Oscillations of von Karman's plate in a~potential flow of gas

L. Boutet de Monvel ; I. D. Chueshov

Izvestiya. Mathematics , Tome 63 (1999) no. 2, pp. 219-244.

Résumé

The paper deals with the problem of non-linear oscillations of a clamped plate in a flow of gas. The dynamics of the plate is described by a modification of von Karman's evolution equations, in which the rotatory inertia of the elements of the plate is taken into account. To describe the influence of the gas flow we apply the linearized theory of potential flows. We prove the global existence and uniqueness of weak solutions of the problem under investigation and study their properties. We show that under certain conditions on the initial data the problem can be reduced to a retarded non-linear partial differential equation for the displacement of the plate. We justify certain heuristic formulae for aerodynamic pressure. Our approach is a general one and enables us to consider both subsonic and supersonic flows.

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