功能梯度输流管的非线性自由振动分析

摘要
图/表
参考文献(26)
相关文章 (15)

全文: PDF (1722 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要应用一个适用于管的高阶梁模型，分析并计算了功能梯度管在内流作用下的自由振动问题，该模型能够满足管内外表面剪应力为零的边界条件。基于该模型和哈密顿原理，得出了管道振动的控制方程。然后利用Galerkin方法将非线性偏微分控制方程离散，保留一阶振型，采用多尺度法得到了管道振动的自然频率和非线性频率的解析表达式。最后数值计算验证了方法的正确性，并且分析了内流流速、管厚和功能梯度参数等对管道振动频率的影响。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章

关键词 ：功能梯度管道, 内流, 非线性振动

Abstract：A higherorder beam model for tubes which can satisfy the shear stress boundary conditions on the inner and outer surfaces was applied to do the dynamic analysis of FG (functionally graded) tubes conveying fluid. By the model and according to the Hamilton’s principle, the governing equations were derived. By reserving the first order mode shape and using the multiscale method, the natural frequency and the nonlinear frequency were obtained. Numerical simulations justified the correctness of these results. Discussion on the relationship between the frequencies and the fluid’s velocity, the tube’s thickness, and the FG tube’s parameters were also performed.

Key words： functionally graded tubes inner fluid nonlinear vibration

收稿日期: 2017-01-20 出版日期: 2018-07-15

引用本文:

朱晨光徐思朋. 功能梯度输流管的非线性自由振动分析[J]. 振动与冲击, 2018, 37(14): 195-201.
ZHU Chenguang,XU Sipeng. Nonlinear free vibration analysis of FG tubes conveying fluid. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(14): 195-201.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2018/V37/I14/195

[1] Jing LL, Ming PJ, Zhang WP, et al. Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method[J]. Composite Structures, 2016, 138: 192-213.
[2] Şimşek M. Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions[J]. Composite Structures, 2015, 133: 968-978.
[3] Ebrahimi F, Zia M. Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities[J]. ActaAstronautica, 2015, 116: 117-125.
[4] Su H, Banerjee J R. Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams[J]. Computers & Structures,2015, 147: 107-116.
[5] Zhang LW, Song ZG, Liew K M. Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method[J]. Composite Structures, 2015, 128: 165-175.
[6] Zhang B, He YM, Liu DB, et al. Free vibration analysis of four-unknown shear deformable functionally graded cylindrical microshells based on the strain gradient elasticity theory[J]. Composite Structures, 2015, 119: 578–597.
[7] Zhang P, Fu YM. A higher-order beam model for tubes[J]. European Journal of Mechanics - A/Solids, 2013, 38: 12–19.
[8] Fu YM, Zhong J, Shao X F, et al. Thermal postbuckling analysis of functionally graded tubes based on a refined beam model[J]. International Journal of Mechanical Sciences, 2015, 96–97: 58-64.
[9] YangTZ, Ji S, Yang XD, et al. Microfluid-induced nonlinear free vibration of microtubes[J]. International Journal of Engineering Science, 2014, 76: 47-55.
[10] Hu K, Wang Y K, Dai H L, et al. Nonlinear and chaotic vibrations of cantilevered micropipes conveying fluid based on modified couple stress theory[J]. International Journal of Engineering Science, 2016, 105: 93-107.
[11] Yin L, Qian Q, Wang L. Strain gradient beam model for dynamics of microscale pipes conveying fluid[J]. Applied Mathematical Modelling,2011, 35: 2864-2873.
[12] 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 Y D, Yang Y R, Wen H B. 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.
[13] 孟丹, 郭海燕, 徐思朋. 输流管道的流体诱发振动稳定性分析[J]. 振动与冲击, 2010, 29(6): 80-84.
Meng D, Guo H Y, Xu S P. Stability analysis on flow-induced vibration of fluid-conveying pipes [J]. Journal of Vibration and Shock, 2010, 29(6): 80-84.
[14] Sheng G G, Wang X. Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads[J]. Composite Structures, 2010, 93: 162–170.
[15] An C, Su J. Dynamic behavior of axially functionally graded pipes conveying fluid[J]. Mathematical Problems in Engineering, 2017, 2017, Article ID 6789634, 11 pages.
[16] Liang F, Yang X D, Bao R D, et al. Frequency analysis of functionally graded curved pipes conveying fluid [J]. Advances in Materials Science and Engineering, 2016, 2016, Article ID 7574216, 9 pages.
[17] Paidoussis M P. Fluid-structure interactions. Volume 1: slender structures and axial flow[M], Second Edition. Cambridge University Press, 2014. 285-287.
[18] REDDY J N, WANG C M. Dynamics of fluid-conveying beams[M]. CORE Report No. 2004-03, National University of Singapore, 2004.1-6.
[19] Setoodeh A R, Afrahim S. Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory[J]. Composite Structures, 2014, 116: 128-135.
[20] Zhong J, Fu Y M, Wan D T, et al. Nonlinear bending and vibration of functionally graded tubes resting on elastic foundations in thermal environment based on a refined beam model[J].Applied Mathematical Modelling, 2016, 40: 7601-7614.
[21] Wang B, Deng Z C, Ouyang H J, et al. Free vibration of wavy single-walled fluid-conveying carbon nanotubes in multi-physics fields[J]. Applied Mathematical Modelling, 2015, 39: 6780-6792.
[22] Chen L Q, Tang Y Q, Lim C W. Dynamic stability in parametric resonance of axially accelerating viscoelastic Timoshenko beams[J]. Journal of Sound and Vibration, 2009, 329: 547-565.
[23] Xu M R, Xu S P, Guo H Y. Determination of natural frequencies of fluid-conveying pipes using homotopy perturbation method[J]. Computers and Mathematics with Applications, 2010, 60: 520-527.
[24] 刘延柱, 陈立群. 非线性振动[M]. 北京: 高等教育出版社, 2001. 83-95.
[25] Yas MH, Samadi N. Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation[J]. International Journal of Pressure Vessels and Piping, 2012, 98: 119-128.
[26] Fathi N. Mayoof, Muhammad A. Hawwa. Chaotic behavior of a curved carbon nanotube under harmonic excitation[J]. Chaos, Solitons & Fractals, 2009, 42(3): 1860-1867.