基于分层模型的功能梯度输流管道耦合振动

PDF(1975 KB)

振动与冲击 ›› 2019, Vol. 38 ›› Issue (20) : 203-209.

论文

基于分层模型的功能梯度输流管道耦合振动

朱竑祯 1，王纬波 2，殷学文 2，高存法1

作者信息 +

Coupled vibration of functionally graded pipes conveying fluid based on a multi-layered model

ZHU Hongzhen1,WANG Weibo2,YIN Xuewen2,GAO Cunfa1

Author information +

文章历史 +

摘要

基于Timoshenko梁模型，研究了材料属性沿管道壁厚方向呈梯度变化的输流管道的耦合振动。沿厚度方向将功能梯度材料离散为若干层均质材料；考虑流体在轴向的可压缩性及管壁与流体间的摩擦，通过Hamilton原理及流体动量方程、连续方程建立了功能梯度输流管道的耦合振动模型；采用动刚度法对管道单元进行求解，并通过算例分析了功能梯度材料的梯度指数变化对管道动态特性的影响。

Abstract

The coupled vibration of fluid conveying pipes with gradient material property along the thickness was investigated based on the Timoshenko beam theory.A multi-layered homogeneous model was employed to discretize the functionally graded material(FGM).With the consideration of axial compressibility of fluid and its friction with pipe wall, the coupled equations were established through the Hamilton’s principle, as well as the fluid momentum and continuum equations.The dynamic stiffness method was used to solve the governing equations of the pipe element.Afterwards, the effects of gradient index of FGM on the dynamic characteristics of pipes were discussed.

导出引用

朱竑祯 1，王纬波 2，殷学文 2，高存法1. 基于分层模型的功能梯度输流管道耦合振动[J]. 振动与冲击, 2019, 38(20): 203-209

ZHU Hongzhen1,WANG Weibo2,YIN Xuewen2,GAO Cunfa1. Coupled vibration of functionally graded pipes conveying fluid based on a multi-layered model[J]. Journal of Vibration and Shock, 2019, 38(20): 203-209

