On proper motions of the flat cosserat type structure

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅存取

详细

The problem of natural vibrations of a flat strip of anisotropic two-dimensional Cosserat medium under the assumption of small deformations and in the absence of external forces and moments is investigated. It is shown that two natural frequencies correspond to each wave number. The natural forms of oscillations and the relationship between them are found. It is concluded that at oscillations with the lower of the two frequencies the inclusion rotations accompany the longitudinal displacement of the strip, and at oscillations with a higher frequency they prevent it. The obtained results are illustrated on the example of a medium model with specific parameter values. The plots show the dependences of natural frequencies, phase and group velocities on the wave number, and their asymptotic behavior is studied.

作者简介

G. Brovko

Lomonosov Moscow State University

编辑信件的主要联系方式.
Email: glb@mech.math.msu.su
俄罗斯联邦, Moscow

V. Kozhukhov

Lomonosov Moscow State University

Email: vladislav.kozhukhov@student.msu.ru
俄罗斯联邦, Moscow

E. Martynova

Lomonosov Moscow State University

Email: glb@mech.math.msu.su
俄罗斯联邦, Moscow

参考

  1. Alexei Antonovich Ilyushin (to the seventieth anniversary of his birth) // Bulletin of Moscow University. Series 1. Mathematics. Mechanics. 1981. № 1. P. 104.
  2. Kiyko I.A. Alexey Antonovich Ilyushin (2.0. 01.11-31.05. 98) // Bulletin of Moscow University. Series 1: Mathematics. Mechanics. 1999. № 3. P. 63–65.
  3. Brovko G.L., Bykov D.L., Vasin R.A. et al. Scientific Heritage of A.A. Ilyushin and Development of His Ideas in Mechanics // Izv. RAS. MTT. 2011. № 1. P. 5–18.
  4. Ilyushin A.A. Dynamics // Bulletin of Moscow University. Series 1: Mathematics. Me-chanics. 1994. № 3. P. 79–87.
  5. Alexey Antonovich Ilyushin (to the 100th anniversary of his birth) // Bulletin of Tyumen State University. Physico-mathematical modeling. Oil, gas, energetica. 2010. № 6. P. 198–203.
  6. Ilyushin A.A. Non-symmetry of strain and stress tensors in continuum mechanics // Bulletin of Moscow University. Series 1: Mathematics. Mechanics. 1996. № 5. P. 6–14.
  7. Ilyushin A.A., Lomakin V.A. Moment theories in mechanics of solid deformable bodies // Strength and Plasticity. Moscow: Nauka. 1971. P. 54–61.
  8. Brovko G.L. Modeling of inhomogeneous media of complex structure and Cosser continuum (in Russian) // Bulletin of Moscow University. Series 1: Mathematics. Mechanics. 1996. № 5. P. 55–63.
  9. Brovko G.L. About one structural model of the Kosser medium (in Russian) // Izv. RAS. MTT. 2002. № 1. P. 75–91.
  10. Brovko G.L. Models and problems for filled porous media // Bulletin of Moscow University. Series 1. Mathematics. Mechanics. 2010. № 6. P. 33–44.
  11. Atoyan A.A., Sarkisyan S.O. Study of free vibrations of micropolar elastic thin plates // Dokl. of NAS of Armenia. 2004. Т. 104. № 2. P. 18–33.
  12. Brovko G.L., Ivanova O.A. Modeling of properties and motions of an inhomogeneous one-dimensional continuum of a complex microstructure of the Kosser type (in Russian) // Izv. RAS. MTT. 2008. № 1. P. 22–36.
  13. Brovko G.L., Kuzichev S.A. Stability of the forced torsional oscillations of the equipped rod (in Russian) // Moscow University Vestnik. Series 1. Mathematics. Mechanics. 2010. № 1. P. 57–62.
  14. Ivanova O.A. About limit forms of equilibrium of the model of one-dimensional Cosser continuum with plastic properties // Mechanics of composite materials and structures. 2017. Т. 23. № 1. P. 52–68.
  15. Kantor M.M., Nikabadze M.U., Ulukhanyan A.R. Equations of motion and physical boundary conditions of the micropolar theory of thin bodies with two small dimensions // Izv. RAS. MTT. 2013. № 3. P. 96–110.
