Parametric resonance of axially functionally graded pipes conveying pulsating fluid

doi:10.1007/s10483-024-3083-6

摘要/Abstract

Abstract:

Based on the generalized Hamilton's principle, the nonlinear governing equation of an axially functionally graded (AFG) pipe is established. The non-trivial equilibrium configuration is superposed by the modal functions of a simply supported beam. Via the direct multi-scale method, the response and stability boundary to the pulsating fluid velocity are solved analytically and verified by the differential quadrature element method (DQEM). The influence of Young's modulus gradient on the parametric resonance is investigated in the subcritical and supercritical regions. In general, the pipe in the supercritical region is more sensitive to the pulsating excitation. The nonlinearity changes from hard to soft, and the non-trivial equilibrium configuration introduces more frequency components to the vibration. Besides, the increasing Young's modulus gradient improves the critical pulsating flow velocity of the parametric resonance, and further enhances the stability of the system. In addition, when the temperature increases along the axial direction, reducing the gradient parameter can enhance the response asymmetry. This work further complements the theoretical analysis of pipes conveying pulsating fluid.

Key words: pipe conveying fluid, axially functionally graded, supercritical resonance, multi-scale method, parametric resonance

中图分类号:

34A34
70K50

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 239-260.

Jie JING, Xiaoye MAO, Hu DING, Liqun CHEN. Parametric resonance of axially functionally graded pipes conveying pulsating fluid[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 239-260.

