Stability improvement of the transfer matrix method when calculating the high requency vibration of a pipeline conveying fluid
CAO Yinhang1,LIU Gongmin2,HU Zhi1
1.College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, China;
2.Yantai Research Institute and Graduate School, Harbin Engineering University, Yantai 264006, China
Abstract:The transfer matrix method (TMM) is a common calculation method for studying structural vibration, but it suffers from numerical instability in the high-frequency transverse vibration calculation of large-span pipe conveying fluid, which limits its further application. The global transfer matrix method (GTMM) based on the subunit division criterion obtained from the dimensionless results, the hybrid energy transfer matrix method (HETMM) and the transfer matrix method combined with the variable precision algorithm—transfer matrix method (VPA-TMM) can solve this problem. Among these three methods, the GTMM is the most commonly used method to improve the stability of the TMM; the HETMM is extend from the calculation of wave propagation in layered media to the vibration analysis of pipeline system for the first time, the dimension and form of the HETMM calculation matrix do not change with the number of subunits, and the calculation time is the shortest; the VPA-TMM does not require subunit division, it can be seen as a solution to the TMM long-span high-frequency numerical instability problem from the root, but the computation time will increase significantly.
曹银行1,柳贡民2,胡志1. 传递矩阵法在计算输流管路高频振动时的稳定性改进[J]. 振动与冲击, 2024, 43(2): 138-145.
CAO Yinhang1,LIU Gongmin2,HU Zhi1. Stability improvement of the transfer matrix method when calculating the high requency vibration of a pipeline conveying fluid. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(2): 138-145.
[1] 李帅军. 管路系统流固耦合动力学计算与特性分析[D]. 哈尔滨, 哈尔滨工程大学, 2015.
Li Shuaijun. Dynamic analysis of fluid-structure interaction of pipe systems conveying fluid[D]. Harbin, Harbin Engineering University, 2015 (in Chinese).
[2] You J. H. and Inaba K. Fluid-structure interaction in water-filled thin pipes of anisotropic composite materials[J]. Journal of Fluids and Structures, 2013, 36: 162-173.
[3] Abdelaziz Ghodhbani and Ezzeddine Haj Taïeb. A four-equation friction model for water hammer calculation in quasi-rigid pipelines[J]. International Journal of Pressure Vessels and Piping, 2017, 151:54-62.
[4] Kandil M, Kamel A and El-Sayed M. Analytical and CFD analysis investigation of fluid-structure interaction during water hammer for straight pipe line[J]. International Journal of Pressure Vessels and Piping, 2021, 194: 104528.
[5] Gale J. and Tiselj I. Eight equation model for arbitrary shaped pipe conveying fluid[C]. Proceedings of the International Conference Nuclear Energy for New Europe, Slovenia, September 18-21, 2006.
[6] Guo Q., Zhou J. and Li Y., et al. Fluid-Structure Interaction Response of a Water Conveyance System with a Surge Chamber during Water Hammer[J]. Water, 2020, 12(4): 1025.
[7] Tentarelli S. C. Propagation of noise and vibration in complex hydraulic tubing systems[D]. PhD, Bethlehem, Pennsylvania; Lehigh University, 1990.
[8] Xu Y., Johnston D. N. and Jiao Z., et al. Frequency modelling and solution of fluid–structure interaction in complex pipelines[J]. Journal of Sound and Vibration, 2014, 333(10): 2800-2822.
[9] Guo X., Cao Y. and Ma H., et al. Dynamic analysis of an L-shaped liquid-filled pipe with interval uncertainty[J]. International Journal of Mechanical Sciences, 2022, 217: 107040.
[10] Wiggert D. C. and Tijsseling A. S. Fluid transients and fluid-structure interaction in flexible liquid-filled piping[J]. Applied Mechanics Reviews, 2001, 54(5): 455-481.
[11] Wu J. S. and Shih P. Y. The dynamic analysis of a multi-span fluid-conveying pipe subjected to external load[J]. Journal of Sound and Vibration, 2001, 239(2): 201-215.
[12] De Jong. Analysis of pulsations and vibrations in fluid-filled pipe systems [D]. Eindhoven University of Technology, 1996.
[13] 王泽超. 复杂多跨输流管道振动特性分析及其损伤检测方法研究[D]. 武汉, 武汉理工大学, 2019.
Wang Zechao. The vibration properties analyzation and damage detection for the complex multi-span pipe conveying fluid[D]. Wuhan, Wuhan University of Technology, 2019 (in Chinese).
[14] Horner G C, and Pilkey W D. The Riccati Transfer Matrix Method[J]. Journal of Mechanical Design, 1978, 100(2): 297-302.
[15] Chen Z., Luo Z. and Xiong S. A study of the calculation method of transverse vibration for ship’s shafting system[J]. Shipbuilding of China, 1988, 000(003): 35-45.
[16] Gorman D. G., Reese J. M. and Zhang Y. Vibration of a flexible pipe conveying viscous pulsating fluid flow [J]. Journal of Sound and Vibration, 2000, 230(2): 379-392.
[17] Gao Q. and Zhang Y. Stable and Accurate Computation of Dispersion Relations for Layered Waveguides, Semi-Infinite Spaces and Infinite Spaces [J]. Journal of vibration and acoustics, 2019, 141(3): 031012.1-031012.16.
[18] 张燕辉. 分层介质中弹性波散射和频散的稳定高精度算法[D]. 大连, 大连理工大学,2020.
Zhang Yanhui. Stable high-precision algorithms for scattering and dispersion of elastic waves in layered media [D]. Dalian, Dalian University of Technology, 2020.