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

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Generalized Models and Non-classical Approaches in Complex Materials 2

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 90))

Abstract

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.

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Acknowledgements

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.).

Author information

Authors and Affiliations

  1. Mechanical Engineering Research Institute of Russian Academy of Sciences, 85 Belinskogo str., 603024, Nizhny Novgorod, Russia

    Vladimir I. Erofeev & Igor S. Pavlov

  2. Nizhny Novgorod Lobachevsky State University, 23 Gagarin av., 603950, Nizhny Novgorod, Russia

    Vladimir I. Erofeev & Igor S. Pavlov

  3. Institute of Problems in Mechanical Engineering, 61 Bolshoy, V.O., 199178, Saint-Petersburg, Russia

    Alexey V. Porubov

  4. St. Petersburg State University, 7–9 Universitetskaya nab., V.O., 199034, Saint-Petersburg, Russia

    Alexey V. Porubov

  5. St. Petersburg State Polytechnical University, 29 Polytechnicheskaya st., 195251, Saint-Petersburg, Russia

    Alexey V. Porubov

  6. Department of Mathematical Modelling, Tver State University, 35 Sadoviy per., 170002, Tver, Russia

    Alexey A. Vasiliev

Authors
  1. Vladimir I. Erofeev
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  2. Igor S. Pavlov
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  3. Alexey V. Porubov
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  4. Alexey A. Vasiliev
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Corresponding author

Correspondence to Vladimir I. Erofeev .

Editor information

Editors and Affiliations

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

    Holm Altenbach

  2. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Joël Pouget

  3. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Martine Rousseau

  4. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Bernard Collet

  5. Centre National de la Recherche Scientifique, UMR 7190, Institut Jean Le Rond d’Alembert, Sorbonne Université, Paris, France

    Thomas Michelitsch

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Erofeev, V.I., Pavlov, I.S., Porubov, A.V., Vasiliev, A.A. (2018). Dispersion Properties of a Closed-Packed Lattice Consisting of Round Particles. In: Altenbach, H., Pouget, J., Rousseau, M., Collet, B., Michelitsch, T. (eds) Generalized Models and Non-classical Approaches in Complex Materials 2. Advanced Structured Materials, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-77504-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-77504-3_5

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77503-6

  • Online ISBN: 978-3-319-77504-3

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