Analysis of reservoir’s mass influence on the system free – surfaced liquid and spherical reservoir

Authors

  • O. S. Limarchenko Taras Shevchenko National University of Kyiv https://orcid.org/0000-0002-2068-8987
  • Y. A. Sliusarchuk Taras Shevchenko National University of Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2019/1.25

Abstract

Within the framework of combined motion the effect of ratio of masses of reservoir and liquid on the behavior of a free surface of liquid in the reservoir of spherical shape is studied. We suppose that liquid is ideal and it fills partially the reservoir. Mathematical modelling is done on the basis of the model, which takes into account combined character of nonlinear dynamics of liquid and the reservoir. Examples were done based on mathematical model of combined motion of liquid in spherical reservoir and free-surfaced liquid under harmonic force disturbance in horizontal direction. Two cases of the ratio of masses in the system are considered. First, the mass of the reservoir is 5 times less than the mass of the liquid; the mass of the reservoir is 5 times greater than the mass of the liquid. In order to identify specific features of the system behavior, the results were compared with the results for liquid behavior in cylindrical and conical reservoirs. It was ascertained that mass increasing has no tendency of converging to a steady mode of motion, which was confirmed experimentally. Distinctions of manifestation of nonlinear processes for the below-resonance, near-resonance and above-resonance modes are shown. We note manifestation of nonlinear effects such as modulation, the presence of high-frequency normal modes of oscillations, antiresonance and drift of the mean of oscillations.

Key words: reservoir, free-surfaced liquid, drift of oscillation, modulation.

Pages of the article in the issue: 110-113

Language of the article: Ukrainian

References

LIMARCHENKO, O., YASINSKIY, V. (1997) Nely`nejnaya dy`namy`ka konstrukcy`j s zhy`dkost`yu. NTUU "KPI".

LIMARCHENKO, O., PARANKINA, O. & SLYSARCHUK, Yu. (2017) Dy`namichna povedinka rezervuara v formi tila obertannya pid diyeyu garmonichnoyi syly v dorezonansnomu diapazoni chastot. Mathematical Modeling and Computing. 4(2). P. 156-161.

LIMARCHENKO, O., SLYSARCHUK, Yu. & PARANKINA, O. (2016) Rezonansna povedinka vil`noyi poverhni ridyny v rezervuari v formi tila obertannya. Zbirnyk prac' Instytutu matematyky NAN Ukrainy. 13(2). P. 1–9.

LIMARCHENKO, O., SLYSARCHUK, Yu. & PARANKINA O. (2018) Povedinka systemy necylindrychnyj rezervuar – ridyna u zarezonansnomu diapazoni zminy chastot. Mehanika giroskopichnyh system. P.5–10.

No 1 (2019)

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How to Cite

Limarchenko, O. S., & Sliusarchuk, Y. A. (2019). Analysis of reservoir’s mass influence on the system free – surfaced liquid and spherical reservoir. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 110–113. https://doi.org/10.17721/1812-5409.2019/1.25

Issue

No. 1 (2019)

Section

Differential equations, mathematical physics and mechanics

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