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

1 1998

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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.