A Fast Semi-Analytic Solution of Liquid Sloshing in a 2-D Tank with Dual Elastic Vertical Baffles and Walls

Liquid sloshing characteristics in a lateral excited two-dimensional (2-D) rectangular tank with dual elastic vertical baffles and walls have been investigated analytically. The elastic baffle or wall is regarded as an Eulerian Bernoulli beam. The complex liquid domain divides into six simple sub-domains according to the superposition principle. The formal solution of the potential function in each sub-domain is obtained using the separation of variables method. Then the formal baffle or wall deflection solution can be derived from the transverse vibration equation. The Eigen equation can be established according to the free surface, interface, and coupled vibration conditions. The coupled frequency can be obtained by solving the Eigen equation. The velocity potential under lateral excitation consists of the rigid container velocity potential and the disturbance potential. Then the coupled dynamic response equation is established using the free liquid surface equation and the coupled vibration equation. The correctness of the semi-analytic solution is verified against available data. Therefore, the numerical model of the present work can be computed quickly with semi-analytic solution and obtain the mechanism of liquid-structure interaction. Finally, the effect of baffle parameters and excitation frequency on liquid sloshing is discussed in detail.