In-plane forced vibration of curved pipe conveying fluid by Green function method

doi:10.1007/s10483-017-2246-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (10): 1397-1414.doi: https://doi.org/10.1007/s10483-017-2246-6

In-plane forced vibration of curved pipe conveying fluid by Green function method

Qianli ZHAO, Zhili SUN

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

收稿日期:2016-12-13 修回日期:2017-02-21 出版日期:2017-10-01 发布日期:2017-10-01
通讯作者: Qianli ZHAO E-mail:zql20081841@163.com
基金资助:
Project supported by the National Science and Technology Major Project (NMP) of China (No. 2013ZX04011-011)

In-plane forced vibration of curved pipe conveying fluid by Green function method

Qianli ZHAO, Zhili SUN

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

Received:2016-12-13 Revised:2017-02-21 Online:2017-10-01 Published:2017-10-01
Contact: Qianli ZHAO E-mail:zql20081841@163.com
Supported by:
Project supported by the National Science and Technology Major Project (NMP) of China (No. 2013ZX04011-011)

摘要/Abstract

摘要：

The Green function method (GFM) is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.

关键词: variational principle, shallow shell, large displacement, finite element method, in-plane forced vibration, motion constraint, Green function method(GFM), curved pipe conveying fluid

Abstract:

Key words: variational principle, shallow shell, large displacement, finite element method, curved pipe conveying fluid, in-plane forced vibration, Green function method(GFM), motion constraint

中图分类号:

70J35
74F10

Qianli ZHAO, Zhili SUN. In-plane forced vibration of curved pipe conveying fluid by Green function method[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(10): 1397-1414.

参考文献

[1] Paidoussis, M. P. and Li, G. X. Pipes conveying fluid:a model dynamical problem. Journal of Fluids and Structures, 7, 137-204(1993)
[2] Paidoussis, M. P. The canonical problem of the fluid conveying pipe and radiation of the knowledge gained to other dynamics problems across applied mechanics. Journal of Sound and Vibration, 310, 462-492(2008)
[3] Wang, S. Z., Liu, Y. L., and Huang, W. H. Research on solid-liquid coupling dynamics of pipe conveying fluid. Applied Mathematics and Mechanics (English Edition), 19(11), 1065-1071(1998) DOI 10.1007/BF02459195
[4] Ghavanloo, E., Rafiei, M., and Daneshmand, F. In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium. Physics Letters A, 375, 1994-1999(2011)
[5] Jung, D. H. and Chung, J. T. A steady-state equilibrium configuration in the dynamic analysis of a curved pipe conveying fluid. Journal of Sound and Vibration, 294, 410-417(2006)
[6] Wang, L., Dai, H. L., and Qian, Q. Dynamics of simply supported fluid-conveying pipes with geometric imperfections. Journal of Fluids and Structures, 29, 97-106(2012)
[7] Karami, H. and Farid, M. A new formulation to study in-plane vibration of curved carbon nanotubes conveying viscous fluid. Journal of Vibration and Control, 21, 2360-2371(2015)
[8] Misra, A. K., Paidoussis, M. P., and Van, K. S. On the dynamics of curved pipes transporting fluid, part Ⅱ:extensible theory. Journal of Fluids and Structures, 2, 245-261(1988)
[9] Dai, H. L.,Wang, L., Qian, Q., and Gan, J. Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method. Applied Mathematics and Computation, 219, 2453-2464(2012)
[10] Li, S. J., Liu, G. M., and Kong, W. T. Vibration analysis of pipes conveying fluid by transfer matrix method. Journal of Fluids and Structures, 266, 78-88(2014)
[11] Ni, Q., Zhang, Z. L., and Wang, L. Application of the differential transformation method to vibration analysis of pipes conveying fluid. Applied Mathematics and Computation, 217, 7028- 7038(2011)
[12] Wang, L., Ni, Q., and Huang, Y. Y. Dynamical behaviors of a fluid-conveying curved pipe subjectedto motion constraints and harmonic excitation. Journal of Sound and Vibration, 306, 955-967(2007)
[13] Wang, L. and Ni, Q. In-plane vibration analyses of curved pipes conveying fluid using the generalized differential quadrature rule. Computers and Structures, 86, 133-139(2008)
[14] Foda, M. A. and Abduljabbar, Z. A dynamic Green function formulation for the response of a beam structure to a moving mass. Journal of Sound and Vibration, 210, 295-306(1998)
[15] Abu-Hilal, M. Forced vibration of Euler-Bernoulli beams by means of dynamic Green functions. Journal of Sound and Vibration, 267, 191-207(2003)
[16] Abu-Hilal, M. Dynamic response of a double Euler-Bernoulli beam due to a moving constant load. Journal of Sound and Vibration, 297, 477-491(2006)
[17] Li, X. Y., Zhao, X., and Li, Y. H. Green's functions of the forced vibration of Timoshenko beams with damping effect. Journal of Sound and Vibration, 333, 1781-1795(2014)
[18] Chen, S. S. and Chen, C. K. Application of the differential transformation method to the freevibrations of strongly non-linear oscillators. Nonlinear Analysis:Real World Applications, 10, 881-888(2009)
[19] Yalcin, H. S., Arikoglu, A., and Ibrahim, O. Free vibration analysis of circular plates by differential transformation method. Applied Mathematics and Computation, 212, 377-386(2009)
[20] Mei, C. Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam. Computers and Structures, 86, 1280-1284(2008)
[21] Lee, S. I. and Chung, J. Newnon-linear modeling for vibration analysis of a straight pipe conveying fluid. Journal of Sound and Vibration, 254, 313-325(2002)
[22] Chung, J. and Hulbert, G. M. A time integration algorithm for structural dynamics with improved numerical dissipation:the generalized-α method. Journal of Applied Mechanics, 60, 371-375(1993)

In-plane forced vibration of curved pipe conveying fluid by Green function method

In-plane forced vibration of curved pipe conveying fluid by Green function method

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