Nonlinear dynamics of intricate constrained fluid-conveying pipelines based on the global modal method

doi:10.1007/s10483-025-3308-7

Abstract

Abstract:

In recent years, scholars around the world have shown increasing interest in elastic support structures, leading to significant progress in dynamic modeling techniques for pipeline systems. Although multiple analytical approaches exist, engineers increasingly prioritize computationally efficient, precise low-order models for practical implementation. In order to address this need, this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities. The proposed solution methodology initiates with global mode extraction using the global mode technique, followed by a detailed implementation procedure. Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions, where strong agreement between the proposed model’s predictions and finite-element benchmark solutions demonstrates its reliability. Subsequently, a comprehensive parametric study investigates the combined effects of foundation stiffness, boundary constraints, excitation intensity, and nonlinear interaction terms on the vibrational response of the cantilever pipe. This systematic approach yields critical insights for practical engineering designs and applications.

Key words: fluid-conveying pipeline, complex constraint, nonlinear dynamics, global modal method

2010 MSC Number:

O322

Ye TANG, Yuxiang WANG, Hujie ZHANG, Tianzhi YANG, Fantai MENG. Nonlinear dynamics of intricate constrained fluid-conveying pipelines based on the global modal method. Applied Mathematics and Mechanics (English Edition), 2025, 46(10): 1851-1866.

TrendMD

Figures/Tables 13

Fig. 1

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Table 1

The parameters of a cantilevered pipe with nonlinear elastic foundation and boundaries"

Parameter	Symbol	Value
Length of the pipeline	$L$	0.45 m
Length of the sub-pipeline	$L 1 = L 2 = L 3$	0.15 m
Young’s modulus	$E$	$8.5 × 108$ GPa
Pipeline surface mass	$m e$	0.115 6 kg · m^-1
Fluid surface mass	$m l$	0.254 5 kg · m^-1
Outer diameter of the pipeline	$D 2$	0.22 m
Internal diameter of the pipeline	$d 2$	0.18 m
Sectional moment of inertia	$I$	$6.346 × 10 − 9$ m⁴
Initial length of the horizontal spring	$L 0$	0.1 m
Length after compression of the spring	$L g$	0.1 m

