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Computer visualization of regular and chaotic vibrations

Łuczko J.

Vibrations in Physical Systems

2002

Vol. 20

214--215

Nonlinear, regular and chaotic vibrations of an airfoil with a trailing and edge flap in supersonic flow

Dżygadło Z., Nowotarski I., Olejnik A.

Journal of Technical Physics

2000

Vol. 41, no 3

219-229

An airfoil in supersonic flow, having deformable nonlinear supports, is an aeroelastic system for which various types of instability, bifurcations and regular or chaotic motions can appear. The airfoil has three degrees of freedom - that is, plunge displacement, angle of pitch and angle of flap deflection. The stiffness force and moments for all those motions are assumed to be nonlinear ones. The airfoil is subjected to the pressure difference produced by its motion in supersonic flow. Stability and bifurcations occurring in the system, limit cycles of self-excited vibrations and regions of regular or chaotic motions have been investigated. The effect of some parameters of the system on the course of linear and nonlinear vibrations has been studied.

Non-linear, regular and chaotic vibrations of a plate in supersonic flow

Dżygadło Z., Nowatorski I., Olejnik A.

Research Bulletin / Warsaw University of Technology, Institute of Aeronautics and Applied Mechanics

1998

nr 8

153-160

Aeroelasticity of surface structures in supersonic flow is a domain which involves various linear and nonlinear vibrations, static and dynamic instabilites and limit cycle motions (cf. [1] - [4]). There can appear various types of bifurcations and regular or chaotic motions depending on the value of parameters of the system under investigation [3] -[7] In this paper nonlinear bending vibrations of a plate of finite length and infinite width in supersonic flow are considered under assumption that a in-plane compressing force is acting in the The dynamic pressure difference produced by the motion in gas stream is determined on the of the potential theory of supersonic flow [1], [2]. Finally, we obtain a nonlinear partial integro-equation describing the motion of the under investigation. The solution of this is obtained in the form of a series of eigenfunctions of the self-adjoined boundary-value vibration problem of the same plate In the vacuum. Making use of the Galerkin method we then obtain a set of nonlinear ordinary differential which can be analysed by means of methods. Types of bifurcations occurring in the problem are investigated, limit cycles of self-vibrations and regions of regular and chaotic can be determined.