Symmetries and Conservation Laws of Plates and Shells Interacting with Fluid Flow

Abstract

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 considered fluid-structure system are established.