Aeroelastic vibrations and stability in cyclic symmetric domains

Abstract

This paper deals with rotating cyclic symmetric structures, immersed in light fluid flow. Firstly, general and usual cyclic symmetric properties are recovered from the Floquet theorem for differential equations, having space periodic coefficients in conjunction with a discrete space Fourier series development. The approach for aeroelastic problem having cyclic symmetry is then formulated based on the twin mode approach. In addition to modal one, rotating and stationary wave bases are introduced to derive the equilibrium equations for a non-dissipative system subjected to aerodynamic loading. Rotating wave basis is the natural one, and it also permits consistently to prescribe the aerodynamic pressure on the boundary between the fluid and the structure. The aerodynamic load is then derived from a harmonic analysis of the fluid flow extending to turbomachinery as in the case of aeroplane wing. In this way, aerodynamic forces may be obtained as general as required, depending on successive time derivatives of degrees of freedom in addition to themselves. Finally, some special cases are given and stability is studied for a cyclic periodic blade assembly, even when mistuning between sectors can occur. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.