Buckling and parametric excitation stability optimization of fluid-conveying pipes by frequency design

doi:10.1007/s10483-026-3372-6

Abstract

Abstract:

A methodology is proposed to enhance the buckling and parametric excitation stability of fluid-conveying pipes by designing their natural frequencies. As a direct indicator of structural stiffness with respect to deformation, which is intrinsically related to the overall structural stability, the natural frequency is adopted as the primary design criterion for enhancing system stability. Based on the generalized Hamilton’s principle, the governing equation for a multi-restrained pipe system is derived. The analysis reveals that, the natural frequencies can be maximized by appropriately selecting the constraint locations, which induces the best buckling stability. Although increasing the flow velocity generally reduces the natural frequency, the optimal constraint location remains relatively unchanged, eventually approaching the location of the maximal critical flow speed, beyond which the pipe loses its static stability. Furthermore, the proposed method introduces additional nodes into the natural mode shape, indicating that a higher energy threshold is required to trigger the resonance. Consequently, the parametric resonance under pulsating flow conditions becomes more difficult to initiate. Meanwhile, with the frequency design, the pipe can prevent the occurrence of parametric resonance with smaller critical damping. Compared with other approaches aimed at enhancing the stability of fluid-conveying pipe systems, the proposed method offers greater practicality for engineering applications, as it only requires adjusting the constraint locations and the optimal location is insensitive to the flow speed.

Key words: fluid-conveying pipe, frequency design, static bifurcation, stability of parametric resonance, optimal stability

2010 MSC Number:

O322

Xiaoye MAO, Kexin CHANG, Jie JING, Tianchang DENG, Hu DING, Liqun CHEN. Buckling and parametric excitation stability optimization of fluid-conveying pipes by frequency design. Applied Mathematics and Mechanics (English Edition), 2026, 47(4): 675-694.

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Figures/Tables 10

Fig. 1

Table 1

Physical parameters of the fluid-conveying pipe"

Parameter	Symbol	Value	Unit
Inner diameter	d	0.005	m
Outer diameter	D	0.006	m
Young’s modulus	E	194	GPa
Axial force	T₀	10	N
Viscous damping coefficient	α	$2 × 107$	$N ⋅ s/m 2$
Pipe density	$ρ p$	7 390	kg/m³
Fluid density	$ρ f$	872	kg/m³
Fluid velocity	v	30	m/s
Pipe length	$L p$	1	m

Table 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 2

Critical pulsating flow speed and damping with different constraint locations"

a	Critical pulsating flow speed/(m·s^-1) (vs. uniform optimization rate)	Critical damping/(N·s·m^-2) (vs. uniform optimization rate)
$0 L p$	0.096 $(− 94.66 %)$	$8.333 7 × 106$ (1 773.92%)
$0.33 L p$	1.798 1	$4.447 2 × 105$
$0.35 L p$	2.264 (25.91%)	$3.534 × 105$ ( $− 20.53 %$ )
$0.5 L p$	0.771 1 $(− 57.12 %)$	$1.037 4 × 106$ (133.27%)

Table 2

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