Transfer matrix modelling for the 3-dimensional vibration analysis of piping system containing fluid flow

For three dimensional vibration analysis of piping system containing fluid flow, a transfer matrix formulation is presented. The fluid velocity and pressure were considered, that coupled to longitudinal and flexural vibrations. Transfer matrices were derived from direct solutions of the differential equations of motion of pipe conveying fluids, and the variations of natural frequency with flow velocities for straight and curved pipes were investigated. The results were confirmed to the corrections of known data. The scheme of this study can be easily applied to the related fields, using small size personal computers with core memory about 200kbytes.