RITZ METHOD AND SUBSTRUCTURING IN THE STUDY OF VIBRATION WITH STRONG FLUID–STRUCTURE INTERACTION

Abstract

The free vibrations of structures coupled with heavy and inviscid fluids are studied considering that there is no cavitation at the interface. Different formulations of the Rayleigh quotient for structures coupled to compressible and incompressible fluids are obtained either considering or neglecting the free surface waves. The Rayleigh-Ritz method is also introduced. It gives a linear eigenvalue problem for an incompressible liquid when the free surface waves are neglected. When the free surface waves are considered, the eigenvalue problem is generally nonlinear both for incompressible and compressible fluids; however, this study proves that a linear eigenvalue problem may be obtained for incompressible fluids and free surface waves included by solving a problem of larger dimension. When the solid coupled with the fluid is a structure modeled with simple components (substructures), it is useful to use the artificial spring method to synthesise substructures. However, this method was never applied to liquid-structure systems before the present study. It was observed that all the substructures in contact with the same fluid volume are not only coupled by the joints, but also by the fluid. An application of the method to a storage tank partially filled with water is also presented.