Spatial oscillations of a liquid in a vertical cylindrical container

Abstract

Using the nonlinear Narimanov–Moiseev modal system with linear damping coefficients corresponding to the logarithmic decrement of the sloshing eigenmodes, steady-state damped resonant sloshing in a cylindrical tank has been investigated. The usage of Miles formula to estimate the damping coefficients shows that these effects can be of significant importance in laboratory conditions. Asymptotic steady-state solutions of the modal system have been obtained for a given motion of a cylindrical tank with four degrees of freedom when the forcing frequency approaches the lowest eigenfrequency of the fluid. This solution turns out to be asymptotically equivalent to a horizontal elliptical trajectory of the container. The response curves, which depend on the ratio of the semiaxes of the elliptical orbit and are related to the amplitudes of the two lowest eigenmodes of the sloshing, have been analyzed.