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Vibrations and stability of a biself-excited surface structure in supersonic flow subjected to a follower force

Dżygadło Z., Nowotarski I., Olejnik A.

Journal of Technical Physics

2003

Vol. 44, no 4

349-362

A surface structure in supersonic flow having a deformable support and subjected to a follower compressing force, which preserves its direction tangential to the deformed surface, is a biself-excited system enclosing two independent physical factors being the reason of self-excited vibrations. In the paper, a study of vibrations and stability of such a structure is presented using the example of a rectangular plate in one-side supersonic flow subjected to a follower force. The plate is considered under the assumption that the conditions of rigid support are satisfied at the plate edges parallel to the unperturbed flow direction. One of the remaining edges is clamped, while the second one has a deformable support. For comparison, the results of analysis in the case of a plate of finite length and infinite width are also presented. A number of numerical calculations have been performed. The analysis indicates a variety of phenomena resulting from simultaneous action of the two independent factors decisive for self-excitation of the structure under consideration.

Nonlinear, regular and chaotic vibrations of a plate in supersonic flow

Dżygadło Z., Nowotarski I., Olejnik A.

Journal of Technical Physics

2000

Vol. 41, no 4

361-374

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). Various types of bifurcations and regular or chaotic motions can appear depending on the values of parameters of the system under investigation [3-11]. In this paper, nonlinear bending vibrations of a plate of finite length and infinite width in supersonic flow are considered under the assumption that a nonlinear in-plane compressing force is acting in the plate. The dynamic pressure difference produced by the plate motion in gas stream is determined on the basis of the potential theory of supersonic flow [1, 2]. Finally, we obtain a nonlinear partial integro-differential equation describing the motion of the structure under investigation. The solution of this equation is obtained in the form of a series of normalised eigenfunctions of the self-adjoint 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 equations which can be analysed by means of numerical methods. Types of bifurcations occurring in the problem are investigated, limit cycles of self-excited vibrations and regions of regular and chaotic motions can be determined.