Linearized formulation for fluid–structure interaction: Application to the linear dynamic response of a pressurized elastic structure containing a fluid with a free surface

Abstract

To control the linear vibrations of structures partially filled with liquids is of prime importance in various industries such as aerospace, naval, civil and nuclear engineering. It is proposed here to investigate a linearized formulation adapted to a rational computation of the vibrations of such coupled systems. Its particularity is to be fully Lagrangian since it considers the fluid displacement field with respect to a static equilibrium configuration as the natural variable describing the fluid motion, as classically done in structural dynamics. As the coupled system considered here is weakly damped in the low frequency domain (low modal density), the analysis of the vibrations of the associated undamped conservative system constitutes the main objective of this paper. One originality of the present formulation is to take into account the effect of the pressurization of the tank on the dynamics of the system, particularly in the case of a compressible liquid. We propose here a new way of deriving the linearized equations of the coupled problem involving a deformable structure and an inner inviscid liquid with a free surface. A review of the classical case considering a heavy incompressible liquid is followed by an application to the new case involving a light compressible liquid. A solution procedure in the frequency domain is proposed and a numerical discretization using the finite element method is discussed. In order to reduce the computational costs, an appropriate reduced order matrix model using modal synthesis approach is also presented.