参考文献

[1] Koizumi M. FGM activities in Japan[J]. Composites Part B Engineering, 1997, 28(1–2):1-4.
[2] 邢世凯．李聚霞，吴立勋．金属-陶瓷梯度功能材料在内燃机上的应用[J]．机械工程材料，2005，29(5)：6I-63．
XING Shi-kai, LI Ju-xia, WU Li-xun.Application of Metal-ceramic Functionally Gradient Material to Internal Combustion Engines[J]. Materials for mechanical engineering,2005,29(5):61-63.
[3] 刘华炜, 刘学武, 张广文. 功能梯度材料制备工艺及研究进展[J]. 机械设计与制造, 2012,4:265-267.
LIU Hua-wei, LIU Xue-wu, ZHANG Guang-wen. Research progress and preparing technology of functionally graded material[J]. Machinery Design & Manufacture,2012,4: 265-267.
[4] Khan S M , Jordaan M. Assessment of filament-wound glass reinforced plastic(GRP) pipe technology for RAN surface ship application[R]. Australia: Defence Science and Technology Organisation,2003.
[5] Mouritz, A P , Gellert E, Burchill P, et al. Review of advanced composite structures for naval ships and submarines[J]. Composite structures,2001, 53(1):21-42.
[6] Kane C, Dow R. Marine propulsors design in fibre reinforced plastics[J]. Journal of Defense Science, 1994, 4: 301-308.
[7] 李泓运. 复合材料螺旋桨的设计研究[D]. 无锡：中国舰船研究院, 2014.
LI Hong-yun. Design of composite marine propeller[D].Wuxi: China Ship Research and Development Academy,2014.
[8] Searle T , Shot D. Are composite propellers the way forward for small boats[J]. Materials World: The Journal of the Institute of Materials ,1994, 2:69–70.
[9] 孟光，瞿叶高.复合材料结构振动与声学[M].北京：国防工业出版社,2017.
MENG Guang, QU Yegao. Vibration and acoustics of composite structures[M].Beijing: National defense industry press,2017.
[10] Feodos'Ev V P. Vibrations and stability of a pipe when liquid flows through it[J].Inzhenernyi Sbornik, 1951,10:169-170.
[11] Housner G W. Bending vibrations of a pipe line containing flowing fluid[J]. Journal of Applied Mechanics, 1952, 19: 205-208.
[12] Niordson FIN. Vibration of a cylindrical tube containing flowing fluid[J]. Trans.roy.inst.tech.stockholm, 1953,3(73).
[13] Caf J D. Analysis of pulsations and vibrations in fluid-filled pipe systems[D]. Eindhoven: Eindhoven University of Technology,1994.
[14] Williams D J . Water hammer in non-rigid pipes: precursor waves and mechanical damping[J].Journal of Mechanical Engineering Science, 1977,19(6):237–242.
[15] Walker J S, Phillips J W. Pulse propagation in fluid tubes[J]. Journal of Applied Mechanics , 1977,99:31–35.
[16] Wiggert D C, Hatfield F J, Stuckenbruck S. Analysis of liquid and structural transients in piping by the method of characteristics[J].Journal of Fluids Engineering, 1987, 109(2): 161–165.
[17] Lesmez M W, Wiggert D C, Hatfield F J. Modal analysis of vibrations in liquid-filled piping systems[J]. Journal of Fluids Engineering,1990,109(3):311–318.
[18] Lee U, Pak C H, Hong S C. The dynamics of a piping system with internal unsteady flow[J]. Journal of Sound & Vibration, 1995, 180(2):297–311.
[19] Gorman D G, Reese J M, Zhang Y L. Vibration of a flexible pipe conveying viscous pulsating fluid flow[J]. Journal of Sound and Vibration, 2000,230(2):379–92.
[20] 于涛, 仲政. 均布荷载作用下功能梯度悬臂梁弯曲问题的解析解[J]. 固体力学学报, 2006, 27(1):15-20.
YU Tao, ZHONG Zheng. A general solution of a clamped functionally graded cantilever-beam under uniform loading[J]. Acta mechanica solida sinica, 2006, 27(1):15-20.
[21] Ke L L, Yang J. Flexural Vibration and Elastic Buckling of a Cracked Timoshenko Beam Made of Functionally Graded Materials[J]. Mechanics of Advanced Materials & Structures, 2009, 16(6):488-502.
[22] Kang Y A, Li X F. Bending of functionally graded cantilever beam with power-law non-linearity subjected to an end force[J]. International Journal of Non-Linear Mechanics, 2009, 44(6):696-703.
[23] Reddy J N, Wang C M, Kitipornchai S. Axisymmetric bending of functionally graded circular and annular plates[J]. European Journal of Mechanics - A/Solids, 1999, 18(2):185-199.
[24] Wu L. Thermal buckling of a simply supported moderately thick rectangular FGM plate[J]. Composite Structures, 2004, 64(2):211-218.
[25] Ebrahimi F, Rastgo A. An analytical study on the free vibration of smart circular thin FGM plate based on classical plate theory[J]. Steel Construction, 2009, 46(12):1402-1408.
[26] Sheng G G, Wang X. Thermomechanical vibration analysis of a functionally graded shell with flowing fluid[J]. European Journal of Mechanics - A/Solids, 2008, 27(6): 1075-1087.
[27] Setoodeh A R, Afrahim S. Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory[J]. Composite Structures, 2014, 116(1): 128-135.
[28] Deng J, Liu Y, Zhang Z, et al. Dynamic behaviors of multi-span viscoelastic functionally graded material pipe conveying fluid[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2016, 231(17): 3181-3192.
[29] Wang Z M, Liu Y Z. Transverse vibration of pipe conveying fluid made of functionally graded materials using a symplectic method[J]. Nuclear Engineering and Design, 2016, 298: 149-159.
[30] Chen A, Su J. Dynamic behavior of axially functionally graded pipes conveying fluid[J]. Mathematical Problems in Engineering, 2017, 1: 1-11.
[31] Deng J, Liu Y, Liu W. A hybrid method for transverse vibration of multi-span functionally graded material pipes conveying fluid with various volume fraction laws[J]. International Journal of Applied Mechanics, 2017, 9(7): 1750095.
[32] Rastgoo M, Fazelzadeh S A, Eftekhari M, et al. Flow-induced flutter instability of functionally graded cantilever pipe[J]. The International Journal of Acoustics and Vibration, 2017, 22(3):320-325.
[33] Tang Y, Yang T. Bi-directional functionally graded nanotubes: fluid conveying dynamics[J]. International Journal of Applied Mechanics,2018,10(4):1850041.
[34] Zhou, X. w., H.L. Dai, and L. Wang, Dynamics of axially functionally graded cantilevered pipes conveying fluid[J]. Composite Structures, 2018,190: 112-118.
[35] 刘辰. 功能梯度输流管的振动和失稳分析[D]. 北京：北京交通大学, 2012.
LIU Chen. Flow-induced vibration and instability analysis of functionally graded pipes[D].Beijing: Beijing Jiaotong University,2012.
[36] Nefovska-Danilovic M, Petronijevic M. In-plane free vibration and response analysis of isotropic rectangular plates using the dynamic stiffness method[J].Computers and Structures,2015,152: 82-95.
[37] Tanigawa Y, Akai T, Kawamura R, et al. Transient heat conduction and thermal stress problems of a non- homogeneous plate with temperature dependent material properties[J]. Journal of Thermal Stresses,1996, 19 (1):77–102.
[38] Fan J R, Zhang J Y. Analytical solution for thick, doubly curved, laminated shells[J]. Journal of Engineering Mechanics, 1992,118(7):1338-1356.
[39] Taigawa Y. Some basic thermoelestic problems for nonhomogeneous structural materials[J].Applied Mechanics Reviews,1995,48(6):287-300.
[40] 边祖光，陈伟球，丁皓江.正交各向异性功能梯度圆柱壳的自由振动[J].应用力学学报,2004,21(3):75-78.
BIAN Zuguang, CHEN Weiqiu, DING Haojiang.Free vibration of orthotropic functionally graded cylindrical shells[J].Chinese Journal of Applied Mechanics,2004,21(3):75-78.
[41] White F M. Fluid mechanics[M].Boston: McGraw-Hill,2005.
[42] Wylie E B, Streeter V L . Fluid Transients in Systems[M]. USA: Prentice-Hall, 1993.
[43] Lee U, Kim J. Dynamics of branched pipeline systems conveying internal unsteady flow[J].Journal of Vibration and Acoustics,1999,121(1):114-122.
[44] Lee U. Spectral element method in structural dynamics[M]. Singapore: John Wiley &Sons(Asia),2009.