Thermo-Elastic Vibration Analysis of Functionally Graded Material Pipes in Elastic Matrix
-
摘要: 为了研究嵌入弹性基体功能梯度输流管的流固耦合振动问题，首先根据欧拉梁模型理论推导得到功能梯度输流管道的振动控制方程，然后采用微分求积法对振动控制方程进行求解，最后根据计算结果详细讨论了材料组分的体积分数、温度、长细比及弹性基体的弹性系数对系统的固有频率及临界流速的影响. 研究结果表明：（1） 内部材料组分的体积分数增大会使系统的无量纲固有频率增大，临界流速减小（指数n由0增大到10，流速为0时的固有频率增大约13%，临界流速减小约6%）；（2） 随着温度的升高，系统的固有频率和其临界流速都会降低（长径比为100时，温度升高30 K，流速为0时的固有频率减小约4%，临界流速减小约14%），减小长径比会使得系统的固有频率明显下降（长径比为100、50和20时，系统的固有频率分别为160、41.1和11.87.）；（3） 系统的固有频率随着管道外径的增大而降低，管壁越薄变化越快，管壁越厚变化越慢（外径由0.1 m增大到0.11 m时，其固有频率的下降幅度约为外径由0.19 m增大到0.2 m时的100倍）；（4） 弹性基体弹性系数k增大会提高系统的固有频率（k增大3倍，系统的固有频率提高了约74%）.Abstract: In order to investigate the fluid-structure coupled vibration problems of functionally graded material (FGM) fluid conveying pipes embedded in elastic matrix. Firstly, the vibration control equation of the FGM pipe was derived according to Euler-beam model theory. Then, the differential quadrature method was used to solve the vibration control equation. Finally, the influence of the volume fraction of the material component, temperature, slenderness ratio and elastic coefficient of elastic matrix on natural frequency and critical velocity of the system was discussed according to the calculated results.The following conclusions are obtained: (1) The increase of the volume fraction of the internal material components will lead to the dimensionless natural frequency of the system increase and the critical velocity decrease (exponential n increases from 0 to 10, the natural frequency increases by about 13% and the critical velocity decreases by about 6% when the flow velocity is 0). (2) With the increase of temperature, the natural frequency and the critical velocity of the system will decrease (when the length-diameter ratio is 100, the temperature increases by 30 K, the natural frequency decreases by about 4% wand the critical velocity decreases by about 14% hen the flow rate is 0). The natural frequency of the system decrease obviously when the slenderness ratio decreases (when the length-diameter ratio is 100, 50 and 20, the natural frequencies of the system are 160, 41.1 and 11.87, respectively). (3) The natural frequency of the system decreases with the increase of the external radius, the thinner the tube wall the faster it changes, the thicker the tube wall the slower it changes (the decrease of natural frequency caused by the increase of outer diameter from 0.1 m to 0.11 m is about 100 times that from 0.19 m to 0.2 m). (4) The increase of the elastic coefficient k will improve the natural frequency of the system (the natural frequency of the system increased by about 74% when k increases by three times).
-
图 1 功能梯度输流管分析模型
Figure 1. Analysis model of functionally graded material fluid conveying pipes
图 4 长细比不同对应的无量纲临界固有频率关于流速的变化
Figure 4. Dimensionless vibration frequency corresponding to different slenderness ratio vary with the velocity
图 5 无量纲固有频率随管道外部半径变化情况
Figure 5. Dimensionless vibration frequency vary with outer radius
-
仲政,吴林志,陈伟球. 功能梯度材料与结构的若干力学问题研究进展[J]. 力学进展,2010,40(5): 528-541.ZHONG Zheng, WU Linzhi, CHEN Weiqiu. Progress in the study on mechanics problems of functionally graded materials and structures[J]. Advances in Mechanics, 2010, 40(5): 528-541. 邸克,杨月诚. 功能梯度界面层模型断裂问题研究进展[J]. 兵器装备工程学报,2012,33(10): 116-119. doi: 10.11809/j.issn.1006-0707.2012.10.040DI Ke, YANG Yuecheng. Research progress on fracture of functional gradient interface layer model[J]. Journal of Sichuan Ordnance, 2012, 33(10): 116-119. doi: 10.11809/j.issn.1006-0707.2012.10.040 王琳,匡友弟,黄玉盈,等. 输液管振动与稳定性研究的新进展:从宏观尺度到微纳米尺度[J]. 固体力学学报,2010,31(5): 481-495.WANG Lin, KUANG Youdi, HUANG Yuying, et al. Recent development on vibration and stability of pipes conveying fluid:from macro-scale to micro-and nano-scales[J]. Chinese Journal of Solid Mechanics, 2010, 31(5): 481-495. 