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A model of continuous granular medium. Waves in the reduced Cosserat continuum

doi: 10.5862/MCE.31.8

A model of continuous granular medium. Waves in the reduced Cosserat continuum

V.V. Lalin, Ye.V. Zdanchuk, Saint-Petrsburg State Polytechnical University, Saint-Petersburg, Russia

In the description of vibrational properties of deformable bodies, it is usually assumed that the size of the oscillating particles is negligible in comparison with the average distance between them, so to describe the kinematics of such media only the displacement vector is used. In the majority of work is considered that when the independent rotational degrees of freedom are taken into account it become necessary to introduce the couple stress. Such models of continuous media are well known, for example, moment theory of elasticity or Cosserat media.

A distinctive feature of the reduced Cosserat medium is that the stress tensor is asymmetric, and in static problems, this tensor becomes symmetric. Thus, in statics the reduced Cosserat media is indistinguishable from the the classical continuum in which the rotational degrees of freedom are not independent, as they are expressed in terms of displacement and the stress tensor is symmetric.

In this paper we investigate the wave motion of a three-dimensional, isotropic, elastic reduced Cosserat medium, the characteristic velocities of wave propagation are finding, we also construct and analyze the dispersion curve for the dynamic equations.

Key words:

reduced Cosserat continuum; additional elastic constant; analytical solution; volume waves; dispersion; band gap

Read the whole article (rus) in pdf

(Lalin V.V., Zdanchuk Ye.V. A model of continuous granular medium. Waves in the reduced Cosserat continuum // Magazine of Civil Engineering. 2012. №5(31). Pp. 65-71).


References:

  1. Achenbach J. D. Wave propagation in elastic solids. Amsterdam, N-HPC. 1973. 426 p.

  2. Uayt J. E. Vozbuzhdeniye i rasprostraneniye seysmicheskikh voln [Seismic wave excitation and propagation]. Moscow: Nedra, 1986. 263 p. (rus)

  3. Linton C. M., McIver P. Handbook of Mathematical Techniques for Wave. Structure Interactions. CRC Press LLC, 2001. 298 p.

  4. Toupin R. A. Elastic materials with couple stresses. Arch. Rat. Mech. Anal. 1962. V.11. No. 5. Pp. 1189-1196.

  5. Kuvshinskiy Ye. V., Aero E. L. FTT. 1963. Vol. 5. No. 9. Pp. 2591-2597. (rus)

  6. Palmov V. A. PMM. 1964. Vol. 28. Pp. 401-408. (rus)

  7. Toupin R. A. Theories of elasticity with couple stress. Arch. Rat. Mech. Anal. 1964. V.17. Pp. 85-112.

  8. Mindlin R. D., Tiersten H. F. Effects of couple-stresses in linear elasticity. Arch. Rat. Mech. Anal. 1965. Vol. 11. No. 5. Pp. 1183-1188.

  9. Eringen A. Linear theory of micropolar elasticity. J. Math. Mech. 1966. Vol. 15. Pp. 909-923.

  10. Novatskiy V. Teoriya uprugosti [Theory of elasticity]. Moscow: Mir, 1975. 872 p. (rus)

  11. Lalin V. V. VII mezhdunarodnaya konferentsiya «Problemy prochnosti materialov i sooruzheniy na transporte». Tezisy [VII international conference “Problems of material and building strength in transport”. Theses]. Saint-Ptersburg, 2008. Pp. 123. (rus)

  12. Lawrence M. Schwartz, David Linton Johnson and Shechao Feng. Vibrational Modes in Granular Materials. Physical Review Letters. 1984. Vol. 52, No. 10. Pp. 831–834.

  13. Grekova E. F., Kulesh M. A., Herman G. C. Waves in linear elastic media with microrotations, part 2: Isotropic reduced Cosserat model. Bull. Seismol. Soc. Am. 2009. Vol. 99, No. 2B. Pp. 1423-1428.

  14. Kulesh M. A., Grekova Ye. F., Shardakov I. N. Akusticheskiy zhurnal. 2009. Tom 55, No. 2. Pp. 216-225. (rus)

  15. Zdanchuk E., Lalin V. The theory of continuous medium with free rotation without coupled stresses. Proceedings of the XXXVIII Summer School – Conference ADVANCED PROBLEMS IN MECHANICS. 2010. Pp. 771-775.

  16. Lalin V., Zdanchuk E. On the Cauchy problem for nonlinear reduced Cosserat continuum. Proceedings of the XXXIX Summer School – Conference ADVANCED PROBLEMS IN MECHANICS. 2011. Pp. 549-552.

  17. Erofeyev V. I. Volnovyye protsessy v tverdykh telakh s mikrostrukturoy [Wave processes in solid bodies with microstructure]. Moscow: Izd-vo MGU, 1999. 328 p.

  18. Kulesh M. A., Shardakov I. N. Volnovaya dinamika uprugikh sred: metodicheskiy material k spetskursu [Wave dynamics of elastic media: student guide for special course]. Perm: Perm. gos. un-t, 2007. 60 p. (rus)


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