  16. Sarkisyan S.O. Micropolar rod model for nanocrystalline material consisting of linear chains of atoms // Physical Mesomechanics. 2016. V. 19. № 4. P. 14–20.
  17. Brovko G.L., Ilyushin A.A. About one plane model of perforated plates (in Russian) // Bulletin of Moscow University. Series 1: Mathematics. Mechanics. 1993. № 2. P. 83–91.
  18. Ivanova O.A. Model of the equipped rod with viscoelastic internal interactions // Mechanics of composite materials and structures. 2018. V. 24. № 1. P. 70–81.
  19. Carta G., Jones I.S., Movchan N.V. et al. “Deflecting elastic prism” and unidirectional localisation for waves in chiral elastic systems // Scientific reports. 2017. V. 7. № 1. P. 1–11. https://doi.org/10.1038/s41598-017-00054-6
  20. Carta G., Nieves M.J., Jones I.S. et al. Elastic chiral waveguides with gyro-hinges // The Quarterly Journal of Mechanics and Applied Mathematics. 2018. V. 71. № 2. P. 157–185. https://doi.org/10.1093/qjmam/hby001
  21. Garau M., Nieves M.J., Carta G., Brun M. Transient response of a gyro-elastic structured medium: Unidirectional waveforms and cloaking // International Journal of Engineering Science. 2019. V. 143. P. 115–141. https://doi.org/10.1016/j.ijengsci.2019.05.007
  22. De Borst R., Sluys L.J. Localisation in a Cosserat continuum under static and dynamic loading conditions // Computer Methods in Applied Mechanics and Engineering. 1991. V. 90. № 1–3. P. 805–827. https://doi.org/10.1016/0045-7825(91)90185-9
  23. Lakes R. Experimental methods for study of Cosserat elastic solids and other generalized elastic continua // Continuum models for materials with microstructure. 1995. V. 70. P. 1–25.
  24. Sadati S.M., Naghibi S.E., Shiva A. et al. Mechanics of continuum manipulators, a comparative study of five methods with experiments. 2017. P. 686–702. https://doi.org/10.1007/978-3-319-64107-2
  25. Wang J. Rubin M.B., Dong H. A nonlinear Cosserat interphase model for residual stresses in an inclusion and the interphase that bonds it to an infinite matrix // International Journal of Solids and Structures. 2015. V. 62. P. 186–206. https://doi.org/10.1016/j.ijsolstr.2015.02.028.
  26. Suiker A.S.J., De Borst R., Chang C.S. Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media // Acta Mechanica. 2001. V. 149. № 1. P. 181–200. https://doi.org/10.1007/bf01261671
  27. Madeo A., Neff P., Ghiba I.-D. et al. Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps // Continuum Mechanics and Thermodynamics. 2015. V. 27. № 4. P. 551–570.https://doi.org/10.1007/s00161-013-0329-2
  28. Grekova E.F., Kulesh M.A., Herman G.C. Waves in linear elastic media with microrotations, part 2: Isotropic reduced Cosserat model // Bulletin of the Seismological Society of America. 2009. V. 99. № 2B. P. 1423–1428. https://doi.org/10.1785/0120080154
  29. Grekova E.F. Plane waves in the linear elastic reduced Cosserat medium with a finite axially symmetric coupling between volumetric and rotational strains // Mathematics and Mechanics of Solids. 2016. V. 21. № 1. P. 73–93. https://doi.org/10.1177/1081286515577042
  30. Abreu R., Thomas C., Durand S. Effect of observed micropolar motions on wave propagation in deep Earth minerals // Physics of the Earth and Planetary Interiors. 2018. V. 276. P. 215–225. https://doi.org/101016/j.pepi.2017.04.006
  31. Xiu Chenxi, Chu Xihua, Wang Jiao et al. A micromechanics-based micromorphic model for granular materials and prediction on dispersion behaviors // Granular Matter. 2020. V. 22. № 4. P. 1–22. https://doi.org/10.1007/s10035-020-01044-8

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2024