Nonlinear stress analysis of aero-engine pipeline based on semi-analytical method

doi:10.1007/s10483-025-3225-8

Abstract

Abstract:

Fatigue failure caused by vibration is the most common type of pipeline failure. The core of this research is to obtain the nonlinear dynamic stress of a pipeline system accurately and efficiently, a topic that needs to be explored in the existing literature. The shell theory can better simulate the circumferential stress distribution, and thus the Mindlin-Reissner shell theory is used to model the pipeline. In this paper, the continuous pipeline system is combined with clamps through modal expansion for the first time, which realizes the coupling problem between a shell and a clamp. While the Bouc-Wen model is used to simulate the nonlinear external force generated by a clamp, the nonlinear coupling characteristics of the system are effectively captured. Then, the dynamic equation of the clamp-pipeline system is established according to the Lagrange energy equation. Based on the resonance frequency and stress amplitude obtained from the experiment, the nonlinear parameters of the clamp are identified with the semi-analytical method (SAM) and particle swarm optimization (PSO) algorithm. This study provides a theoretical basis for the clamp-pipeline system and an efficient and universal solution for stress prediction and analysis of pipelines in engineering.

Key words: pipeline modeling, stress analysis, nonlinear-clamp support, nonlinear vibration

2010 MSC Number:

O322

Weijiao CHEN, Xiaochi QU, Ruixin ZHANG, Xumin GUO, Hui MA, Bangchun WEN. Nonlinear stress analysis of aero-engine pipeline based on semi-analytical method. Applied Mathematics and Mechanics (English Edition), 2025, 46(3): 521-538.

TrendMD

Figures/Tables 19

Fig. 1

Fig. 2

Fig. 3

Table 1

Spring stiffness values for three classical boundary constraints adopted in calculations"

Boundary type	Stiffness value
Boundary type	$k ¯ u / (N ⋅ m − 1)$	$k ¯ v / (N ⋅ m − 1)$	$k ¯ w / (N ⋅ m − 1)$	$k ¯ φ / (N ⋅ rad − 1)$	$k ¯ ϕ / (N ⋅ rad − 1)$
Free	0	0	0	0	0
Simply supported	10¹⁴	10¹⁴	10¹⁴	0	0
Clamped	10¹⁴	10¹⁴	10¹⁴	10¹⁴	10¹⁴

Table 1

Fig. 4

Table 2

Parameters of pipeline and clamp"

Parameter	Value	Parameter	Value
h/m	0.001	l/m	0.6
E/Pa	$2.04 × 1011$	$ρ p$ /(kg·m^-3)	$7.8 × 103$
$ξ 1, ξ 2$	0.02	$k ϕ$ / $(N ⋅ m ⋅ rad − 1)$	45.69
$μ$	0.3	$k v$ / $(N ⋅ m − 1)$	$1.43 × 106$
$R$ /m	0.009 5	$k φ$ / $(N ⋅ m ⋅ rad − 1)$	59.54
$k u / (N ⋅ m − 1)$	$1 × 107$	$k w$ / $(N ⋅ m − 1)$	$2.33 × 106$

Table 2

Fig. 5

Fig. 6

Table 3

Comparison of simulated and measured natural frequencies"

Order	Experiment/Hz	FE model/Hz	Proposed model/Hz	Error 1 $e 1$ /%	Error 2 $e 2$ /%
1	313.45	297.74	299.15	0.47	4.56
2	998.12	969.26	962.97	0.65	2.89
3	1 875.36	1 868.70	1 840.84	1.49	1.84
4	2 901.31	2 913.80	2 917.69	0.13	0.58
Note: $e 1$ represents difference of natural frequencies obtained from FE model and proposed model divided by that obtained from FE model, while $e 2$ represents difference of natural frequencies obtained from experiment and proposed model divided by that obtained from experiment

Table 3

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 4

Stress testing system"

Equipment	Type	Sensitivity	Note
Strain collection and analysis system	SCADAS mobile	–	LMS 216 channels
Uniaxial strain gauge	TSK-1B-120-1A	$2.1 % ± 1.0 %$	Resistance value 120 $Ω$

Table 4

Table 5

Nonlinear mechanical parameters of clamp"

Excitation amplitude	$k Θ n / (N ⋅ m − 3)$	$α$	$β$	$γ$
1g	$6.51 × 107$	0.62	$1.2 × 103$	$9 × 102$
2g	$6.47 × 107$	0.62	$5.1 × 103$	$6 × 102$
3g	$6.35 × 107$	0.64	$7.5 × 103$	$2 × 102$
4g	$6.21 × 107$	0.65	$8.6 × 103$	$1 × 102$
5g	$6.11 × 107$	0.66	$9.4 × 103$	$6 × 101$

Table 5

Fig. 12

Fig. 13

Fig. 14

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