Bifurcation of the self-excited oscillations of a plate with slight damping in a supersonic gas flow |
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| Authors: | A.N. Kulikov |
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| Affiliation: | 1. Department of Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran;2. Department of Aerospace Engineering and Centre of Excellence in Computational Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran;3. Department of Aerospace Engineering, Sharif University of Technology, Tehran, Iran;1. School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shinlim-dong, Kwanak-ku, Seoul 151-742, South Korea;2. Institute of Advanced Aerospace Technology, School of Mechanical and Aerospace Engineering, Seoul National University, San 56-1, Shinlim-dong, Kwanak-ku, Seoul 151-742, South Korea |
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| Abstract: | A non-linear boundary-value problem is considered which simulates the oscillations of a plate in a supersonic gas flow. The classical version of the formulation of the problem, proposed by Bolotin, as well as several of its modifications considered by Holmes and Marsden, are taken as a basis. The oscillations of the plate are studied assuming that the damping coefficient is small. This version of the formulation of the problem leads to the need to investigate the bifurcations of the self-excited oscillations in a non-linear boundary-value problem in a case which is close to the critical case of a double pair of pure imaginary values of the stability spectrum. The bifurcation problem is reduced to the investigation of a complex second order non-linear differential equation by the method of normal forms. All the stages in the investigation are carried out without using the Bubnov method. |
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