MATHEMATICAL STUDY OF THE SMALL OSCILLATIONS OF A CATENOIDAL LIQUID BRIDGE BETWEEN TWO EQUAL MEMBRANES UNDER ZERO GRAVITY

✍ Scribed by P. CAPODANNO

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 384 KB
• Volume: 12
• Category: Article
• ISSN: 0889-9746
• DOI: 10.1006/jfls.1997.0129

✦ Synopsis

This paper deals with the mathematical study of the problem of small oscillations of a liquid bridge with a free surface, held together by surface tension between two elastic coaxial circular disks considered as membranes, under zero gravity, in the case of a catenoidal liquid bridge in the equilibrium position. The equations, which give the reciprocal displacements of the free surface and of the membranes, are reduced to a variational equation. The existence of the eigenfrequencies depends on the coerciveness of the bilinear form which appears in this equation. It is shown that these eigenfrequencies exist under two simple conditions involving the ratio between the distance of the planes of the disks and the tensions of the membranes.