Coupled vibration analysis of partially liquid-filled cylindrical shell considering free surface sloshing

Abstract

In this paper, a semi-analytical method is proposed to analyze the dynamic behavior of horizontal cylindrical shells partially filled with liquid, considering the sloshing effect of the free surface. Two coordinate systems are set at the midpoint of the free liquid surface and the geometric center of the cylindrical shell’s cross-section, respectively. The internal fluid is an inviscid, irrotational, and incompressible fluid. The liquid potential functions which satisfy the Laplace function are described in the anti-symmetrical/symmetrical forms based on the liquid surface coordinate system. Meanwhile, the coupled motion functions of the shell are established on the structural coordinate system using the Flugge shell theory. Through the continuous condition on the internal wet surface, the coupled system’s governing equations are achieved and solved by the coordinate transformation and the Galerkin method. The fluid sloshing frequencies and the coupled vibration frequencies of the shell are simultaneously obtained in this coupled model. The accuracy of this method is verified by the published data and the finite element method. Furthermore, the influences of the coupled system’s parameters on the shell’s natural frequencies and sloshing frequencies are discussed, and the coupling effect is revealed between the shell’s vibration and the sloshing of the free surface.