Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity
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This paper deals with the mathematical study of the small motions of a system formed by a cylindrical liquid column bounded by two parallel circular rings and an internal cylindrical column constituted by a barotropic gas under zero gravity. From the equations of motion, the authors deduce a variational equation. Then, the study of the small oscillations depends on the coerciveness of a hermitian form that appears in this equation. It is proved that this last problem is reduced to an auxiliary eigenvalues problem. The discussion shows that, under a simple geometric condition, the problem is a classical vibration problem.
2011 ◽
Vol 62
(5)
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pp. 849-868
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1995 ◽
Vol 9
(7)
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pp. 773-786
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1931 ◽
Vol 134
(823)
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pp. 170-192
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2013 ◽
Vol 430
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pp. 53-59
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