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On the propagation of 1D solitary waves in Mindlin-type microstructured solids

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  • Tamm, Kert
  • Salupere, Andrus

Abstract

The Mindlin model and hierarchical approach by Engelbrecht and Pastrone are used for modelling 1D wave propagation in microstructured solids. After introducing the free energy function, one gets from Euler–Lagrange equations a system of equations of motion. Making use of the slaving principle, a nonlinear hierarchical wave equation can be derived. Equations are solved numerically under localized initial conditions. For numerical integration, the pseudospectral method based on the Fourier transform is used. The influence of free energy parameters on the character of dispersion and wave propagation is studied. Numerical results of hierarchical approximation and the full equation system will be compared and the quality of the approximation will be discussed.

Suggested Citation

  • Tamm, Kert & Salupere, Andrus, 2012. "On the propagation of 1D solitary waves in Mindlin-type microstructured solids," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(7), pages 1308-1320.
    • Handle: RePEc:eee:matcom:v:82:y:2012:i:7:p:1308-1320
    DOI: 10.1016/j.matcom.2010.06.022
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    References listed on IDEAS

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    1. Salupere, A. & Engelbrecht, J. & Peterson, P., 2003. "On the long-time behaviour of soliton ensembles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 137-147.
    2. Ilison, Lauri & Salupere, Andrus, 2009. "Propagation of sech2-type solitary waves in hierarchical KdV-type systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3314-3327.
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    Cited by:

    1. Peets, Tanel, 2016. "Internal scales and dispersive properties of microstructured materials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 127(C), pages 220-228.

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