体积分数随机场作用下复合材料层合板固有振动特性不确定性分析

于汝雨; 张旭方

doi:10.13801/j.cnki.fhclxb.20210310.004

体积分数随机场作用下复合材料层合板固有振动特性不确定性分析

doi: 10.13801/j.cnki.fhclxb.20210310.004

于汝雨,
张旭方^,

东北大学　机械工程与自动化学院，沈阳 110819

基金项目: 国家自然科学基金(51775095)；中央高校基本科研业务费项目(N2003029)

详细信息

通讯作者:
张旭方，博士，特聘研究员，博士生导师，研究方向为工程结构可靠性设计方法　E-mail：zhangxf@mail.neu.edu.cn

中图分类号: TB333
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- 被引次数: 0
出版历程
- 收稿日期: 2021-01-13
- 修回日期: 2021-02-17
- 录用日期: 2021-02-25
- 网络出版日期: 2021-03-10
- 刊出日期: 2022-01-15

Uncertainty analysis of natural vibration characteristics of composite laminated plates with spatially varied stochastic volume fractions

YU Ruyu,
ZHANG Xufang^,

School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China

摘要

摘要: 考虑复合材料层合板中每层体积分数空间不确定性的影响，采用指数型自相关函数模拟每层体积分数同空间位置的依赖关系，结合伽辽金-里兹正交多项式逼近和K-L展开方法，研究了体积分数随机场的自相关长度特征对材料属性随机场离散精度的影响；进而通过体积分数随机场作用下复合材料层合板的随机有限元模型，研究了T300碳纤维/QY8911环氧树脂复合材料垂尾蒙皮结构的固有频率均值、标准差和变异系数与层合板层数之间的关系，基于Monte-Carlo模拟方法验证了采用本文方法开展复合材料层合板固有振动特性分析的有效性。数值结果表明：复合材料层合板结构固有频率的变异系数随铺层数减少而增大，层数越少，纤维体积分数的不确定性对固有振动特性分散性的影响越大。
- 体积分数随机场 /
- 不确定性分析 /
- 固有振动特性 /
- 复合材料层合板 /
- 随机有限元法
Abstract: In each layer of the composite laminate, the spatial uncertainty effect of the volume fraction was considered. Using exponential autocorrelation function, the relationship between the volume fraction of each layer and the spatial position was simulated. Combining the Galerkin-Riza discretization and K-L series expansion methods, the influence of autocorrelation length on the discretization accuracy was carried out. The stochastic finite element model of composite laminates with spatially random material properties was established. Taking the T300 carbon fiber/QY8911 epoxy aircraft vertical tail thin-gauge skin structure as an example, the relationships between the mean value, standard deviation and coefficient of variation of the natural frequency and the number of laminate layers were obtained. And the Monte-Carlo simulation method was used to verify the effectiveness of the method in this paper to carry out the natural frequency and mode uncertainty analysis of composite laminates. The results show that: the coefficient of variation of the natural frequency of the composite laminate structure increases with the decrease of the number of layers, and the less the number of layers, the greater influence of uncertainty of the fiber volume fraction on dispersion of the natural vibration characteristics.
- random field of the volume fraction /
- uncertainty analysis /
- natural vibration characteristics /
- composite laminates /
- stochastic finite element method

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图 1 T300碳纤维/QY8911环氧树脂复合材料层合板垂尾蒙皮结构示意图

Figure 1. Schematic diagram of vertical tail structure of T300 carbon fiber/QY8911 epoxy composite laminate

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图 2 T300碳纤维/QY8911环氧树脂复合材料垂尾蒙皮结构随机场模拟的离散网格

Figure 2. Discrete mesh of random field of vertical tail structure of T300 carbon fiber/QY8911 epoxy composite laminate

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图 3 T300/QY8911复合材料层合板不同角度铺层的体积分数随机场标准差相对误差

Figure 3. Relative error of standard deviation for random field of different layer angles of T300/QY8911 composite laminates

δ_y—Correlation length perpendicular to fiber direction; δ_x—Correlation length along fiber direction

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图 4 T300/QY8911复合材料层合板不同角度铺层体积分数随机场的两个实现结果

Figure 4. Two realizations of the volume fraction random field of different layer angles of T300/QY8911 composite laminates

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图 5 不同角度铺层体积分数随机场模拟结果的均值(a)和标准差(b)

Figure 5. Results for mean-value (a) and standard deviation (b) of random field realizations of various layer angles of T300/QY8911 composite laminates

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图 6 不同角度铺层体积分数随机场模拟结果的均值相对误差(a)和标准差相对误差(b)

Figure 6. Relative errors for mean-value (a) and relative errors for standard deviation (b) of random field realizations of various layer angles of T300/QY8911 composite laminates

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图 7 T300碳纤维/QY8911环氧树脂复合材料层合板垂尾蒙皮结构前6阶固有频率概率密度函数

Figure 7. Probability density function (PDF) of the first 6-order natural frequency of the T300 carbon fiber/QY8911 epoxy composite laminate vertical tail skin structure

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图 8 T300碳纤维/QY8911环氧树脂复合材料层合板垂尾蒙皮结构前6阶振型逐点均值(a)和标准差(b)

Figure 8. Mean value (a) and standard deviation (b) for the first-six modes of the T300 carbon fiber/QY8911 epoxy composite laminate vertical tail skin structure

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图 9 T300碳纤维/QY8911环氧树脂复合材料层合板垂尾蒙皮结构基于5000次模拟的前6阶固有频率均值(a)、标准差(b)和变异系数(c)

Figure 9. Mean value (a), standard deviation (S.D. )(b) and coefficient of variation (COV) (c) for the first-six natural frequencies of the T300 carbon fiber/QY8911 epoxy composite laminate vertical tail skin structure based on 5000 simulations

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图 10 T300碳纤维/QY8911环氧树脂复合材料层合板垂尾蒙皮结构两种铺层方案的前6阶固有频率变异系数：(a)方案1：45°和−45°交替铺层；(b)方案2：0°和90°交替铺层

Figure 10. Coefficient of variation (COV) of the first 6-order natural frequencies of the T300 carbon fiber/QY8911 epoxy composite laminate vertical tail skin structure with two laying schemes: (a) Scheme 1: 45° and −45° alternate laying; (b) Scheme 2: 0° and 90° alternate laying

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表 1 T300碳纤维/QY8911环氧树脂复合材料层合板的材料属性

Table 1. Material properties of T300 carbon fiber/QY8911 epoxy composite laminates

E_f1/GPa	E_f2/GPa	G_f12/GPa	G_f23/GPa	ν₁₂	E_m/GPa	G_m/GPa	ν_m	ρ/(kg·m⁻³)
221	13.8	9	4.8	0.25	3.6	2.34	0.3	1578
Notes：E_f1, E_f2—Fiber longitudinal and transverse elasticity moduli; G_f12, G_f23—Fiber longitudinal and transverse shear moduli; ν₁₂—Longitudinal Poisson’s ratio of fiber; E_m, G_m—Elasticity modulus and shear modulus of matrix; ν_m—Poisson's ratio of matrix; ρ—Equivalent density of composites.

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