Modeling and Control of Asymptotic Shells
Michel C. Delfour · Birkhäuser Basel eBooks · 2003
The object of this paper is twofold. We first present new results for the asymptotic model associated with the P(2, 1)-model of thin shells introduced and studied in [ 3 ]. This asymptotic model involved a system of two equations: a generalized membrane shell equation and a generalized bending equation for the projection of the asymptotic solution onto the space of inextensible deformations. A new choice of the projection leads to the disappearance of the coupling term in the second asymptotic equation. After reduction of the number of variables, we obtain the classical bending equation for this new projection of the asymptotic solution without coupling with the membrane shell equation. The new choice of projection changes the form of the second equation to achieve the complete decoupling of the membrane and bending equations. In the second part of this paper we present a dynamical thin shell model for small vibrations and investigate the corresponding dynamical asymptotic model.