A numerical method for the computation of the resonance frequencies and modes of a fluid-loaded plate: application to the transient response of the system

In previous papers, we have shown that the time response of a fluid-loaded structure can be expressed in terms of the resonance modes of the fluid/structure system. We first show the efficiency of such a representation by comparing numerical predictions to experimental results. The main objective of this paper is to consider the numerical aspects of this representation, namely the computation of the coupling term in the variational equation and the computation of the resonance frequencies and modes. Three methods are proposed to compute the resonance frequencies: an iterative technique, a Warburton approximation and a perturbation technique (light fluid approximation). Numerical results are presented to compare these three methods, for air and water-loading. The last part of the paper discusses the choice of the number of resonance modes which is required to obtain a representation of the transient radiated pressure with a sufficient accuracy.