Усталені резонансні коливання рідини у вертикальному циліндричному баці при орбітальних збуреннях

Abstract

The nonlinear Narimanov-Moiseev multimodal equations are used to study the swirling-type resonant sloshing in a circular base container occurring due to an orbital (rotary) tank motion in the horizontal plane with the forcing frequency close to the lowest natural sloshing frequency. These equations are equipped with linear damping terms associated with the logarithmic decrements of the natural sloshing modes. The surface tension is neglected. An asymptotic steady-state solution is constructed and the response amplitude curves are analyzed to prove their hard-spring type behavior for the finite liquid depth (the mean liquid depth-to-the-radius ratio h>1). For the orbital forcing only swirling occurs. This behavior type is supported by the existing experimental data. Phase lags, which are piecewise functions along the continuous amplitude response curves in the undamped case, become of the non-constant character when the damping matters. The wave elevations at the vertical wall are satisfactory predicted except for a frequency range where the model test observations reported wave breaking and/or mean rotational flows.