Rossikhin YA, Shitikova MV (2015) Transient wave velocities in pre-stressed thin-walled beams of open profile with Cosserat-type micro-structure. Compos Part B Eng 83:323–332. https://doi.org/10.1016/j.compositesb.2015.07.007

    Article  Google Scholar 

  • Rossikhin YA, Shitikova MV (2017) A new approach for studying the transient response of thin-walled beams of open profile with Cosserat-type micro-structure. Comp Struct 169:153–166. https://doi.org/10.1016/j.compstruct.2017.01.053

    Article  Google Scholar 

  • Rossikhin YA, Shitikova MV (2018) Analysis of transient waves in Cosserat-type shells (in Russian). Uchenye Zapiski Komsomol’skogo-na-Amure Gosudarstvennogo Tehnicheskogo Universiteta 2(4)

    Google Scholar 

  • Thomas TY (1961) Plastic flow and fracture in solids. Academic, New York

    MATH  Google Scholar 

  • Timoshenko SP (1916) Course of theory of elasticity (in Russian). Part II. A.E. Kollins Publishing House, Petrograd

    Google Scholar 

  • Timoshenko SP (1921) On the correction for shear of the differential equation for transverse vibrations of prismatic bar. Phil Mag Ser 6 41(245):744–746

    Article  Google Scholar 

  • Uflyand YaS (1948) Wave propagation under transverse vibrations of rods and plates (in Russian). Prikl Mat Mech 12(3):287–300

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, Voronezh, Russia

    Yury A. Rossikhin & Marina V. Shitikova

Authors
  1. Yury A. Rossikhin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marina V. Shitikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marina V. Shitikova .

Editor information

Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Institut für Mechanik, Magdeburg, Germany

    Holm Altenbach

  2. Griffith University (Gold Coast Campus), Griffith School of Engineering Griffith University (Gold Coast Campus), Southport, QLD, Australia

    Andreas Öchsner

Section Editor information

  1. Research Center on Dynamics of Solids and Structures, Voronezh State Technical University, Voronezh, Russia

    Marina V. Shitikova

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer-Verlag GmbH Germany, part of Springer Nature

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Rossikhin, Y.A., Shitikova, M.V. (2018). Transient Waves in Cosserat Beams: Ray Expansion Approach. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_103-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-53605-6_103-1

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53605-6

  • Online ISBN: 978-3-662-53605-6

  • eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation