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**A finite element solution of an added mass formulation for coupled fluid-solid vibrations.**
*(English)*
Zbl 0998.76046

Summary: We analyze a finite element method to approximate vibration modes of a structure in contact with an incompressible inviscid fluid. The effect of the fluid is taken into account by means of an added mass formulation. Gravity waves on the free surface of the liquid are also considered in the model. We use piecewise-linear continuous elements to discretize solid displacements and the vertical displacement of free surface. Our approach can be considered as a non-conforming method for the coupled spectral problem. Error estimate are derived for approximate eigenfunctions and eigenfrequencies. We discuss implementation issues and report numerical experiments. In particular, the method is compared with other numerical scheme based on a pure displacement formulation.

### MSC:

76M10 | Finite element methods applied to problems in fluid mechanics |

76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

74H45 | Vibrations in dynamical problems in solid mechanics |

74S05 | Finite element methods applied to problems in solid mechanics |