Dispersion Properties of a Closed-Packed Lattice Consisting of Round Particles

  • Vladimir I. ErofeevEmail author
  • Igor S. Pavlov
  • Alexey V. Porubov
  • Alexey A. Vasiliev
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 90)


A two-dimensional discrete model for a hexagonal (closed-packed) lattice with elastically interacting round particles possessing two translational and one rotational degrees of freedom is considered. The linear differential-difference equations are obtained by the method of structural modeling to describe propagation of longitudinal, transverse and rotational waves in the medium. The dispersion properties of the model are analyzed. Existence of a backward wave is revealed. The numerical estimations of threshold frequencies of acoustic and rotational waves are given for some values of microstructure parameters.


Structural modeling Hexagonal lattice Round particles Microstructure parameters Dispersion properties 



The research was carried out within the framework of the Russian State assignment to IAP RAS (topic No 0035-2014-0402, State Registration No 01201458047, V.I.E. and I.S.P.), as well as under the financial support of the Russian Foundation for Basic Research (projects No 18-08-00715-a, 16-08-00776-(V.I.E. and I.S.P.), 16-08-00971-a (I.S.P. and A.A.V.), and 16-01-00068-a (A.V.P.)) and the Ministry of Education and Science of the Russian Federation within the framework of the basic part of State Work for scientific activity (project 9.7446.2017/8.9, A.A.V.).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Vladimir I. Erofeev
    • 1
    • 2
    Email author
  • Igor S. Pavlov
    • 1
    • 2
  • Alexey V. Porubov
    • 3
    • 4
    • 5
  • Alexey A. Vasiliev
    • 6
  1. 1.Mechanical Engineering Research Institute of Russian Academy of SciencesNizhny NovgorodRussia
  2. 2.Nizhny Novgorod Lobachevsky State UniversityNizhny NovgorodRussia
  3. 3.Institute of Problems in Mechanical EngineeringSaint-PetersburgRussia
  4. 4.St. Petersburg State UniversitySaint-PetersburgRussia
  5. 5.St. Petersburg State Polytechnical UniversitySaint-PetersburgRussia
  6. 6.Department of Mathematical ModellingTver State UniversityTverRussia

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