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Symmetries and conservation laws of plates and shells interacting with fluid flow. (English) Zbl 1194.74177
Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 183-190 (2005).
Summary: The present study is concerned with thin isotropic shallow shells interacting with inviscid fluid flow of constant velocity. It is assumed that the dynamic behaviour of the shells is governed by the Marguerre-von Kármán equations. The influence of the fluid flow is taken into account by introducing additional differential and external load terms in the shell equations. It is shown that the system of equations governing such a fluid-structure interaction is equivalent to the von Kármán equations. Thus, the symmetries and conservation laws of the fluid-structure system considered are established.
MSC:
74K20Plates (solid mechanics)
74K25Shells (solid mechanics)
35A30Geometric theory for PDE, characteristics, transformations