Mathematical study of the small oscillations of a spherical layer of viscoelastic fluid about a rigid spherical core in the gravitational field

2021 ◽  
Vol 72 (3) ◽  
Author(s):  
Hilal Essaouini ◽  
Pierre Capodanno
Keyword(s):  
Gravitational Field ◽  
Viscoelastic Fluid ◽  
Spherical Layer ◽  
Mathematical Study ◽  
Small Oscillations ◽  
Spherical Core

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.  

Free Vibrations of Imperfect Cantilever Bars under Self-Weight Loading

1987 ◽  
Vol 201 (5) ◽  
pp. 345-347 ◽  
Author(s):  
L N Virgin
Keyword(s):  
Gravitational Field ◽  
Natural Frequency ◽  
Free Vibrations ◽  
Equilibrium States ◽  
Small Oscillations ◽  
Initial Imperfections ◽  
The Relationship ◽  
Weight Loading

This brief study examines the relationship between the natural frequency of small oscillations and the length of vertical cantilever struts in a gravitational field. The analysis uses a Rayleigh approach and includes post-buckled equilibrium states and emphasizes the influence of initial imperfections.

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