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Propagation of converging spherical deformation waves in a heteromodular elastic medium

  • V. E. Ragozina
  • O. V. Dudko
Article

Abstract

The unsteady one-dimensional boundary-value problem of shock deformation of a medium bounded by a sphere is solved. The propagation of converging deformation wave fronts in an elastic material with different tensile and compressive strengths is studied. A boundary condition is obtained that provides the formation of a converging spherical shock wave with constant velocity. The impact conditions on the boundary of the heteromodular sphere are determined that can lead to the formation of a transition zone (a spherical layer of constant density) between the compression and tension regions.

Keywords

elasticity heteromodular deformation dynamics strain discontinuity converging spherical wave shock wave 

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References

  1. 1.
    V. P. Maslov and P. P. Mosolov, “General Theory of Equations of Motion of an Elastic Heteromodular Medium,” Prikl. Mat. Mekh. 49 (3), 419–437 (1985).MathSciNetGoogle Scholar
  2. 2.
    V. P. Maslov and P. P. Mosolov, Theory of Elasticity for a Heteromodular Medium (Moscow Inst. of Electron. Eng., Moscow 1985) [in Russian].Google Scholar
  3. 3.
    A. G. Kulikovskii and L. A. Pekurovskaya, “On LongitudinalWaves in an Elastic Medium with Piecewise Linear Stress–Strain Relations,” Prikl. Mat. Mekh. 54 (5), 807–813 (1990).MathSciNetGoogle Scholar
  4. 4.
    S. N. Gavrilov and G. C. Herman, “Wave Propagation in a Semi-Infinite Heteromodular Elastic Bar Subjected to a Harmonic Loading,” J. Sound Vibrat. 331 (20), 4464–4480 (2012).ADSCrossRefGoogle Scholar
  5. 5.
    O. V. Dudko, A. A. Lapteva, and K. T. Semenov, “Propagation of One-Dimensional Plane Waves and Their Interaction with Obstacles in a Medium with Different Tensile and Compressive Strengths,” Dal’nevost. Mat. Zh. 6 (1/2), 94–105 (2005).Google Scholar
  6. 6.
    O. V. Dudko, A. A. Lapteva, and V. E. Ragozina, “On the Formation of Plane and SphericalWaves in an Elastic Medium with Different Tensile and Compressive Strengths,” Vestn. Chuvash. Gos. Ped. Univ. Yakovleva, Ser. Mekh. Predel. Sost., No. 4, 147–155 (2012).Google Scholar
  7. 7.
    D. E. Bessonov, Yu. P. Zezin, and E. V. Lomakin, “Heteromodular Granular Composites Based on Unsaturated Polyesters,” Izv. Sarat. Univ., Ser. Mat. Mekh. Inform. 9 (4), part 2, 9–13 (2009).Google Scholar
  8. 8.
    O. V. Sadovskaya and V. M. Sadovskii, Mathematical Modeling in Problems of Mechanics of Granular Media (Fizmatlit, Moscow, 2008) [in Russian].zbMATHGoogle Scholar
  9. 9.
    S. A. Ambartsumyan and A. A. Khachatryan, “Basic Equations of the Theory of Elasticity for Materials with Different Tensile and Compressive Strengths,” Inzh. Zh. Mekh. Tverd. Tela, No. 2, 44–53 (1966).Google Scholar
  10. 10.
    V. P. Myasnikov and A. I. Oleinikov, “Basic General Relations of Isotropically Elastic Heteromodular Media,” Dokl. Akad. Nauk SSSR 332 (1), 57–60 (1992).Google Scholar
  11. 11.
    V. P. Myasnikov and A. I. Oleinikov, Fundamentals of Mechanics of Heteromodular Media, (Dal’nauka, Vladivostok 2007) [in Russian].Google Scholar
  12. 12.
    A. H. Nayfeh, Perturbation Methods (Wiley, 1973).zbMATHGoogle Scholar
  13. 13.
    D. R. Bland, Nonlinear Dynamic Elasticity (Blaisdell, 1969).zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Institute of Automation and Control Processes, Far Eastern BranchRussian Academy of SciencesVladivostokRussia
  2. 2.Far Eastern Federal UniversityVladivostokRussia

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