The effect of overload on the axisymmetric oscillations of a circular diaphragm located on a free surface of a liquid in a cylindrical tank
A frequency equation of axisymmetric oscillations of a circular membraneon the free surface of an ideal incompressible fluid in an upright circularcylindrical tank is derived. The frequency equation is simplified and one isshown that it can be represented in a unified invariant form with respectto the...
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| Date: | 2017 |
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| Keywords: | keywords |
| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Інститут математики НАН України
2017
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/331 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | A frequency equation of axisymmetric oscillations of a circular membraneon the free surface of an ideal incompressible fluid in an upright circularcylindrical tank is derived. The frequency equation is simplified and one isshown that it can be represented in a unified invariant form with respectto the frequency which is looked for. Accounting for two terms in a seriesfrom the frequency equation, an approximate condition for the stabilityof the coupled axisymmetric fluid-membrane vibrations is derived. Thecondition is independent of the membrane mass of and the fluid depth. Itis shown that instability can only be associated with a negative overload.An algorithm leading to an exact stability condition is proposed. A noteis that taking two terms in series provides a sufficient practical accuracy. |
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