Abstract
In this paper the non-linear modal interaction is examined between liquid hydrodynamic impact and an elastic support structure. The liquid impact is modelled based on a phenomenological concept by introducing a power non-linearity with a higher exponent. A special saw-tooth time transformation (STTT) technique is used analytically to describe the in-phase and out-of-phase strongly non-linear periodic regimes. Based on explicit forms of analytical solutions, all basic characteristics of the non-linear free and forced response regimes, such as the time history, the amplitude–frequency dependence and the non-linear parametric resonance curves, are estimated. The response behaviour reveals that a high frequency out-of-phase non-linear mode takes place with a relatively small tank amplitude, and is more stable than the in-phase oscillation mode under small perturbations. The in-phase mode has relatively large tank amplitudes and does not preserve its symmetry under periodic parametric excitation.
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