Williams-Wittrick Approach Application for an Effective Search for Natural Vibration Frequencies of Pipeline Systems With Fluid-Structure Interaction

The approach for quick and effective search of natural vibration frequencies of multibranched beam systems with distributed mass, developed by F.W. Williams and W.H. Wittrick, is adopted for complex pipe systems with fluid-structure interaction. The general principle of the matrix composition is formulated for the case of beam systems of arbitrary complexity. The flexibility of such principle allows to extend it and to take into account the fluid free vibration. The special approach is developed to consider the fluid boundary conditions at the ends of the pipeline and a volumetric balance equation in the junctions. The formulated methods are implemented in an effective calculation procedure for the search of natural frequencies of coupled vibrations of the system with fluid-structure interaction, i.e. taking into account junction coupling as well as Poisson coupling. The procedure accuracy is demonstrated for a number of comparison examples.