| Research Abstract |
The nonlinear random interaction of an elastic structure with liquid sloshing in a cylindrical tank is investigated in the neighborhood of a 1 : 2 internal resonance. The structure, modeled by a mass-spring-dashpot system carrying an upright cylindrical liquid tank, is vertically subjected to a narrow-band random excitation. The excitation is generated from the response of a linear shaping filter subjected to a Gaussian white noise. By using the Galerkin method, the analytical model is constructed taking into account three sloshing modes ; (1,1), (0,1) and (2,1). In addition, the modes whose nodal diameters are perpendicular to those of the original modes (1,1) and (2,1) are also taken into account. The validity of the analytical model was certified by experiments when the excitation was sinusoidal. In the case of random excitation, the system response statistics are numerically estimated using Monte Carlo simulation. The influence of the center frequency and the bandwidth of the random excitation and the liquid level on the system responses are presented. It is found that there is an irregular energy exchange between the structure and the liquid free surface motion when the center frequency is close to the structure natural frequency. Close to this condition, the liquid rotational (swirl) motion takes place due to the nonlinear coupling of orthogonal modes of the same frequency. Depending on the excitation power spectral density, the liquid free surface experiences zero motion, uncertain motion (intermittency), partially developed motion, and fully developed random motion. The structure response probability density function is almost Gaussian, while the liquid elevation deviates from normality. The unstable region, where the liquid motion occurs, becomes wider as the excitation intensity increases or as the bandwidth decreases. In addition, it is found that the statistics of the structure displacement can be obtained if only one sloshing mode is considered.
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