Open AccessSteady-state sloshing in an orbitally-forced square-base tank
Author(s) -
Alexander Timokha,
O.E. Lahodzinskyi
Publication year - 2019
Publication title -
vìsnik. serìâ fìziko-matematičnì nauki/vìsnik kiì̈vsʹkogo nacìonalʹnogo unìversitetu ìmenì tarasa ševčenka. serìâ fìziko-matematičnì nauki
Language(s) - English
Resource type - Journals
eISSN - 2218-2055
pISSN - 1812-5409
DOI - 10.17721/1812-5409.2019/1.49
Subject(s) - slosh dynamics , square (algebra) , steady state (chemistry) , mechanics , reciprocating motion , nonlinear system , container (type theory) , oblique case , eccentricity (behavior) , forcing (mathematics) , base (topology) , diagonal , mathematical analysis , physics , mathematics , modal , classical mechanics , geometry , engineering , materials science , thermodynamics , chemistry , mechanical engineering , linguistics , philosophy , quantum mechanics , political science , law , polymer chemistry , gas compressor
The paper conducts a series of analytical studies on the resonant steady-state sloshing in a rigid square base container, which have been originated by Faltinsen & Timokha who derived and applied the Narimanov-Moiseev—type nonlinear modal equations for investigation in the sloshing problem. The modal equations, which consist on nine-dimensional system of ordinary differential equations, should be applicable for sway/pitch/surge/roll periodic excitations but, due to, basically, mathematical difficulties, the previous papers exclusively concentrated on the reciprocating (longitudinal, oblique and diagonal) motions of the container. This article is showed that the steady-state waves caused by this kind of forcing are asymptotically identical to those occurring when the tank performs horizontal orbital motions. We generalize the previous results by Faltinsen & Timokha to classify the steady-state wave regimes versus the semi-axes ratio of the forcing ellipse in the tank which is filled by a liquid with a finite depth.