Resonant many-mode periodic and chaotic self-sustained aeroelastic vibrations of cantilever plates with geometrical non-linearities in incompressible flow

• Published in: Nonlinear dynamics 2012-10, Vol.70 (2), p.1335-1354
• Main Authors: Avramov, K. V., Strel’nikova, E. A., Pierre, C.
• Format: Article
• Language: English
• Subjects: Aeroelasticity; Automotive Engineering; Cantilever plates; Chaos theory; Classical Mechanics; Computational fluid dynamics; Control; Dynamical Systems; Engineering; Fluid flow; Galerkin method; Gas flow; High aspect ratio; Hopf bifurcation; Incompressible flow; Mechanical Engineering; Nonlinear dynamics; Original Paper; Partial differential equations; Singular integral equations; Vibration; Vibration mode
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-012-0537-5

The plates interacting with inviscid, incompressible, potential gas flow are analyzed. Many modes interaction is considered to describe self-sustained vibrations of plates. The singular integral equation is solved to obtain gas pressures acting on the plate. The Von Karman equations with respect to three displacements are used to describe the plate geometrical non-linear vibrations. The Galerkin method is applied to each partial differential equation to obtain the finite-degree-of-freedom model of the plate vibrations. Self-sustained vibrations, which take place due to the Hopf bifurcation, are investigated. These vibrations undergo the Naimark–Sacker bifurcation and the periodic motions are transformed into the almost periodic ones. If the stream velocity is increased, almost periodic motions are transformed into chaotic ones. As a result of the internal resonance, the saturation of the vibration mode is observed. The non-linear dynamics of low- and high-aspect-ratio plates is analyzed.