基于矩积分的有限元不确定性量化方法及其橡胶隔振器可靠性分析应用

doi:10.7527/S1000-6893.2025.33132

Abstract

Abstract:

Rubber isolators are important connecting and vibration-damping components in the auxiliary systems of aero-engines. Their vibration isolation performance is susceptible to material aging and uncertainties in service environments， making reliability assessment an urgent need. However， the traditional Monte Carlo method， which relies on a large number of random samples， incurs high computational costs. For typical aviation components like isolators-characterized by complex structures， multiple uncertain factors， and high test costs-existing methods still struggle to achieve reliability assessment with both computational efficiency and statistical accuracy. To address this issue， The study proposes an uncertainty quantification method based on moment quadrature and maximum entropy theory， enabling efficient reliability assessment of the vibration isolation performance of rubber isolators. First， an elastic modulus degradation model is established based on the accelerated aging test data of rubber materials. Optimal integration nodes and weights are derived by constructing a Hankel matrix through moment quadrature， replacing large-scale random sampling with a small number of key samples. Subsequently， the elastic moduli corresponding to the integration nodes are input into the random vibration finite element model to obtain the vibration isolation rate response and its statistical moments. The maximum entropy principle is then used to reconstruct the probability density function of the vibration isolation rate without the need to preset a distribution form. This method features significant advantages of being non-sampling and analytical quadrature. It can obtain multi-order statistical characteristics of vibration isolation performance with only a few optimal integration nodes， greatly reducing the number of finite element calls while maintaining accuracy. It provides an efficient technical approach for reliability analysis of complex structures.

Key words: rubber isolator, random vibration, moment quadrature, rubber degradation, reliability evaluation

CLC Number:

V240.2

Jingjing HE, Xunqi LIU, Weitao LOU, Xuefei GUAN. Finite element-based uncertainty quantification method using moment quadrature and its application in reliability analysis of rubber isolators[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(12): 233132.

Figures/Tables 20

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阶数	原点矩	阶数	原点矩
1阶	2.57×10⁶	6阶	2.87×10³⁸
2阶	6.60×10¹³	7阶	7.39×10⁴⁴
3阶	1.69×10¹⁹	8阶	1.89×10⁵¹
4阶	4.35×10²⁶	9阶	4.88×10⁵⁷
5阶	1.12×10³³	10阶	1.25×10⁶⁴

弹性模量关键采样点/Pa	关键采样点权重
2 500 789	0.011 3
2 536 349	0.222 3
2 568 481	0.532 7
2 600 613	0.222 3
2 636 172	0.011 3

材料	温度/℃	密度/（kg·m^-3）	弹性模量/MPa	泊松比
天然橡胶	25	1 150	0.86	0.4
7075铝	25	2 810	71 700	0.33

弹性模量特征值/Pa	权重	隔振率/dB
2 500 789	0.011 3	18.658 3
2 536 349	0.222 3	18.607 3
2 568 481	0.532 7	18.561 9
2 600 613	0.222 3	18.516 6
2 636 172	0.011 3	18.467 1

指标	矩积分	拉丁超立方采样	相对差异/%
均值/dB	18.561 9	18.563 1	0.006 5
标准差/dB	0.033 5	0.033 1	1.2
可靠度	0.99	0.97	2
抽样次数	5	50	90

Finite element-based uncertainty quantification method using moment quadrature and its application in reliability analysis of rubber isolators

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