Vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method

Branched pipes of arbitrary shapes are prevalent in pipe systems. Considering fluid–structure interaction (FSI), an absorbing transfer matrix method in frequency domain for fluid-filled pipelines with any branched pipes is proposed in this paper. A dominant chain of pipeline would be selected, and the point transfer matrix of each junction on the dominant chain would be determined. Here, the point transfer matrix, representing the influence of branched pipes at the junction on the dominant pipeline, was “absorbed” by the dominant chain. Based on these, with transfer matrixes of other elements, the fluid and structure dynamics problem could be solved following the chain transfer matrix method process. l numerical examples with different constraints are presented to illustrate the application of the proposed method. Moreover, the experiment of cross-shaped pipes with various boundary conditions was carried out. And results from the present approach were validated by measured and numerical data. Then, the forced vibrations of branched pipes were analyzed by considering the effects of various parameters, which shows the fluid pressure and vibrations can be optimized by changing the branch angles and positions. Through these examples, it is shown that the proposed method is efficient and can be used to calculate branched pipes of any shape.