It is proposed to investigate in this paper the damped vibrations of an incompressible liquid contained in a deformable tank. A linearized formulation describing the small movements of the system is presented. At first, a diagonal damping is introduced in the reduced equations of the hydroelastic sloshing problem. We obtain a nonclassically damped coupled system with a damping matrix that is not symmetric. Then, by projecting the system onto its complex modes, the frequency and time responses for different type of loads are built. A numerical application is illustrated on a test case.
The coupling between a rigid body under large rotations and incompressible fluids is investigated within the arbitrary Lagrangian-Eulerian framework. We use here a staggered type of coupling with a predictor/corrector approach for the forces applied to the rigid body. Adaptive time stepping based on feedback control theory imposing a CFL condition on the mesh is investigated. The coupling scheme is first tested on a case illustrating vortex-induced vibrations around a rotating plate. We show the advantages of using the residual-based variational multiscale method for the fluid in the present context. Also, the time-step control and the role of the parameters introduced for the predictor/corrector approach are illustrated using the same test case. A reduced model FPSO ship is then studied, comparing its pitch decay with experimental results. A complex wave-rigid body interaction calculation is finally presented. Results demonstrated the robustness of the predictor/corrector staggered approach with adaptive time-step control for simulating complex interactions of a rigid body under large rotations and free-surface flows.
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