In this paper, the stability of a periodic cantilevered pipe conveying fluid is studied theoretically by means of a novel transfer matrix method. This method is first validated by comparing the results to those available in the literature for a uniform pipe, showing that it is capable of high accuracy and displaying good convergence characteristics. Then, the stability of periodic pipes is investigated, with geometric, material-properties periodicity, and a combination of the two, showing that a considerable stabilizing effect may be achieved over different ranges of the mass parameter β (, where mf and mp are the fluid and pipe masses per unit length). The effect of other different system parameters is also probed.
Issue Section:
Research Papers
References
1.
Chen
, S. S.
, 1987
, Flow-Induced Vibration of Circular Cylindrical Structures
, Hemisphere
, Washington, DC
.2.
Païdoussis
, M. P.
, and Li
, G. X.
, 1993
, “Pipes Conveying Fluid: A Model Dynamical Problem
,” J. Fluids Struct.
, 7
(2
), pp. 137
–204
.10.1006/jfls.1993.10113.
Païdoussis
, M. P.
, 1998
, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol. 1, Academic
, London
.4.
Païdoussis
, M. P.
, 2004
, Fluid-Structure Interactions: Slender Structures and Axial Flow
, Vol. 2, Elsevier
, London
.5.
Païdoussis
, M. P.
, 2008
, “The Canonical Problem of the Fluid-Conveying Pipe and Radiation of the Knowledge Gained to Other Dynamics Problems Across Applied Mechanics
,” J. Sound Vib.
, 310
(3
), pp. 462
–492
.10.1016/j.jsv.2007.03.0656.
Païdoussis
, M. P.
, 1993
, “Some Curiosity-Driven Research in Fluid Structure Interactions and Its Current Applications
,” ASME J. Pressure Vessel Technol.
, 115
, pp. 2
–14
.10.1115/1.29294917.
Païdoussis
, M. P.
, 2010
, “The Dynamics of Cylindrical Conduits Containing Flowing Fluid
,” 10th International Conference on Computational Structures Technology and 7th International Conference on Engineering Computational Technology, Valencia, Spain, September 14–17
, B. H. V.
Topping
, J. M.
Adam
, F. J.
Pallarés
, R.
Bru
, and M. L.
Romero
, eds., Civil-Comp Press
, Stirlingshire, UK
.8.
Gregory
, R. W.
, and Païdoussis
, M. P.
, 1966
, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. I. Theory
,” Proc. R. Soc. London, Ser. A
, 293
(1435
), pp. 512
–527
.10.1098/rspa.1966.01879.
Gregory
, R. W.
, and Païdoussis
, M. P.
, 1966
, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. II. Experiments
,” Proc. R. Soc. London, Ser. A.
, 293
(1435
), pp. 528
–542
.10.1098/rspa.1966.018810.
Guo
, C. Q.
, Zhang
, C. H.
, and Païdoussis
, M. P.
, 2010
, “Modification of Equation of Motion of Fluid-Conveying Pipe for Laminar and Turbulent Flow Profiles
,” J. Fluids Struct.
, 26
(5
), pp. 793
–803
.10.1016/j.jfluidstructs.2010.04.00511.
Giacobbi
, D. B.
, Rinaldi
, S.
, Semler
, C.
, and Païdoussis
, M. P.
, 2012
, “The Dynamics of a Cantilevered Pipe Aspirating Fluid Studied by Experimental, Numerical and Analytical Methods
,” J. Fluids Struct.
, 30
, pp. 73
–96
.10.1016/j.jfluidstructs.2011.11.01112.
Ghayesh
, M. H.
, Païdoussis
, M. P.
, and Modarres-Sadeghi
, Y.
, 2011
, “Three-Dimensional Dynamics of a Fluid-Conveying Cantilevered Pipe Fitted With an Additional Spring-Support and an End-Mass
,” J. Sound Vib.
, 330
(12
), pp. 2869
–2899
.10.1016/j.jsv.2010.12.02313.
Vassilev
, V. M.
, and Djondjorov
, P. A.
, 2006
, “Dynamic Stability of Viscoelastic Pipes on Elastic Foundations of Variable Modulus
,” J. Sound Vib.
, 297
(1
), pp. 414
–419
.10.1016/j.jsv.2006.03.02514.
Doaré
, O.
, and de Langre
, E.
, 2002
, “Local and Global Instability of Fluid-Conveying Pipes on Elastic Foundations
,” J. Fluids Struct.
