航空管路系统布局形式复杂多变,如“L”形管路、“U”形管路、“Z”形管路等,这些管路布局中均包含“直管—曲管”这一典型管道基本元件。对此,文中提出“直管—曲管”组集(直曲组集)算法,实现复杂管路的高效建模和模态分析。分别从直管单元与曲管单元的三维振动控制方程出发,基于频散关系,推导了管道单元自由振动的离散模式和动力刚度矩阵。然后在全局坐标系下实现直曲组集,建立了管路系统动力刚度矩阵和特征方程。最后,对所提算法进行了验证,并采用该法分析了管路布局对“Z”形管固有频率的影响规律,建立了经验公式。通过试验发现,公式与试验结果基本相符,对比误差在5%以内,说明在误差许可范围内,所拟公式可用于“Z”形管设计。
Abstract
The geometry of air pipeline system is generally complicated, such as, L-shaped, U-shaped, Z-shaped configurations and so on, but they contain a typical pipeline basic element of “straight pipe-curved pipe”. Here, an algorithm based on straight-curved assembly pipeline was proposed to realize more efficient modeling and modal analysis of complex pipeline systems. Starting from 3-D vibration governing equations of a straight pipe element and a curved one, respectively, discrete modes and dynamic stiffness matrices of pipe elements were derived based on frequency dispersion relation. Then all straight pipe elements and curved ones were assembled under a global coordinate system, the whole pipeline system’s dynamic stiffness matrix and characteristic equation were established. Finally, the proposed algorithm was validated. This method was used to analyze the influence law of piping layout on natural frequencies of Z-shaped pipes and deduce the empirical formula. Tests showed that the results of the empirical formula agree well with those of tests, their error is less than 5%,, so the empirical formula can be used to design Z-shaped pipes within an allowable error range.
关键词
管道组集 /
动力刚度矩阵 /
固有频率
{{custom_keyword}} /
Key words
pipeline assembly /
dynamic stiffness matrix /
natural frequency
{{custom_keyword}} /
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] PAISOUSSIS M P, LI G X. Pipes Conveying Fluid: A Model Dynamical Problem[J]. Journal of Fluids & Structures, 1993, 7(2):137-204.
[2] HOUSNER G W. Bending vibration of a pipe line containing flowing fluid[J]. Journal of Applied Mechanics, 1952, 19(3):205-208.
[3] CHEN S S. Vibration and Stability of a Uniformly Curved Tube Conveying Fluid[J]. Journal of Acoustic Society of America, 1972, 51(1B):223–232.
[4] CHEN S S. Flow induced in-plane instabilities of curved pipes[J]. Nuclear Engineering and Design, 1972, 23(1): 29-38.
[5] MISRA A K, PAIDOUSSIS M P, VAN K S. On the dynamics of curved pipes transporting fluid. Part I: Inextensible theory[J]. Journal of Fluids and Structures, 1988, 2(3): 221-244.
[6] MISRA A K, PAIDOUSSIS M P, VAN K S. On the dynamics of curved pipes transporting fluid. PartII: Extensible theory[J]. Journal of Fluids and Structures, 1988, 2(3):245-261.
[7] YANG Xiaodong, YANG Tianzhi, JIN Jiduo. Dynamic stability of a beam-model viscoelastic pipe for conveying pulsative fluid[J]. Acta Mechanica Solida Sinica, 2007, 20(4):350-356.
[8] QIAN Qin, WANG Lin, NI Qiao. Vibration and stability of vertical upward-fluid-conveying pipe immersed in rigid cylindrical channel[J]. Acta Mechanica Solida Sinica, 2008, 21(5):331-340.
[9] MENG Dan, GUO Haiyan, XU Sipeng. Non-linear dynamic model of a fluid-conveying pipe undergoing overall motions[J]. Applied Mathematical Modelling, 2011, 35(2):781-796.
[10] WANG L, NI Q. A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid[J]. Mechanics Research Communications, 2009, 36(36):833-837.
[11] LIANG Feng, WEN Bangchun. Forced vibrations with internal resonance of a pipe conveying fluid under external periodic excitation[J]. Acta Mechanica Solida Sinica, 2011, 24(6):477-483.
[12] YU Dianlong, WEN Jihong, ZHAO Honggang, et al. Vibration reduction by using the idea of phononic crystals in a pipe-conveying fluid[J]. Journal of Sound and Vibration, 2008, 318(1-2):193-205.
