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Nonlinear waves on the surface of a fluid covered by a viscoelastic sheet

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SIPW05 - SIP Follow on: Mathematics of sea ice in the twenty-first century

We study nonlinear waves on the surface of a fluid covered by a viscoelastic sheet where both tension and flexural waves take place. It is assumed that the behavior of the elastic sheet is described by the Antman theory of hyperelastic  Cosserat shells. Within the framework of this theory, the total energy of the shell is represented as the sum of the stored elastic energy and the dissipative function. We  give a derivation of the  system of evolutionary equations for the motion of a free boundary. The main attention is paid to the analysis of the structure of the dissipative function and to the derivation of the energy dissipation law.  We also consider the viscoelastic covers satisfying the Voight constitutive law.

This talk is part of the Isaac Newton Institute Seminar Series series.

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