Nonlinear Sloshing of Liquid in a Rigid Cylindrical Container with a Rigid Annular Baffle under Lateral Excitation

Abstract

Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annular baffle subjected to lateral excitation is studied. A semianalytical approach is presented to determine the natural frequencies and modes of the liquid sloshing. Introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expressed in terms of the natural modes of liquid sloshing. Based on the Bateman–Luke variational principle, the infinite-dimensional modal system is given by the variational procedure. The infinite-dimensional modal system is reduced by using the Moiseev asymptotic relations. The resultant hydrodynamic force and moment of the liquid pressure acting on the container mainly depend on the position vector of the mass center of the liquid. Expanding the integral about the weighted position coordinates into the Taylor series about the surface wave height at the unperturbed free surface gives the formula of the position vector of the mass center, which depends only on the generalized time-dependent coordinates. Excellent agreements have been achieved by comparing the present results with those obtained from Gavrilyuk’s solution and SPH solution. Finally, the surface wave height, resultant hydrodynamic force, and hydrodynamic moment for a container subjected to harmonic lateral excitation are discussed in detail.