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

Authors:
Kert Tamm;Andrus Salupere
Affiliations:
Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, ...;Centre for Nonlinear Studies, Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia and Department of Mechanics, Tallinn University of Technology, ...
Venue:
Mathematics and Computers in Simulation
Year:
2012

Citing 2
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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.