Adjacent mode resonance of a hydraulic pipe system consisting of parallel pipes coupled at middle points

• Published in: Applied mathematics and mechanics 2023-03, Vol.44 (3), p.363-380
• Main Authors: Fan, Xin, Zhu, Changan, Mao, Xiaoye, Ding, Hu
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Brackets; Classical Mechanics; Clips; Coupling; Discretization; Excitation; Fluid- and Aerodynamics; Hamilton's principle; Harmonic balance method; Hydraulics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Pipes; Resonance; Resonant frequencies; Stiffness; Vibration
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-023-2967-6

The coupling vibration of a hydraulic pipe system consisting of two pipes is studied. The pipes are installed in parallel and fixed at their ends, and are restrained by clips to one bracket at their middle points. The pipe subjected to the basement excitation at the left end is named as the active pipe, while the pipe without excitation is called the passive pipe. The clips between the two pipes are the bridge for the vibration energy. The adjacent natural frequencies will enhance the vibration coupling. The governing equation of the coupled system is deduced by the generalized Hamilton principle, and is discretized to the modal space. The modal correction is used during the discretization. The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket. The harmonic balance method (HBM) is used to study the responses in the adjacent natural frequency region. The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket, while the locations of them are not node points. The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes. The stiffness of the clip and bracket can release the vibration coupling. It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough. In this way, the vibration energy is reflected by the almost rigid bracket, and is hard to transfer to the passive pipe via a soft clip. The best choice is to set the clips at the pipe node points. The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.