# Nonlinear sloshing analysis by using concentrated mass model

Tatsuhiro Yoshitake, Satoshi Ishikawa, Takahiro Kondou, Kenichiro Matsuzaki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

## Abstract

Sloshing phenomena in containers under earthquakes often cause serious accidents. In case of an oil tank with floating roof, the sloshing phenomenon and the structural vibration should be treated as the coupled problem.Lagrangian fluid finite element model has been used for the analysis of the coupled problem because the compatibility and the equilibrium condition are automatically satisfied at the boundary between the fluid and the structure. However, the degree of freedom of the Lagrangian model becomes large because the fluid particles in the Lagrangian model move vertically and horizontally. In addition, the Lagrangian model has physically-meaningless spurious modes caused by the redundancy of the degree of freedom. In this paper, the efficient and accurate nonlinear analytical model for vertical horizontal two-dimensional nonlinear sloshing phenomena is established. The model consists of masses, nonlinear connecting springs, and connecting dampers. Some masses move horizontally, the others move vertically. The horizontally movable masses are governed by the equations of motion. The vertical displacements of masses are determined from the displacements of the horizontally movable masses based on the incompressibility of the liquid. The characteristics of the connecting springs are derived from the static and dynamic pressures of the liquid. Furthermore, the degree of freedom of the masses distributed in two-dimensional elements is reduced to that of masses distributed in horizontal one-dimensional elements. The degree of freedom of the proposed model is smaller than that of Lagrangian model and the spurious modes does not occur in the proposed model. The natural frequencies and natural modes are compared with the theoretical values. In addition, the numerical results calculated with the concentrated mass model is compared with experimental results. These numerical results agree well with the theoretical values and the experimental results. Therefore, the validity of the proposed model is confirmed

Original language English Proceedings of the 26th International Congress on Sound and Vibration, ICSV 2019 Canadian Acoustical Association 9781999181000 Published - Jan 1 2018 26th International Congress on Sound and Vibration, ICSV 2019 - Montreal, CanadaDuration: Jul 7 2019 → Jul 11 2019

### Publication series

Name Proceedings of the 26th International Congress on Sound and Vibration, ICSV 2019

### Conference

Conference 26th International Congress on Sound and Vibration, ICSV 2019 Canada Montreal 7/7/19 → 7/11/19

## All Science Journal Classification (ASJC) codes

• Acoustics and Ultrasonics

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