This paper deals with a hydrodynamic sloshing force on a rectangular tank. In particular, we focus on a contribution of the nonlinear sloshing in shallow water depth to the hydrodynamic force. It is well known that the water wave in shallow water depth shows the characteristic behaviors such as the solitary wave by inherent nonlinearities. Therefore, the effect of nonlinearity is crucial for the estimation of the hydrodynamic sloshing force. Although these behaviors arises from the typical feature of the sloshing in shallow water depth, the theoretical analysis is essentially difficult because a lot of higher order nonlinear terms and eigenmodes have to be taken into account for accurate numerical predictions. Consequently, it yields complicated algebraic procedures. This study presents a formulation based on the Hamiltonian dynamics. In addition, the Dirichlet-Neumann operators (DNO) developed by Craig and Sulem was introduced to obtain an asymptotic description for the kinematic boundary condition of the liquid surface. The proposed approach facilitates the consideration of the nonlinearity for the formulation. Moreover, experiments were conducted to measure time histories of the wave height and the nonlinear fluid force due to the sloshing in a rectangular tank subjected to a horizontal excitation. As the results of frequency analyses for the time histories of the hydrodynamic force, many frequency spectra with the odd multiple of the dominant frequency were observed. These features were also obtained by the theoretical predictions by the proposed method.

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