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): 14-19.LI Yundong, YANG Yiren, WEN Huabin. Parametric vibration of a cantilevered pipe conveying pulsating fluid on a nonlinear elastic foundation[J]. Journal of Vibration and Shock, 2016, 35(24): 14-19. YANG T Z, YANG X D, LIU Y H, et al. Passive and adaptive vibration suppression of pipes conveying fluid with variable velocity[J]. Journal of Vibration and Control, 2013, 20(9): 1293-1300. XU Y Z, JIAO Z X. Exact solution of axial liquid-pipe vibration with time-line interpolation[J]. Journal of Fluids and Structures, 2017, 70: 500-518. doi: 10.1016/j.jfluidstructs.2016.12.011 段伦良,郑东生,张启博,等. 半埋式海底管道周围海床瞬态液化稳定性研[J]. 西南交通大学学报,2017,52(4): 671-677. doi: 10.3969/j.issn.0258-2724.2017.04.004DUAN Lunliang, ZHENG Dongsheng, ZHANG Qibo, et al. Numerical study on wave-induced oscillatory soil liquefaction around a partially buried pipeline[J]. Journal of Southwest Jiaotong University, 2017, 52(4): 671-677. doi: 10.3969/j.issn.0258-2724.2017.04.004 郑爽英,杨立忠. 隧道爆破地震下输气管道动力响应数值试验[J]. 西南交通大学学报,2017,52(2): 264-271. doi: 10.3969/j.issn.0258-2724.2017.02.008ZHENG Shuangying, YANG Lizhong. Numerical experiments of dynamic response of buried gas pipeline under the action of seismic waves induced by tunnel blasting[J]. Journal of Southwest Jiaotong University, 2017, 52(2): 264-271. doi: 10.3969/j.issn.0258-2724.2017.02.008 黄茜,臧峰刚,张毅雄. 带滞变支撑悬臂输流管的稳定性[J]. 西南交通大学学报,2011,46(5): 841-846. doi: 10.3969/j.issn.0258-2724.2011.05.022HUANG Qian, ZANG Fenggang, ZHANG Yixiong. Stability analysis of cantilevered pipes conveying fluid with hysteretic supports[J]. Journal of Southwest Jiaotong University, 2011, 46(5): 841-846. doi: 10.3969/j.issn.0258-2724.2011.05.022 LI Y S, ZHANG Z J, LI B H. Dynamic stiffness method for free vibration analysis of variable diameter pipe conveying fluid[J]. Journal of Vibroengineering, 2014, 16(2): 832-845. 赵千里,孙志礼,柴小冬,等. 具有弹性支承输流管路的强迫振动分析[J]. 机械工程学报,2017,53(12): 186-191. doi: 10.3901/JME.2017.12.186ZHAO Qianli, SUN Zhili, CHAI Xiaodong, et al. Forced vibration analysis of fluid-conveying pipe with elastic supports[J]. Journal of Mechanical Engineering, 2017, 53(12): 186-191. doi: 10.3901/JME.2017.12.186 LI B H, GAO H S, LI Y S, et al. Transient response analysis of multi-span pipe conveying fluid[J]. Journal of Vibration and Control, 2013, 19(14): 2164-2176. doi: 10.1177/1077546312455836 DENG J Q, LI Y S, ZHANG Z J, et al. Stability analysis of multi-span viscoelastic functionally graded material pipes conveying fluid using a hybrid method[J]. European Journal of Mechanics A/Solids, 2017, 65: 257-270. doi: 10.1016/j.euromechsol.2017.04.003 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. doi: 10.1016/j.nucengdes.2015.12.007 SHEN H J, MICHAEL P, PAIDOUSSI S, et al. The beam-mode stability of periodic functionally-graded-material shells conveying fluid[J]. Journal of Sound and Vibration, 2014, 333(10): 2735-2749. doi: 10.1016/j.jsv.2014.01.002 LIU 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: 1-9. ANSARI R, GHOLAMI R, NOROUZZADEH A, et al. Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory[J]. Microfluidics and Nanofluidics, 2015, 19(3): 509-522. doi: 10.1007/s10404-015-1577-1 SETOODEH A R, AFAHIM S. Nonlinear dynamic analysis of FG micro-pipes conveying fluid based on strain gradient theory[J]. Composite Structures, 2014, 116(1): 128-135. FUNG T C. Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method[J]. International Journal of Numerical Mathematic Engineering, 2003, 56(3): 405-432. doi: 10.1002/nme.571 -
下载:
点击查看大图
图(6)
计量
- 文章访问数: 587
- HTML全文浏览量: 279
- PDF下载量: 9
- 被引次数: 0