针对输流管道在恶劣的动力学环境所受到多方向载荷所引起的管道结构失效或破坏等问题，提出一种新型三维功能梯度材料构造输流管道来提升管道的载荷忍耐力。基于 欧拉伯努利梁理论，考虑流体和管道的耦合关系，利用哈密顿变分原理建立复杂约束下三维功能梯度输流管道的运动微分方程。利用微分求积法求解，分析流体流速提升所引起的三维功能梯度输流管道振动的固有频率变化，当第一阶固有频率首次降低为0系统失稳，所对应的流体流速被确定为系统的临界流速。研究复杂约束线性和扭转弹簧刚度、轴向、径向和环向功能梯度指数等物理参数对输流管道振动频率和临界流速的影响。研究结果表明，流速较小时，增加轴向功能梯度指数和降低径向和环向功能梯度指数会降低系统的基频和提高系统的临界流速，而流速较大时，系统的基频随着三维功能梯度指数的变化会展现相反的趋势。增大三维功能梯度指数都能降低系统的第二阶固有频率。这说明通过调节复杂约束和三维功能梯度参数能够实现对输流管道稳定性的调控。
Abstract
Aiming at the failure or damage of the pipeline structure caused by multi-directional loads on the pipe conveying fluid in the harsh dynamic environment, a new type of fluid-conveying pipe composed by three directional functionally graded materials is proposed to improve the load endurance of the pipeline. Based on the Euler-Bernoulli beam theory, considering the coupling relationship between the fluid and the pipeline, Hamilton’s principle is used to establish the differential equation of motion of fluid-conveying pipes composed by three directional functionally graded materials under complex constraints. The differential quadrature method is employed to analyze variations of natural frequency of the fluid-conveying pipes composed by three directional functionally graded materials with the increase of fluid velocity. When the first-order natural frequency decreases to zero for the first time, the system is unstable, and the corresponding fluid velocity is determined to be the critical flow velocity. The effects of physical parameters such as complex constrained linear and torsional spring stiffness, axial, radial and circumferential functional gradient indexes on the vibration frequency and critical velocity of pipe conveying fluid are studied. The research results show that when the flow velocity is small, increasing the axial functional graded index and decreasing the radial and circumferential functional graded indexes will reduce the fundamental frequency of the system and increase the critical flow velocity, when the flow velocity is very large, the fundamental frequency will show the opposite trend with the change of the three-dimensional functional graded indexes. Increasing the three-dimensional functional graded indexes can reduce the second-order natural frequency. This shows that the stability of the pipe conveying fluid can be regulated by tuning the complex constraints and three-dimensional functional graded parameters.
关键词
三维功能梯度管道 /
复杂约束 /
固有频率 /
临界流速
{{custom_keyword}} /
Key words
3D functionally graded pipeline /
complex constraints /
natural frequency /
critical flow velocity
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] Dai H L, Wang L, Ni Q. Dynamics of a fluid-conveying pipe composed of two different materials[J]. International Journal of Engineering Science, 2013, 73: 67-76.
[2] Wang L, Dai H, Ni Q. Mode exchange and unstable modes in the dynamics of conical pipes conveying fluid[J]. Journal of Vibration and Control, 2016, 22(4): 1003-1009.
[3] Yang X, Yang T, Jin J. Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid[J]. Acta Mechanica Solida Sinica, 2007, 20(4): 350-356.
[4] Dai H L, Wang L, Qian Q, et al. Vortex-induced vibrations of pipes conveying pulsating fluid[J]. Ocean Engineering, 2014, 77: 12-22.
[5] Tong G, Liu Y, Cheng Q, et al. Stability analysis of multi-span aluminum-based functionally graded material fluid-conveying pipe reinforced by carbon nanotubes[J]. International Journal of Pressure Vessels and Piping, 2019, 176: 103971.
[6] Wang Z, Wang X, Xu G, et al. Free vibration of two-directional functionally graded beams[J]. Composite structures, 2016, 135: 191-198.
[7] 肖斌,周玉龙,高超,曹贻鹏,石双霞,刘志刚.考虑流体附加质量的输流管道振动特性分析[J].振动与冲击,2021,40(15):182-188.
XIAO Bin, ZHOU Yulong, GAO Chao, CAO Yipeng, SHI Shuangxia, LIU Zhigang. Analysis of vibration characteristics of pipeline with fluid added mass [J]. Journal of Vibration and Shock, 2021, 40(15): 182-188.
[8] 周坤,倪樵,代胡亮,王琳,熊夫睿,姜乃斌.周期性输流管道的非线性动力学特性研究[J].振动与冲击,2020,39(10):75-80.
ZHOU Kun, NI Qiao, DAI Huliang, WANG Lin, XIONG Furui, JIANG Naibin. Analysis of nonlinear dynamic characteristics of periodic pipe conveying fluid [J]. Journal of Vibration and Shock, 2020, 39(10): 75- 80.
[9] 李效民,李胜,顾洪禄,郭海燕.段塞流作用下海底悬跨管道涡激振动特性分析[J].振动与冲击,2022,41(06):37-43+146.
LI Xiaomin, LI Sheng, GU Honglu, GUO Haiyan. Vortex-induced vibrations of a free spanning pipeline with slug flow [J]. Journal of Vibration and Shock, 2022,41(06):37-43+146.
[10] Tang Y, Yang T. Post-buckling behavior and nonlinear vibration analysis of a fluid-conveying pipe composed of functionally graded material[J]. Composite Structures, 2018, 185: 393-400.
[11] 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.
[12] 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.
[13] 朱竑祯,王纬波,殷学文,高存法.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+259.
ZHU Hongzhen, WANG Weibo, YIN Xuewen, GAO Cunfa. 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+259.
[14] 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+247.
ZHU Chenguang, XU Sipeng. Nonlinear free vibration analysis of FG tubes conveying fluid [J]. Journal of Vibration and Shock, 2018,37(14):195-201+247.
[15] Li L, Hu Y. Torsional vibration of bi-directional functionally graded nanotubes based on nonlocal elasticity theory[J]. Composite Structures, 2017, 172: 242-250.
[16] Tang Y, Yang T. Bi-directional functionally graded nanotubes: fluid conveying dynamics[J]. International Journal of Applied Mechanics, 2018, 10(04): 1850041.
[17] Shu C, Chew Y T. On the equivalence of generalized differential quadrature and highest order finite difference scheme[J]. Computer methods in applied mechanics and engineering, 1998, 155(3-4): 249-260.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}
PDF(2817 KB)