Table 1

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References 30

[1]	ZHANG, J. N., DING, H., MAO, X. Y., and CHEN, L. Q. Multi-frequency harmonic balance method for nonlinear vibration of pipe conveying fluid under arbitrary dual-frequency excitation. Nonlinear Dynamics, 113, 6181–6196 (2025)
[2]	JING, J., MAO, X. Y., DING, H., LI, H. G., and CHEN, L. Q. Modeling and mechanism of vibration reduction of pipes by visco-hyperelastic materials. Applied Mathematics and Mechanics (English Edition), 46(6), 1029–1048 (2025) https://doi.org/10.1007/s10483-025-3263-6
[3]	HAO, M. Y., DING, H., MAO, X. Y., WEI, S., and CHEN, L. Q. Natural vibration of critical double-span functionally graded pipe conveying fluid reinforced by graphene platelets. Journal of Vibration Engineering & Technologies, 13(1), 40 (2025)
[4]	TANG, Y., ZHANG, H. J., CHEN, L. Q., DING, Q., GAO, Q. Y., and YANG, T. Z. Recent progress on dynamics and control of pipes conveying fluid. Nonlinear Dynamics, 113, 6253–6315 (2025)
[5]	LI, H. F., SUN, Y. B., WEI, S., DING, H., and CHEN, L. Q. Random vibration of a pipe conveying fluid under combined harmonic and gaussian white noise excitations. Acta Mechanica Solida Sinica (2025) https://doi.org/10.1007/s10338-025-00586-9
[6]	HAO, M. Y., DING, H., JI, J. C., MAO, X. Y., and CHEN, L. Q. Nonlinear vibration and regulation of a double-span functionally graded pipe conveying pulsating flow. Nonlinear Dynamics, 113(18), 4245–4262 (2025)
[7]	BU, Y., TANG, Y., and DING, Q. Novel vibration self-suppression of periodic pipes conveying fluid based on acoustic black hole effect. Journal of Sound and Vibration, 567, 118077 (2023)
[8]	BU, Y., TANG, Y., YANG, T. Z., and DING, Q. Enhanced dynamic modeling of pipes conveying fluid with multiple constraints and accessories based on spectral element method. Mechanical Systems and Signal Processing, 237, 113097 (2025)
[9]	KHEIRI, M. Nonlinear dynamics of imperfectly-supported pipes conveying fluid. Journal of Fluids and Structures, 93, 102850 (2020)
[10]	MAO, X. Y., SHU, S., FAN, X., DING, H., and CHEN, L. Q. An approximate method for pipes conveying fluid with strong boundaries. Journal of Sound and Vibration, 505, 116157 (2021)
[11]	ZHOU, J., CHANG, X. P., XIONG, Z. J., and LI, Y. H. Stability and nonlinear vibration analysis of fluid-conveying composite pipes with elastic boundary conditions. Thin-Walled Structures, 179, 109597 (2022)
[12]	ZHOU, K., NI, Q., GUO, Z. L., YAN, H., DAI, H. L., and WANG, L. Nonlinear dynamic analysis of cantilevered pipe conveying fluid with local rigid segment. Nonlinear Dynamics, 109, 1571–1589 (2022)
[13]	LI, M., CHEN, X. C., CHANG, X. P., QIN, Y., and LI, Y. H. General analytical solution for vibrations of pipes with arbitrary discontinuities and generalized boundary condition on Pasternak foundation. Mechanical Systems and Signal Processing, 162, 107910 (2022)
[14]	YAN, X., WEI, S., MAO, X. Y., DING, H., and CHEN, L. Q. Study on natural characteristics of fluid-conveying pipes with elastic supports at both ends. Chinese Journal of Theoretical and Applied Mechanics, 54, 1341–1352 (2022)
[15]	YAMASHITA, K., KITAURA, K., NISHIYAMA, N., and YABUNO, H. Non-planar motions due to nonlinear interactions between unstable oscillatory modes in a cantilevered pipe conveying fluid. Mechanical Systems and Signal Processing, 178, 109183 (2022)
[16]	GUO, X. M., GE, H., XIAO, C. L., MA, H., SUN, W., and LI, H. Vibration transmission characteristics analysis of the parallel fluid-conveying pipes system: numerical and experimental studies. Mechanical Systems and Signal Processing, 177, 109180 (2022)
[17]	ZHANG, Y., SUN, W., MA, H. W., JI, W. H., and MA, H. Semi-analytical modeling and vibration analysis for U-shaped, Z-shaped and regular spatial pipelines supported by multiple clamps. European Journal of Mechanics-A/Solids, 97, 104797 (2023)
[18]	ELNAJJAR, J. and DANESHMAND, F. Stability of horizontal and vertical pipes conveying fluid under the effects of additional point masses and springs. Ocean Engineering, 206, 106943 (2020)
[19]	WANG, Y. X., TANG, Y., and YANG, T. Z. Nonlinear vortex-induced vibration analysis of a fiber-reinforced composite pipes transporting liquid-gas two-phase flow. Communications in Nonlinear Science and Numerical Simulation, 142, 108516 (2025)
[20]	LIANG, F. and CHEN, Z. Q. Enhanced dynamical stability of rotating composite pipes conveying fluid by a smart piezoelectric design. Applied Mathematical Modelling, 138, 115798 (2025)
[21]	ALVIS, T. and ABDELKEFI, A. Stochastic investigation of the input uncertainty effects on the dynamic responses of constrained pipelines conveying fluids. Nonlinear Dynamics, 111, 3981–4015 (2023)
[22]	ALVIS, T., SAUNDERS, B. E., and ABDELKEFI, A. Dynamical responses of constrained pipe conveying fluids and its dependence on the modeling of the contact force. International Journal of Non-Linear Mechanics, 150, 104364 (2023)
[23]	ALVIS, T., SAUNDERS, B. E., and ABDELKEFI, A. Vibro-impact analysis and characterization of pipeline conveying fluids with multi-segmented motion-limiting constraints. Applied Mathematical Modelling, 122, 731–760 (2023)
[24]	ALVIS, T., SAUNDERS, B. E., and ABDELKEFI, A. Consequences and benefits of utilizing continuous vibro-impact representations in constrained pipeline conveying fluid systems. Nonlinear Dynamics, 111, 9095–9125 (2023)
[25]	DENG, T. C., DING, H., MAO, X. Y., and CHEN, L. Q. Natural vibration of pipes conveying high-velocity fluids with multiple distributed retaining clips. Nonlinear Dynamics, 111, 18819–18836 (2023)
[26]	CAO, Y. M., GUO, X. M., MA, H., GE, H., LI, H., LIN, J. Z., JIA, D., WANG, B., and MA, Y. C. Dynamic modelling and natural characteristics analysis of fluid-conveying pipeline with connecting hose. Mechanical Systems and Signal Processing, 193, 110244 (2023)
[27]	WANG, Z. C., YAN, W. J., and YUEN, K. V. A. Transfer matrix method-based closed-form solution of sensitivities of dynamic properties and FRF for multi-span pipes under complex boundary conditions. Mechanical Systems and Signal Processing, 198, 110428 (2023)
[28]	RIAZAT, M. and KHEIRI, M. Three-dimensional nonlinear dynamics of imperfectly supported pipes conveying fluid. Journal of Fluids and Structures, 123, 104011 (2023)
[29]	MAO, X. Y., WU, J. B., ZHANG, J. N., DING, H., and CHEN, L. Q. Dirac method for nonlinear and non-homogenous boundary value problems of plates. Applied Mathematics and Mechanics (English Edition), 45(1), 15–38 (2024) https://doi.org/10.1007/s10483-024-3066-7
[30]	JING, J., SHAO, Z. H., MAO, X. Y., DING, H., and CHEN, L. Q. Forced resonance of a buckled beam flexibly restrained at the inner point. Engineering Structures, 303, 117444 (2024)