图/表 17

参考文献 53

1	IBRAHIM,R. A.Overview of mechanics of pipes conveying fluids — part I: fundamental studies.Journal of Pressure Vessel Technology,132,034001(2010)
2	ALI,H. H.,MUSTAFA,A. W., andAL-BAKRI,F. F.A new control design and robustness analysis of a variable speed hydrostatic transmission used to control the velocity of a hydraulic cylinder.International Journal of Dynamics and Control,9(3),1078-1091(2020)
3	GAO,P. X.,YU,T.,ZHANG,Y. L.,WANG,J., andZHAI,J. Y.Vibration analysis and control technologies of hydraulic pipeline system in aircraft: a review.Chinese Journal of Aeronautics,34(4),83-114(2021)
4	GUO,X. M.,CAO,Y. M.,MA,H.,XIAO,C. L., andWEN,B. C.Dynamic analysis of an L-shaped liquid-filled pipe with interval uncertainty.International Journal of Mechanical Sciences,217,107040(2022)
5	LI,M.,XU,Q.,CHEN,X. C.,ZHANG,X. L., andLI,Y. H.Modeling and modal analysis of non-uniform multi-span oil-conveying pipes with elastic foundations and attachments.Applied Mathematical Modelling,88,661-675(2020)
6	LIANG,F.,GAO,A.,LI,X. F., andZHU,W. D.Nonlinear parametric vibration of spinning pipes conveying fluid with varying spinning speed and flow velocity.Applied Mathematical Modelling,95,320-338(2021)
7	PAÏDOUSSIS,M. P., andISSID,N. T.Dynamic stability of pipes conveying fluid.Journal of Sound and Vibration,33(3),267-294(1974)
8	PLAUT,R. H., andHUSEYIN,K.Instability of fluid conveying pipes under axial load.Journal of Applied Mechanics,42(4),889-890(1975)
9	MATSUZAKI,Y., andFUNG,Y. C.Nonlinear stability analysis of a two-dimensional model of an elastic tube conveying a compressible flow.Journal of Applied Mechanics,46(1),31-36(1979)
10	PANDA,L. N., andKAR,R. C.Nonlinear dynamics of a pipe conveying pulsating fluid with combination, principal parametric and internal resonances.Journal of Sound and Vibration,309(3-5),375-406(2008)
11	BURAK-ÖZHAN,B., andPAKDEMIRLI,M.Principal parametric resonances of a general continuous system with cubic nonlinearities.Applied Mathematics and Computation,219(5),2412-2423(2012)
12	ZHU,B.,GUO,Y.,ZHAO,T., andLI,X.Nonlinear dynamics of inclined viscoelastic pipes subjected to pulsatile flow and multi-harmonic excitations.Nonlinear Dynamics,111(13),11823-11849(2023)
13	SHAIK,N. H.,SHARMA,A. K., andBHATTACHARYA,B.Effect of shape memory alloy actuation on parametric instability in pipes conveying pulsating fluid.Journal of Vibration Engineering & Technologies,11,3003-3016(2023)
14	WEI,S.,YAN,X.,LI,X.,DING,H., andCHEN,L. Q.Parametric vibration of a nonlinearly supported pipe conveying pulsating fluid.Nonlinear Dynamics,111(18),16643-16661(2023)
15	GUO,X. M.,GAO,P. X.,MA,H.,LI,H.,WANG,B.,HAN,Q. K., andWEN,B. C.Vibration characteristics analysis of fluid-conveying pipes concurrently subjected to base excitation and pulsation excitation.Mechanical Systems and Signal Processing,189,110086(2023)
16	WANG,Y. K.,TANG,M.,YANG,M., andQIN,T.Three-dimensional dynamics of a cantilevered pipe conveying pulsating fluid.Applied Mathematical Modelling,114,502-524(2023)
17	GUO,Y.,ZHU,B., andLI,Y. H.Nonlinear dynamics of fluid-conveying composite pipes subjected to time-varying axial tension in sub- and super-critical regimes.Applied Mathematical Modelling,101,632-653(2022)
18	ZHU,B.,ZHANG,X., andZHAO,T.Nonlinear planar and non-planar vibrations of viscoelastic fluid-conveying pipes with external and internal resonances.Journal of Sound and Vibration,548,117558(2023)
19	XIE,W. D.,LIANG,Z. L.,JIANG,Z. Y., andZHU,L. X.Dynamic responses of a flexible pipe conveying variable-density fluid and experiencing cross-flow and in-line coupled vortex-induced vibrations.Ocean Engineering,260,111811(2022)
20	GHADIRIAN,H.,MOHEBPOUR,S.,MALEKZADEH,P., andDANESHMAND,F.Nonlinear free vibrations and stability analysis of FG-CNTRC pipes conveying fluid based on Timoshenko model.Composite Structures,292,115637(2022)
21	XU,W. H.,JIA,K.,MA,Y. X.,WANG,Y. Y., andSONG,Z. Y.Multispan classification methods and interaction mechanism of submarine pipelines undergoing vortex-induced vibration.Applied Ocean Research,120,103027(2022)
22	LI,M. W.,YAN,H., andWANG,L.Nonlinear model reduction for a cantilevered pipe conveying fluid: a system with asymmetric damping and stiffness matrices.Mechanical Systems and Signal Processing,188,109993(2023)
23	DING,H.,JI,J. C., andCHEN,L. Q.Nonlinear vibration isolation for fluid-conveying pipes using quasi-zero stiffness characteristics.Mechanical Systems and Signal Processing,121,675-688(2019)
24	WEI,S.,YAN,X.,FAN,X.,MAO,X. Y.,DING,H., andCHEN,L. Q.Vibration of fluid-conveying pipe with nonlinear supports at both ends.Applied Mathematics and Mechanics (English Edition),43(6),845-862(2022) doi: 10.1007/s10483-022-2857-6
25	ZHOU,K.,YI,H. R.,DAI,H. L.,YAN,H.,GUO,Z. L.,XIONG,F. R.,NI,Q.,HAGEDORN,P., andWANG,L.Nonlinear analysis of L-shaped pipe conveying fluid with the aid of absolute nodal coordinate formulation.Nonlinear Dynamics,107(1),391-412(2021)
26	CHEN,F. J.,CHEN,J. Y.,DUAN,R. Q.,HABIBI,M., andKHADIMALLAH,M. A.Investigation on dynamic stability and aeroelastic characteristics of composite curved pipes with any yawed angle.Composite Structures,284,115195(2022)
