Abstract:Here, a pipe axial flow-induced vibration model was built based on Timoshenko beam, and the spectral element method (SEM) was applied in dynamic response analysis of a pipe conveying fluid.By means of discrete Fourier transformation, the pipe’s dynamic equations in time domain were converted into those in frequency domain. Being similar to the finite element method (FEM), the spectral element matrix equation was obtained.Then, the computation method was developed for dynamic response of pipe conveying fluid under point impact loads.The natural frequencies and dynamic responses of the pipe conveying fluid were computed with SEM, and the results were compared with those published in literature to verify the effectiveness of SEM.Finally, the pipe’s dynamic responses were computed using SEM under different fluid flow velocities and transient impact loads.Results showed that the proposed SEM has a high accuracy; only two spectral elements are needed to analyze dynamic responses of a pipe conveying fluid under point impact loads.
李宝辉,景丽娜,王正中. 冲击荷载下输液管道动响应分析的谱单元方法[J]. 振动与冲击, 2020, 39(21): 179-185.
LI Baohui, JING lina, WANG Zhengzhong. Dynamic analysis of pipe conveying fluid under impact load with spectral element method. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(21): 179-185.
[1] Paidoussis M P, Li G. L. Pipes conveying fluid: a model dynamical problem[J]. Journal of Fluids and Structures, 1993, 7: 137-204.
[2] R.D.Firouz-Abadi, M.A. Noorian, H. Haddadpour. A fluid–structure interaction model for stability analysis of shells conveying fluid[J]. Journal of Fluids and Structures, 2010, 26, 747-763.
[3] Lin Wang, Yuanzhuo Hong, Huliang Dai. Natural Frequency and Stability Tuning of Cantilevered CNTs Conveying Fluid in Magnetic Field[J]. Acta Mechanica Solida Sinica, 2016, 29(6), 567-576.
[4] 严浩,熊夫睿,姜乃斌,等. 含非线性能量汇的简支输液管非线性振动控制研究[J]. 固体力学学报, 2019, 40(2): 127-136.
YAN Hao, XIONG Fu-rui, JIANG Nai-bin, et al. Nonlinear Vibration Control of a Simply supported Pipe Conveying Fluid with Nonlinear Energy Sink[J]. Acta Mechanica Solida Sinica, 2019, 40(2): 127-136.
[5] 王琳, 倪樵. 具有非线性运动约束输液曲管振动的分岔[J]. 振动与冲击, 2006, 25(1): 67-69.
WANG Lin, NI Qiao. Vibration bifurcations of a curved pipe conveying fluid with nonlinear constraint[J]. Journal of Vibration and Shock, 2006, 25(1): 67-69.
[6] 唐冶,方勃,张业伟,等. 非线性弹簧支承悬臂输液管道的分岔与混沌分析[J].振动与冲击,2011, 30(8), 269-274.
TANG Ye, FANG Bo, ZHANG Ye-wei, et al. Bifurcation and chaos analysis of cantilever pipeline conveying fluid with nonlinear spring support [J]. Journal of Vibration and Shock, 2011, 30(8), 269-274.
[7] 李云东, 杨翊仁, 文华斌. 非线性弹性地基上悬臂管道的参数振动[J]. 振动与冲击,2016, 35(24), 14-18.
LI Yun-dong, YANG Yi-ren, WEN Hua-bin. Parametric vibration of a cantilevered pipe conveying pulsating fluid on a nonlinear elastic foundation [J]. Journal of Vibration and Shock, 2016, 35(24), 14-18.
[8] 王乙坤, 王琳. 分布式运动约束下悬臂输液管的参数共振研究[J]. 力学学报, 2019, 51(2): 558-568.
WANG Yi-kun, WANG Lin. Parametric resonance of a cantilevered pipe conveying fluid subjected to distributed motion constraints [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(2): 558-568
[9] 金基铎, 杨晓东, 张宇飞. 固定约束松动对输流管道稳定性和临界流速的影响[J]. 振动与冲击, 2009, 28(6): 95-99.
JIN Ji-duo, YANG Xiao-dong, ZHANG Yu-fei. Analysis of critical flow velocities of pipe conveying fluid under relaxation of boundary conditions [J]. Journal of Vibration and Shock, 2009, 28(6): 95-99.
[10] 杨晓东, 金基铎. 输液管道流-固耦合振动的固有频率分析[J]. 振动与冲击, 2008, 27(3): 80-86.
YANG Xiao-dong, JIN Ji-duo. Comparison of Galerkin method and complex mode method in natural frequency analysis of tube conveying fluid[J]. Journal of Vibration and Shock, 2008, 27(3): 80-86.
[11] 杨超, 范士娟. 输液管道流固耦合振动的数值分析[J]. 振动与冲击, 2009, 28(6): 56-59.
YANG Chao, FAN Shi-juan. Numerical analysis of fluid-structure coupled vibration of fluid-conveying pipe[J]. Journal of Vibration and Shock, 2009, 28(6): 56-59.
[12] 齐欢欢, 徐鉴. 输液管道颤振失稳的时滞控制[J]. 振动工程学报, 2009, 26(6): 576-582.
QI Huan-huan, XU Jian. Delayed feedback control for flutter in the pipe conveying fluid[J]. Journal of Vibration Engineering, 2009,26(6): 576-582.
[13] J.F. Doyle, Wave Propagation in Structures: An FFT-Based Spectral Analysis Methodology, Springer, New York, 1989.
[14] Vedula N L. Dynamics and stability of parametrically excited gyroscopic systems[D]. Madras: University of Missouri, 1999.
[15] Win-Jin Chang, Haw-Long Lee. Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model[J]. Physics Letters A, 2009, 373, 982-985.
[16] M. R. Xu, S. P. Xu, H. Y. Guo. Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method[J]. Computers & Mathematics with Applications, 2010, 60, 520-527.
[17] Younghoon Song, Taehyun Kim, Usik Lee. Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis [J]. International Journal of Mechanical Sciences, 2016, 113, 162-174.
[18] J. A. M. Carrer, S. A. Fleischfresser, L. F. T. Garcia. Dynamic analysis of Timoshenko beams by the boundary element method [J]. Engineering Analysis with Boundary Elements, 2013, 37, 1602-1616.