Small oscillations of an inviscid liquid under zero gravity in a container of revolution with elastic bottom and anchored edge

2000 ◽  
Vol 27 (1) ◽  
pp. 43-48
Author(s):  
P. Capodanno ◽  
D. Vivona
Keyword(s):  
Zero Gravity ◽  
Small Oscillations ◽  
Inviscid Liquid ◽  
Elastic Bottom

Non-linear oscillations of an inviscid liquid column under zero-gravity

1988 ◽  
Vol 58 (4) ◽  
pp. 276-284 ◽  
Author(s):  
W. Eidel ◽  
H. F. Bauer
Keyword(s):  
Liquid Column ◽  
Zero Gravity ◽  
Inviscid Liquid ◽  
Non Linear

scholarly journals Mathematical study of the small oscillations of a finite cylindrical column liquid-gas under zero gravity

2019 ◽  
Vol 7 (1) ◽  
pp. 4
Author(s):  
Hilal Essaouini ◽  
Pierre Capodanno
Keyword(s):  
Variational Equation ◽  
Equations Of Motion ◽  
Geometric Condition ◽  
Zero Gravity ◽  
Mathematical Study ◽  
Small Oscillations ◽  
Cylindrical Column ◽  
Barotropic Gas ◽  
Circular Rings ◽  
Classical Vibration

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.  

scholarly journals On the stability of an equilibrium and the small motions of a rigid body containing a liquid, suspended in a uniform flow

2019 ◽  
Vol 46 (2) ◽  
pp. 109-129
Author(s):  
Hilal Essaouini ◽  
Pierre Capodanno
Keyword(s):  
Rigid Body ◽  
Characteristic Equation ◽  
Equilibrium Position ◽  
Suitable Condition ◽  
First Integral ◽  
Complex Conjugate ◽  
Sufficient Condition ◽  
Small Oscillations ◽  
Inviscid Liquid ◽  
The Stability

In this paper, we consider a planar motion of a rigid body partially filled with an inviscid liquid and suspended in a uniform horizontal flow. At first, we write the equations of the problem, prove the existence of an equilibrium under a suitable condition and, using a first integral, we give a sufficient condition of stability of this one. Afterwards, we give the equations of the small oscillations of the system about its equilibrium position. Writing these equations in an operatorial form, we prove the existence of a denumerable infinity of complex conjugate pairs of eigenvalues having the infinity as a point of accumulation and obtain the characteristic equation permitting the calculation of the eigenvalues.

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