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Dispersive waves in microstructured solids

Profile image of Andrus SalupereAndrus Salupere

2013, International Journal of Solids and Structures

https://doi.org/10.1016/J.IJSOLSTR.2013.02.018
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Abstract

The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler-Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a one-dimensional case.

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References (46)

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The dispersive effects due to the presence of microstructure in solids are studied. The basic mathematical model is derived following Mindlin's theory. In the one-dimensional case the governing equations of a linear system are presented. An approximation using the slaving principle indicates a hierarchy of waves. The corresponding dispersion relations are compared with each other. The choice between the models can be made on the basis of physical effects described by dispersion relations.

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