Rayleigh Quotient, Ritz Method and Substructuring to Study Vibrations of Structures Coupled to Heavy Fluids: Potential of the Artificial Spring Method

Abstract

The linear study of free vibrations of structures coupled to incompressible and inviscid fluids are studied by using the Rayleigh-Ritz method. The system is modelled by using different components. The artificial spring method is used to synthesise these components. The advantage is that admissible functions are defined in each component and the continuity condition of translational and rotational displacements between the rigid joints of the structure is no longer required. The fluid-structure interaction can be accurately described by using this method, including the effect of the free surface waves and the dynamic interaction among structural components via the fluid medium. An application of the method to a vertical circular tank partially filled with water is also presented in order to show the potential of the method.