Modeling and mechanism of vibration reduction of pipes by visco-hyperelastic materials

doi:10.1007/s10483-025-3263-6

Abstract

Abstract:

Pipes have been extensively utilized in the aerospace, maritime, and other engineering sectors. However, the vibrations of pipes can significantly affect the system reliability and even lead to accidents. Visco-hyperelastic materials can enhance the dissipative effect, and reduce the vibrations of pipes. However, the mechanism based on the constitutive model for visco-hyperelastic materials is not clear. In this study, the damping effect of a visco-hyperelastic material on the outer surface of a plain steel pipe is investigated. The nonlinear constitutive relation of the visco-hyperelastic material is introduced into the governing equation of the system for the first time. Based on this nonlinear constitutive model, the governing model for the forced vibration analysis of a simply-supported laminated pipe is established. The Galerkin method is used to analyze the effects of the visco-hyperelastic parameters and structural parameters on the natural characteristics of the fluid-conveying pipes. Subsequently, the harmonic balance method (HBM) is used to investigate the forced vibration responses of the pipe. Finally, the differential quadrature element method (DQEM) is used to validate these results. The findings demonstrate that, while the visco-hyperelastic material has a minimal effect on the natural characteristics, it effectively dampens the vibrations in the pipe. This research provides a theoretical foundation for applying vibration damping materials in pipe vibration control.

Key words: pipe conveying fluid, visco-hyperelastic material, harmonic balance method (HBM), vibration damping, passive control

2010 MSC Number:

O322

Jie JING, Xiaoye MAO, Hu DING, Honggang LI, Liqun CHEN. Modeling and mechanism of vibration reduction of pipes by visco-hyperelastic materials. Applied Mathematics and Mechanics (English Edition), 2025, 46(6): 1029-1048.

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Figures/Tables 18

Fig. 1

Table 1

Physical parameters of the laminated pipe—internal steel pipe"

Item	Notation	Value	Unit
Outer diameter	$D$	0.02	m
Inner diameter	$d$	0.018	m
Young's modulus	$E p$	200	GPa
Initial tension	$P 0$	20	N
Viscous damping coefficient	$μ$	$2 × 104$	N·s·m^-2
Density of the pipe	$ρ p$	7 800	Kg·m^-3
Density of the fluid	$ρ f$	872	Kg·m^-3
Length of the pipe	$L$	1	m

Table 1

Table 2

Physical parameters of the laminated pipe—external rubber layer"

Item	Notation	Value	Unit
Diameter of rubber layer	$d r$	0.024	m
Density of rubber layer	$ρ r$	1 000	kg·m^-3
Length of rubber layer	$L$	1	m
Visco-hyperelastic parameters of SHA30 rubber^[37]	$C 1$	0.494 4	MPa
	$C 2$	$− 0.128 3$	MPa
	$C 3$	0.012 1	MPa
	$C 4$	3.49	MPa
	$C 5$	0.83	MPa
	$C 6$	10.267	$μ$ s

Table 2

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Table 3

The average values of Rreal and Rimag in the first two orders of the stable region under the influence of C6"

$C 6$	The average value of $R real$		The average value of $R imag$
$C 6$	First-order	Second-order	First-order	Second-order
$102 C 6b$			34.874 3%	34.666 3%
$103 C 6b$	9.271 7%	10.303 7%	87.244 3%	87.204 3%
$104 C 6b$			98.589 2%	98.584 6%

Table 3

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 4

The flow velocity of the first two orders resonances under different C6"

$Γ$ /(m·s^-1)	$C 6 = 0 C 6b$	$C 6 = 10 2 C 6b$	$C 6 = 10 3 C 6b$	$C 6 = 10 4 C 6b$
$Ω 1st = 96.12$ rad/s	145	143.000 266 2	143.000 266 4	143.000 282 5
$Ω 2nd = 812.97$ rad/s	220	190.652 6	190.652 7	190.661 7

Table 4

Fig. 12

Fig. 13

Table 5

The flow velocities of the first two orders resonances under different dr"

$Γ$ /(m·s^-1)	$d r = 20$ mm	$d r = 40$ mm	$d r = 60$ mm	$d r = 80$ mm
$Ω 1st = 96.12$ rad/s	145	130.776 8	102.903 3	39.018 1
$Ω 2nd = 333.78$ rad/s	304	279.892 9	238.55	169.124 2

Table 5

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