, 16
(1
), pp. 1
–14
.10.1006/jfls.2001.040515.
Doaré
, O.
, 2010
, “Dissipation Effect on Local and Global Stability of Fluid-Conveying Pipes
,” J. Sound Vib.
, 329
(1
), pp. 72
–83
.10.1016/j.jsv.2009.08.02916.
Mead
, D. J.
, 1996
, “Wave Propagation in Continuous Periodic Structures: Research Contributions From Southampton, 1964–1995
,” J. Sound Vib.
, 190
(3
), pp. 495
–524
.10.1006/jsvi.1996.007617.
Aldraihem
, O. J.
, and Baz
, A.
, 2002
, “Dynamic Stability of Stepped Beams Under Moving Loads
,” J. Sound Vib.
, 250
(5
), pp. 835
–848
.10.1006/jsvi.2001.397618.
Aldraihem
, O. J.
, and Baz
, A. M.
, 2004
, “Moving-Loads-Induced Instability in Stepped Tubes
,” J. Vibr. Control
, 10
(1
), pp. 3
–23
.10.1177/10775460477368487619.
Ruzzene
, M.
, and Baz
, A.
, 2006
, “Dynamic Stability of Periodic Shells With Moving Loads
,” J. Sound Vib.
, 296
(296
), pp. 830
–844
.10.1016/j.jsv.2006.03.00820.
Shen
, H. J.
, Wen
, J. H.
, Yu
, D. L.
, and Wen
, X. S.
, 2009
, “The Vibrational Properties of a Periodic Composite Pipe in 3D Space
,” J. Sound Vib.
, 328
(1–2
), pp. 57
–70
.10.1016/j.jsv.2009.07.03221.
Yu
, D. L.
, Wen
, J. H.
, Zhao
, H. G.
, Liu
, Y. Z.
, and Wen
, X. S.
, 2008
, “Vibration Reduction by Using the Idea of Phononic Crystals in a Pipe-Conveying Fluid
,” J. Sound Vib.
, 318
(1–2
), pp. 193
–205
.10.1016/j.jsv.2008.04.00922.
Sorokin
, S.
, 2012
, “On Power Flow Suppression in Straight Elastic Pipes by Use of Equally Spaced Eccentric Inertial Attachments
,” ASME J. Vibr. Acoust.
, 134
, p. 041003
.10.1115/1.400565223.
Wen
, J. H.
, Shen
, H. J.
, Yu
, D. L.
, and Wen
, X. S.
, 2010
, “Theoretical and Experimental Investigation of Flexural Wave Propagating in a Periodic Pipe With Fluid-Filled Loading
,” Chin. Phys. Lett.
, 27
(11
), p. 114301
.10.1088/0256-307X/27/11/11430124.
Yu
, D. L.
, Wen
, J. H.
, Zhao
, H. G.
, Liu
, Y. Z.
, and Wen
, X. S.
, 2011
, “Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory
,” ASME J. Vibr. Acoust.
, 133
(1
), p. 014502
.10.1115/1.400118325.
Marzani
, A.
, Mazzotti
, M.
, Viola
, E.
, Vittori
, P.
, and Elishakoff
, I.
, 2012
, “FEM Formulation for Dynamic Instability of Fluid-Conveying Pipe on Nonuniform Elastic Foundation
,” Mech. Based Des. Struct. Mach.
, 40
(1
), pp. 83
–95
.10.1080/15397734.2011.61844326.
Huang
, Y.
, Zeng
, G.
, and Wei
, F.
, 2002
, “A New Matrix Method for Solving Vibration and Stability of Curved Pipes Conveying Fluid
,” J. Sound Vib.
, 251
(2
), pp. 215
–225
.10.1006/jsvi.2001.398327.
Ma
, X. Q.
, Xiang
, Y.
, and Huang
, Y. Y.
, 2004
, “A Transfer Matrix Method for Solving Stability of Pipes Conveying Fluid on Elastic Foundation With Various End Supports
,” Eng. Mech.
, 21
(4
), pp. 194
–198
(in Chinese).28.
Ryu
, S. U.
, Sugiyama
, Y.
, and Ryu
, B. J.
, 2002
, “Eigenvalue Branches and Modes for Flutter of Cantilevered Pipes Conveying Fluid
,” Comput. Struct.
, 80
(14
), pp. 1231
–1241
.10.1016/S0045-7949(02)00083-4Copyright © 2014 by ASME
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