27	MAKNUN,I. J.,NATARAJAN,S., andKATILI,I.Application of discrete shear quadrilateral element for static bending, free vibration and buckling analysis of functionally graded material plate.Composite Structures,284,115130(2022)
28	CHANDRASEKARAN,S.,HARI,S., andAMIRTHALINGAM,M.Functionally graded materials for marine risers by additive manufacturing for high-temperature applications: experimental investigations.Structures,35,931-938(2022)
29	ZHEN,Y. X.,GONG,Y. F., andTANG,Y.Nonlinear vibration analysis of a supercritical fluid-conveying pipe made of functionally graded material with initial curvature.Composite Structures,268,113980(2021)
30	ZHU,B.,GUO,Y.,CHEN,B., andLI,Y. H.Nonlinear nonplanar dynamics of porous functionally graded pipes conveying fluid.Communications in Nonlinear Science and Numerical Simulation,117,106907(2023)
31	SELMI,A., andHASSIS,H.Vibration analysis of post-buckled fluid-conveying functionally graded pipe.Composites Part C: Open Access,4,100117(2021)
32	JIN,Q.,REN,Y., andYUAN,F. G.Combined resonance of pulsatile flow-transporting FG nanotubes under forced excitation with movable boundary.Nonlinear Dynamics,111(7),6157-6178(2022)
33	DING,H. X.,SHE,G. L., andZHANG,Y. W.Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection.The European Physical Journal Plus,137(12),1329(2022)
34	GUO,X. M.,XIAO,C. L.,GE,H.,MA,H.,LI,H.,SUN,W., andLIU,Z. H.Dynamic modeling and experimental study of a complex fluid-conveying pipeline system with series and parallel structures.Applied Mathematical Modelling,109,186-208(2022)
35	ZHAO,Y.,FENG,J. M.,ZHAO,B.,ZHOU,S. M.,TANG,Z., andPENG,X. Y.Vibration analysis and control of a screw compressor outlet piping system.Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering,233(2),403-411(2018)
36	DAI,J. Y.,LIU,Y. S.,LIU,H. C.,MIAO,C. X., andTONG,G. J.A parametric study on thermo-mechanical vibration of axially functionally graded material pipe conveying fluid.International Journal of Mechanics and Materials in Design,15(4),715-726(2019)
37	AN,C., andSU,J.Dynamic behavior of axially functionally graded pipes conveying fluid.Mathematical Problems in Engineering,2017,6789634(2017)
38	LU,Z. Q.,ZHANG,K. K.,DING,H., andCHEN,L. Q.Nonlinear vibration effects on the fatigue life of fluid-conveying pipes composed of axially functionally graded materials.Nonlinear Dynamics,100(2),1091-1104(2020)
39	GUO,Q.,LIU,Y. S.,CHEN,B. Q., andZHAO,Y. Z.An efficient stochastic natural frequency analysis method for axially varying functionally graded material pipe conveying fluid.European Journal of Mechanics-A/Solids,86,104155(2021)
40	TUO,Y. H.,FU,G. M.,SUN,B. J.,LOU,M., andSU,J.Stability of axially functionally graded pipe conveying fluid: generalized integral transform solution.Applied Ocean Research,125,103218(2022)
41	FAN,X.,WU,N.,LIU,Y., andGUO,Q.Resonance system reliability and sensitivity analysis method for axially FGM pipes conveying fluid with adaptive Kriging model.Acta Mechanica Solida Sinica,35(6),1021-1029(2022)
42	AGHAZADEH,R.Stability analysis of fluid conveying axially functionally graded micro-pipes using a refined tube model.Arabian Journal for Science and Engineering,47(7),8739-8750(2022)
43	AGHAZADEH,R.The effects of gravity and material gradation on the stability of axially functionally graded cantilevered pipes conveying fluid.Journal of the Chinese Society of Mechanical Engineers,43,153-164(2022)
44	FU,G.,TUO,Y.,ZHANG,H.,SU,J.,SUN,B.,WANG,K., andLOU,M.Effects of material characteristics on nonlinear dynamics of viscoelastic axially functionally graded material pipe conveying pulsating fluid.Journal of Marine Science and Application,22(2),247-259(2023)
45	BABILIO,E.Dynamics of functionally graded beams on viscoelastic foundation.International Journal of Structural Stability and Dynamics,14(8),1440014(2014)
46	MAO,X. Y.,JING,J.,DING,H., andCHEN,L. Q.Dynamics of axially functionally graded pipes conveying fluid.Nonlinear Dynamics,111(12),11023-11044(2023)
47	FAN,X.,ZHU,C. A.,MAO,X. Y., andDING,H.Resonance regulation on a hydraulic pipe via boundary excitations.International Journal of Mechanical Sciences,252,108375(2023)
48	CHEN,L. Q., andZU,J. W.Solvability condition in multi-scale analysis of gyroscopic continua.Journal of Sound and Vibration,309(1-2),338-342(2008)
49	WANG,X. W., andGU,H. Z.Static analysis of frame structures by the differential quadrature element method.International Journal for Numerical Methods in Engineering,40(4),759-772(1997)
50	SHU,C.,CHEW,Y. T., andRICHARDS,B. E.Generalized differential and integral quadrature and their application to solve boundary layer equations.International Journal for Numerical Methods in Fluids,21(9),723-733(1995)
51	DING,H.,YAN,Q. Y., andZU,J. W.Chaotic dynamics of an axially accelerating viscoelastic beam in the supercritical regime.International Journal of Bifurcation and Chaos,24(5),1450062(2014)
52	WANG,X. W., andWANG,Y. L.Free vibration analysis of multiple-stepped beams by the differential quadrature element method.Applied Mathematics and Computation,219(11),5802-5810(2013)
53	WANG,Y. L.,WANG,X. W., andZHOU,Y.Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method.International Journal for Numerical Methods in Engineering,59(9),1207-1226(2004)

