膜与不可压缩有界流体接触时的自由振动

S·泰瑞维蒂洛; J·米尔扎普尔; M·萨马达尼; Gh·瑞扎扎德

doi:10.3879/j.issn.1000-0887.2012.09.006

膜与不可压缩有界流体接触时的自由振动

doi: 10.3879/j.issn.1000-0887.2012.09.006

乌尔米大学工程学院土木工程系,乌尔米耶,伊朗;

详细信息

中图分类号: O322;O353.1
计量
- 文章访问数: 1588
- HTML全文浏览量: 68
- PDF下载量: 800
- 被引次数: 0
出版历程
- 收稿日期: 2011-07-26
- 修回日期: 2012-02-13
- 刊出日期: 2012-09-15

Free Vibration of Membrane/Bounded Incompressible Fluid

¹Department of Civil Engineering, Faculty of Engineering, Urmia University, Urmia, Iran;²Department of Mechanical Engineering, Faculty of Engineering, Urmia University, Urmia, Iran

摘要

摘要: 圆形膜与流体接触时的振动被广泛应用于工业中．推导了圆形膜在与不可压缩有界流体接触时，非对称自由振动的自振频率．鉴于膜在不可压缩、非粘性流体中振动引起的小振幅，采用速度势函数来描述流体场．使用两种方法来推导系统的自由振动频率．它们包括变分法及一种近似解法——Rayleigh商法．在用两种方法求得的自由振动频率值之间具有良好的相关性．最后，研究了流体的深度、质量密度以及径向张力对耦合系统自由振动频率的影响．
- Rayleigh商 /
- 非对称自由振动 /
- 薄膜 /
- 变分法
Abstract: Vibration of circular membrane in contact with fluid had extensive applications in the industry. The natural vibration frequencies for asymmetric free vibration of circular membrane in contact with incompressible bounded fluid were derived. Considering small oscillations induced by the membrane vibration in incompressible and inviscid fluid, velocity potential function was used to describe the fluid field. Two approaches were used to derive the free vibration frequencies of the system. These included a variational formulation and an approximate solution employing the Rayleigh quotient method. Good correlation was found between free vibration frequencies evaluated using the two methods. Finally, the effects of the fluid depth and mass density, and radial tension on the free vibration frequencies of the coupled system were investigated.
- Rayleigh quotient /
- asymmetric free vibration /
- membrane /
- variational formulation

HTML全文

参考文献(16)

[1]	Jenkinsa C H M, Kordeb U A. Membrane vibration experiments: a historical review and recent results[J]. Journal of Sound and Vibration, 2006, 295(3): 602-613.
[2]	Chiba M, Watanabe H, Bauer H F. Hydroelastic coupled vibrations in a cylindrical container with a membrane bottom, containing liquid with surface tension[J]. Journal of Sound and Vibration, 2002, 251(4): 717-740.
[3]	Pan L S, Ng T Y, Liu G R, Lam K Y, Jiang T Y. Analytical solutions for the dynamic analysis of a valveless micropump—a fluid-membrane coupling study[J]. Journal of Sensors and Actuators A: Physical, 2001, 93(2): 173-181.
[4]	Hsieh J -C, Plaut R H, Yucel O. Vibrations of an inextensible cylindrical membrane inflated with liquid[J]. Journal of Fluids and Structures, 1989, 3(2): 151-163.
[5]	Gutierrez R H, Laura P A A, Bambill D V, Jederlinic V A, Hodges D H. Axisymmetric vibrations of solid circular and annular membranes with continuously varying density[J]. Journal of Sound and Vibration, 1998, 212(4): 611-622.
[6]	Crighton D G. The Green function of an infinite, fluid loaded membrane[J]. Journal of Sound and Vibration, 1983, 86(3): 411-433.
[7]	Molki M, Breuer K. Oscillatory motions of a prestrained compliant membrane caused by fluid-membrane interaction[J]. Journal of Fluids and Structures, 2010, 26(3), 339-358.
[8]	Ghavanloo E, Daneshmand F. Analytical analysis of the static interaction of fluid and cylindrical membrane structures[J]. European Journal of Mechanics A/Solids, 2010, 29(4): 600-610.
[9]	Meirovitch L. Principles and Techniques of Vibrations[M]. Prentice-Hall International, 1997: 439-443.
[10]	Isshiki H, Nagata S. Variational principles related to motions of an elastic plate floating on a water surface[C]Proceedings of the Eleventh International Offshore and Polar Engineering Conference, Stavanger, Norway, 2001, 1: 190-197.
[11]	Kwak M K, Amabili M. Hydroelastic vibration of free-edge annular plates[J]. ASME, Journal of Vibration and Acoustics, 1999, 121(1): 26-32.
[12]	Espinosa F M, Gallego-Juarez A G. On the resonance frequencies of water-loaded circular plates[J]. Journal of Sound and Vibration, 1984, 94(2): 217-222.
[13]	Nagia K, Takeuchi J. Vibration of a plate with arbitrary shape in contact with a fluid[J]. Journal of the Acoustical Society of America, 1984, 75(3): 1511-1518.
[14]	Amabili M, Kwak M K. Free vibration of circular plates coupled with liquids: revising the Lamb problem[J]. Journal of Fluids and Structures, 1996, 10(7): 743-761.
[15]	Amabili M. Eigenvalue problems for vibrating structures coupled with quiescent fluids with free surface[J]. Journal of Sound and Vibration, 2000, 231(1): 79-97.
[16]	Amabili M. Ritz method and substructuring in the study of vibration with strong fluid-structure interaction[J]. Journal of Fluid and Structures, 1997, 11(5): 507-523.