Vibrations of a Free-Surface Fluid in an Ellipsoidal Tank in the Vicinity Of Resonance

被引:0
作者
Klimenkov, O. L. [1 ]
Konstantinov, O. V. [2 ]
Limarchenko, O. S. [1 ]
机构
[1] Taras Shevchenko Natl Univ Kyiv, 4e Hlushkova Ave, UA-01033 Kiev, Ukraine
[2] Natl Acad Sci Ukraine, Inst Math, 3 Tereshchenkivska St, UA-01024 Kiev, Ukraine
关键词
nonlinear dynamics; combined motion; near-resonance oscillation; ellipsoidal tank;
D O I
10.1007/s10778-023-01224-y
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The problem of the motion of a free-surface fluid in an ellipsoidal tank under a harmonic force with a frequency close to the resonant one is considered. A nonlinear coupled problem statement is used. Additional attention is paid to the solvability condition for the Neumann problem for the Laplace equation, which is auxiliary to solving the problem using asymptotic methods. A mathematical model that allows us to analyze the behavior of the system over a sufficiently long period of time is developed. The evolution of surface waves is analyzed for an elongated and vertically compressed ellipsoid. It is found out that the oscillation does not become steady-state in all the cases. The system shows high sensitivity to changes in excitation frequencies, and modulation is strongly manifested in almost all modes. In addition, it is shown that the mean value of vibration drifts at low excitation frequencies. The manifestation of nonlinearity becomes stronger with increasing vertical deviations of the side wall of the tank near the unperturbed free surface. Under oscillations at frequencies exceeding the resonance and under strong manifestations of nonlinearities, the regularity of oscillations is disturbed, and antiresonance is observed in some modes. The results are consistent with known theoretical and experimental data.
引用
收藏
页码:324 / 335
页数:12
相关论文
共 16 条
[1]  
Abgarian KA., 1969, DYNAMICS ROCKETS
[2]   Transient and steady-state amplitudes of resonant three-dimensional sloshing in a square base tank with a finite fluid depth [J].
Faltinsen, OM ;
Rognebakke, OF ;
Timokha, AN .
PHYSICS OF FLUIDS, 2006, 18 (01)
[3]  
Ibrahim RA, 2005, LIQUID SLOSHING DYNAMICS: THEORY AND APPLICATIONS, P1, DOI 10.1017/CBO9780511536656
[4]   Dynamic Methods of Damping the Oscillation in Structure-Free-Surface Fluid System [J].
Konstantinov, A. V. ;
Limarchenko, O. S. ;
Lukyanchuk, V. V. ;
Nefedov, A. A. .
INTERNATIONAL APPLIED MECHANICS, 2019, 55 (01) :58-67
[5]  
Konstantinov A. V., 2020, PROBL CONT INFORM, P68
[6]   Modeling the Nonlinear Interaction of Standing and Traveling Bending Waves in Fluid-Filled Cylindrical Shells Subject to Internal Resonances [J].
Kubenko V.D. ;
Koval’chuk P.S. .
International Applied Mechanics, 2014, 50 (4) :353-364
[7]   Stability and Nonlinear Vibrations of Closed Cylindrical Shells Interacting with a Fluid Flow (Review) [J].
Kubenko V.D. ;
Koval’chuk P.S. .
International Applied Mechanics, 2015, 51 (01) :12-63
[8]   Nonlinear wave generation on a fluid in a moving parabolic tank [J].
Limarchenko O.S. ;
Semenova I.Yu. .
International Applied Mechanics, 2011, 46 (8) :864-868
[9]  
Limarchenko OS., 2007, Ukr. Math. J, V59, P46, DOI [10.1007/s11253-007-0004-5, DOI 10.1007/S11253-007-0004-5]
[10]  
Lukovsky IA, 2011, J NUMER APPL MATH, V2, P69