Analysis of the Free Vibration of a Coupled Plate/Fluid Interacting System and Interpretation using Sub-system Modal Energy

This paper describes a method for describing and quantifying the vibratory behaviour of interacting structural/fluid systems based upon reference to the relative energy associated with each of the sub-systems. The particular case selected is that of a circular plate in interaction with a cylindrical fluid cavity. A theoretical analysis is performed, based upon the Euler Bernoulli and Helmhotz equations combined through a Galerkin technique, from which the natural frequencies and associated mode functions of the interacting system are calculated. The convergence of the analysis is investigated and the opportunity is taken to investigate the sensitivity of the coupled natural frequencies to different assumed mode shapes of the plate in vacuo. Subsequently the coupled mode functions are used to describe details of the energy associated with the plate and the fluid. It is found that presentation of these relative energies renders a satisfactory insight into the vibration behaviour of the coupled system.