Parametric nonlinear sloshing in a 2D rectangular tank with finite liquid depth

2011 ◽  
pp. 101-108
Author(s):  
C Spandonidis ◽  
K Spyrou
Keyword(s):  
Nonlinear Sloshing ◽  
Rectangular Tank ◽  
Liquid Depth

An adaptive multimodal approach to nonlinear sloshing in a rectangular tank

2001 ◽  
Vol 432 ◽  
pp. 167-200 ◽  
Author(s):  
ODD M. FALTINSEN ◽  
ALEXANDER N. TIMOKHA
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Fluid Motion ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Modal Theory ◽  
Nonlinear Sloshing ◽  
Rectangular Tank ◽  
Wide Range ◽  
Infinite Dimensional System

Two-dimensional nonlinear sloshing of an incompressible fluid with irrotational flow in a rectangular tank is analysed by a modal theory. Infinite tank roof height and no overturning waves are assumed. The modal theory is based on an infinite-dimensional system of nonlinear ordinary differential equations coupling generalized coordinates of the free surface and fluid motion associated with the amplitude response of natural modes. This modal system is asymptotically reduced to an infinite-dimensional system of ordinary differential equations with fifth-order polynomial nonlinearity by assuming sufficiently small fluid motion relative to fluid depth and tank breadth. When introducing inter-modal ordering, the system can be detuned and truncated to describe resonant sloshing in different domains of the excitation period. Resonant sloshing due to surge and pitch sinusoidal excitation of the primary mode is considered. By assuming that each mode has only one main harmonic an adaptive procedure is proposed to describe direct and secondary resonant responses when Moiseyev-like relations do not agree with experiments, i.e. when the excitation amplitude is not very small, and the fluid depth is close to the critical depth or small. Adaptive procedures have been established for a wide range of excitation periods as long as the mean fluid depth h is larger than 0.24 times the tank breadth l. Steady-state results for wave elevation, horizontal force and pitch moment are experimentally validated except when heavy roof impact occurs. The analysis of small depth requires that many modes have primary order and that each mode may have more than one main harmonic. This is illustrated by an example for h/l = 0.173, where the previous model by Faltinsen et al. (2000) failed. The new model agrees well with experiments.

Effect of viscosity on sloshing in a rectangular tank with intermediate liquid depth

2020 ◽  
Vol 118 ◽  
pp. 110148 ◽  
Author(s):  
Xin Jin ◽  
Jinbo Tang ◽  
Xiaochun Tang ◽  
Shuo Mi ◽  
Jiaxin Wu ◽  
...  
Keyword(s):  
Rectangular Tank ◽  
Liquid Depth

Vibration Analysis of a Floating Roof Taking Into Account the Nonlinearity of Sloshing

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
M. Utsumi ◽  
K. Ishida
Keyword(s):  
Linear Approximation ◽  
Nonlinear Effect ◽  
Vibration Analysis ◽  
Numerical Results ◽  
Roof Displacement ◽  
Wave Number ◽  
Nonlinear Sloshing ◽  
Modal Component ◽  
Liquid Depth ◽  
Circumferential Wave

The vibration of a floating roof hydroelastically coupled with nonlinear sloshing is analyzed. Influences of the nonlinearity of sloshing on the magnitude of stresses arising in a floating roof are investigated. Numerical results show that (i) neglecting the nonlinearity of sloshing significantly underestimates the magnitude of the stresses, even when the nonlinear effect is small for the roof displacement; and (ii) the underestimation associated with the use of the linear approximation becomes more marked with the decrease in the liquid depth. The reasons for these results are explained based on the fact that in the nonlinear sloshing, the modal component with circumferential wave number 2 is excited.

Bi-stability in a vertically excited rectangular tank with finite liquid depth

2012 ◽  
Vol 2 (3) ◽  
pp. 229-238
Author(s):  
Christos C. Spandonidis ◽  
Kostas J. Spyrou
Keyword(s):  
Rectangular Tank ◽  
Liquid Depth

scholarly journals Pseudospectral solution of three-dimensional nonlinear sloshing in a shallow water rectangular tank

2012 ◽  
Vol 35 ◽  
pp. 160-184 ◽  
Author(s):  
Ming-Jyh Chern ◽  
Nima Vaziri ◽  
Sam Syamsuri ◽  
Alistair G.L. Borthwick
Keyword(s):  
Shallow Water ◽  
Three Dimensional ◽  
Nonlinear Sloshing ◽  
Rectangular Tank
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