FINITE ELEMENT SOLUTION OF INCOMPRESSIBLE FLUID-STRUCTURE VIBRATION PROBLEMS

In this paper we solve an eigenvalue problem arising from the computation of the vibrations of a coupled system, incompressible uid { elastic structure, in absence of external forces. We use displacement variables for both the solid and the uid but the uid displacements are written as curls of a stream function. Classical linear triangular nite elements are used for the solid displacements and for the stream function in the uid. The kinematic transmission conditions at the uid{solid interface are taken into account in a weak sense by means of a Lagrange multiplier. The method does not present spurious or circulation modes for non-zero frequencies. Numerical results are given for some test cases.