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Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation which considered either the rotational motion or the translational motion of the tank, this formulation can be applied for rigid-liquid-flexible coupling dynamic analysis of tank undergoing translational and rotational motion based on the theorem of momentum and the theorem of moment of momentum. Furthermore, stiffening terms are included in the dynamics equations of the flexible beam. Firstly, the dynamic equations of the rigid-liquid coupling system and the flexible beam are derived, respectively, and then by introducing the Lagrange-multipliers,the rigid-liquid-flexible coupling equations can be combined with acceleration constraint equations. Finally, the mix differential-algebraic equations are solved to investigate the rigid-liquid-flexible coupling dynamic performance of the system.
Considering rigid-liquid-flexible coupling effect, dynamic formulation for a two-dimensional rectangular tank with liquid sloshing connected to a flexible beam is proposed. Differing from the traditional formulation which considered either rotational friction or translational motion of the tank, this formulation can be applied for rigid-liquid-flexible coupling dynamic analysis of tank undergoing translational and rotational motion based on the theorem of momentum and the theorem of moment of momentum. Furthermore, the dynamic equations of the rigid-liquid coupling system and the flexible beam are derived, respectively, and then by introducing the Lagrange-multipliers, the rigid-liquid-flexible coupling equations can be combined with acceleration constraint equations. Finally, the mix differential- algebraic equations are solved to investigate the rigid-liquid-flexible coupling dynamic performanc e of the system.