Abstract
The method of normal forms is applied to the nonlinear equations of the liquid motion in a rectangular tank. The basic idea underlying the method of normal forms is the use of local coordinate transformations so that the dynamical system can take the “simplest form”. In this study, the lowest symmetric and asymmetric modes are considered, and two sets of the transformed equations which correspond to the cases with and without internal resonance are derived. The obtained normal forms show that the stationary responses without internal resonance are described by only one state variable. The calculated frequency responses are compared with the results of the direct numerical integrations of the original nonlinear equations of motion. These results show that the response characteristics change from hardening-type to softening-type when the liquid depth is increasing. And it is observed that the time histories of the symmetric mode shift to the negative region. These phenomena coincide with the well-known results.
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