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Two-Dimensional Modeling of Diatomic Lattice

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Advances in Mechanics of Microstructured Media and Structures

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 87))

Abstract

The two-dimensional nonlinear continuum expressions for the kinetic and potential energies are obtained for nonlinear diatomic lattice. The linear part of the energy is reconstructed using a continuum limit of the two-dimensional discrete model of the lattice. The discrete model considers neighboring spring-like interactions between masses in the lattice for derivation of equations of motion. A connection between the parameters of the lattice and the constants of the continuum model is established. The nonlinear part is added into the continuum model directly in a phenomenological manner. The expressions obtained are useful for finding a solution of a boundary value nonlinear problem.

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Acknowledgements

The work has been supported by the Russian Foundation for Basic Researches, grant No 17-01-00230-a. It was also partially supported by the grant 16-01-00068-a of the Russian Foundation for Basic Researches.

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Authors and Affiliations

  1. Institute for Problems in Mechanical Engineering, Bolshoy 61, V.O., St. Petersburg, 199178, Russia

    A. V. Porubov

  2. Peter the Great St. Petersburg Polytechnic University (SPbPU), Polytechicheskaya st., 29, St. Petersburg, 195251, Russia

    A. V. Porubov

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  1. A. V. Porubov
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Correspondence to A. V. Porubov .

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Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale e Geotecnica, Università di Roma “La Sapienza”, Rome, Italy

    Francesco dell'Isola

  2. Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Gdańsk, Poland

    Victor A. Eremeyev

  3. Department of Micromechanics of Materials, Institute of Problems in Mechanical Engineering, Saint Petersburg, Russia

    Alexey Porubov

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Porubov, A.V. (2018). Two-Dimensional Modeling of Diatomic Lattice. In: dell'Isola, F., Eremeyev, V., Porubov, A. (eds) Advances in Mechanics of Microstructured Media and Structures. Advanced Structured Materials, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-319-73694-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-73694-5_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73693-8

  • Online ISBN: 978-3-319-73694-5

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