Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method

The application of transfer matrix method (TMM) to the vibration analysis of three-dimensional (3D) pipelines conveying fluid is performed in this paper. Based on the equations of motion, in which the steady combined force is essentially included, a 3D straight pipe element and a curved pipe element conveying fluid are formulated by introducing dynamic stiffness matrix in order to apply the TMM. The natural frequencies of simple pipe systems with straight or circular shape are calculated to demonstrate the validity of the proposed treatment. Using TMM, the natural frequencies, frequency response functions and instability of 3D-shaped pipeline systems are analyzed, representing some fresh results. It is shown that, in the application of TMM to the vibration analysis of curved or 3D pipelines conveying fluid, the steady combined force has to be included, otherwise the obtained results may be not reliable.