[13] 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 Jiduo, YANG Xiaodong, ZHANG Yufei. Analysis of critical flow velocities of pipe conveying fluid under relaxation of boundary conditions[J]. Journal of Sound and Vibration, 2009, 28(6): 95-99.
[14] JUNG D, CHUNG J. In-plane and out-of-plane motions of an extensible semi-circular pipe conveying fluid[J]. Journal of
Sound & Vibration, 2008, 311(1-2):408-420.
[15] OLSON L G, JAMISON D. Application of a general purpose finite element method to elastic pipes conveying fluid[J]. Journal of Fluids and Structures, 1997, 11(2): 207-222.
[16] TANG Bin. Combined dynamic stiffness matrix and precise time integration method for transient forced vibration response analysis of beams[J]. Journal of sound and vibration, 2008, 309(3):868-876.
[17] VIOLA E, RICCI P, ALIABADI M H. Free vibration analysis of axially loaded cracked Timoshenko beam structures using the dynamic stiffness method[J]. Journal of Sound & Vibration, 2007, 304(1-2):124-153.
[18] 李宝辉, 高行山, 刘永寿等. 输液曲管平面内振动的波动方法研究[J]. 固体力学学报, 2012, 33(3): 1-7.
Li Baohui, Gao Hangshan, Liu Yongshou, et al. In-plane vibration analysis of curved pipe conveying fluid with wave propagation method[J]. Chinese Journal of Solid Mechanics, 2012, 33(3): 1-7.
[19] KOO G H, PARK Y S. Vibration analysis of a 3-dimensional piping system conveying fluid by wave approach[J]. International Journal of Pressure Vessels & Piping, 1996, 67(3):249-256.
[20] KOO G H, YOO B. Dynamic characteristics of KALIMER IHTS hot leg piping system conveying hot liquid sodium[J]. International journal of pressure vessels and piping, 2000, 77(11):679-689.
[21] KOO G H, PARK Y S. Vibration reduction by using periodic supports in a piping system[J]. Journal of Sound & Vibration,1998,210(1):53-68.
[22] DONG M L, CHOI M J, OH T Y. Transfer matrix modelling for the 3-dimensional vibration analysis of piping system containing fluid flow[J]. Journal of Mechanical Science & Technology, 1996, 10(2):180-189.
[23] JUNG D, CHUNG J, MAZZOLENI A. Mazzoleni A. Dynamic stability of a semi-circular pipe conveying harmonically oscillating fluid[J]. Journal of Sound & Vibration, 2008, 315(1):100-117.
[24] ALDRAIHEM O J. Analysis of the dynamic stability of collar-stiffened pipes conveying fluid[J]. Journal of Sound & Vibration, 2007, 300(3–5):453-465.
[25] SHEN H, WEN J, YU D, et al. The vibrational properties of a periodic composite pipe in 3D space[J]. Journal of Sound and Vibration, 2009, 328(1):57-70.
[26] DAI H L, WANG L, QIAN Q, et al. Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method[J]. Applied Mathematics & Computation, 2012, 219(5):2453-2464.
[27] IBRAHIM R A. Overview of Mechanics of Pipes Conveying Fluids—Part I: Fundamental Studies [J]. ASME Journal of Pressure Vessel Technology, 2010, 132(3):1-32.
[28] PAIDOUSSIS M P. Fluid-Structure Interactions: Slender Structures and Axial Flow[M]. 2004.
[29] 包日东, 梁峰. 两端一般支承裂纹管道的动力学特性[J]. 振动与冲击, 2016, 35(7):220-224.
BAO Ridong, LIANG Feng. Dynamic characteristics of a cracked pipe conveying fluid with both elastically supported ends[J]. Journal of Vibration and Shock, 2016, 35(7):220-224.
[30] 梁峰,包日东.微尺度输流管道考虑热效应的流固耦合振动分析[J].振动与冲击,2015,34(5):141-144.
LIANG Feng , BAO Ridong. Fluid-structure interaction of microtubes conveying fluid considering thermal effect[J]. Journal of Vibration and Shock, 2015,34(5):141-144.
[31] 王忠民, 邹德志, 姜全友. 弹性地基上输流管道主参数共振的主动振动控制[J]. 振动与冲击, 2016, 35(4):182-187.
WANG Zhongmin, ZOU Dezhi, JIANG Quanyou. Active vibration control for principal parametric resonance of pipes conveying fluid resting on an elastic foundation[J]. Journal of Vibration and Shock, 2016, 35(4):182-187.
{{custom_fnGroup.title_cn}}
脚注
{{custom_fn.content}}