[1]	. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 931-946.
[2]	Hongyan CHEN, Youcheng ZENG, Hu DING, Siukai LAI, Liqun CHEN. Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 389-406.
[3]	M. RAHMAN, M. TURKYILMAZOGLU, Z. MUSHTAQ. Effects of multiple shapes for steady flow with transformer oil+Fe₃O₄+TiO₂ between two stretchable rotating disks[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 373-388.
[4]	Hu DING, Yufei SHAO. NES cell[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1793-1804.
[5]	Shichao MA, Xin NING, Liang WANG, Wantao JIA, Wei XU. Complex response analysis of a non-smooth oscillator under harmonic and random excitations[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 641-648.
[6]	Jiren XUE, Yewei ZHANG, Hu DING, Liqun CHEN. Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 1-14.
[7]	李军陈予恕. Transition sets of bifurcations of dynamical systems with two state variables with constraints[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(2): 139-154.
[8]	钟顺陈予恕. Bifurcation of elastic tank-liquid coupled sloshing system[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(9): 1169-1176.
[9]	李军陈予恕. Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(8): 957-972.
[10]	刘延彬陈予恕曹庆杰. Analysis method of chaos and sub-harmonic resonance of nonlinear system without small parameters[J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(1): 1-10.
[11]	M.PAKDEMIRLI Y.AKSOY. Group classification for path equation describing minimum drag work and symmetry reductions[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(7): 911-916.
[12]	Bikash SAHOO. Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(2): 159-173.
[13]	李庶民贺天兰. Dynamical behavior of traveling wave solutions of ion acoustic plasma equations[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(1): 119-124.
[14]	张永新. Eventually vanished solutions of a forced Li´enard system[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(10): 1335-1344.
[15]	钟顺陈予恕. Bifurcation of piecewise-linear nonlinear vibration system of vehicle suspension[J]. Applied Mathematics and Mechanics (English Edition), 2009, 30(6): 677-684.