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Resonances in the problem of the panel flutter in a supersonic gas flow

Abstract

The paper deals with a linear formulation of the problem of plane vibrations in a
supersonic gas flow. Fluctuations of the plane are studied in the case when one of its
ends is rigidly fixed, while the second is free. The flow rate is found for which internal
resonance eigenfrequencies 1:1, 1:2, 1:3 are implemented. The determination of the
speed and the corresponding frequency is reduced to the system of two transcendental
equations. The system is numerically studied.

About the Authors

A. N. Kulikov
Ярославский государственный университет им. П.Г. Демидова
Russian Federation


G. V. Pilipenko
Ярославский государственный университет им. П.Г. Демидова
Russian Federation


References

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2. Наймарк М.А. Линейные дифференциальные операторы. М.: Наука, 1969.

3. Куликов А.Н. Бифуркация автоколебаний пластины при малом демпфировании в сверхзвуковом потоке газа // Прикладная математика и механика. 2000. Т. 73, вып. 2. С. 271-281.

4. Куликов А.Н., Толбей А.О. Определение нижней критической скорости флаттера // Современные проблемы математики и информатики. 2005, вып. 7. С. 157- 163.

5. Holmes P.J., Marsden J.E. Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis // Automatica. 1978. V. 14, №4. P. 367- 384.

6. Holmes P.J. Bifurcations to divergence and flutter in flow-induced oscillations: A finite dimensional analysis // Journal of Sound and Vibration. 1977. V. 53, №4. P. 471-503.


Review

For citations:


Kulikov A.N., Pilipenko G.V. Resonances in the problem of the panel flutter in a supersonic gas flow. Modeling and Analysis of Information Systems. 2011;18(1):56-67. (In Russ.)

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ISSN 1818-1015 (Print)
ISSN 2313-5417 (Online)