复合材料结构振动仿真及其多元统计分析方法

doi:10.16182/j.issn1004731x.joss.24-0129

摘要/Abstract

摘要：

为研究复合材料层合板参数不确定性情况下的固有频率特性，以及在不同边界条件和不同振动阶数的情况下这些参数对固有频率的不同影响程度，建立了二维各向异性中厚板材料模型与三维各向异性圆柱薄壳材料振动模型。针对这类复合材料结构参数的不确定性，开发了复合材料振动仿真与多元统计分析软件，对复合材料的结构振动进行了仿真模拟，提出了一种针对复合材料固有频率不确定性的多元统计分析方法。通过主成分分析和因子分析方法进行数据降维，将材料固有频率可以用少数几个主成分或是因子成分表达，达到更高效、准确处理分析复合材料固有频率不确定性的目的，解决了复合材料不确定性分析过程复杂的难题，提升了各领域复合材料结构设计的效率。

关键词: 复合材料, 振动仿真, 不确定性, 固有频率, 主成分分析, 因子分析

Abstract:

To investigate the natural frequency characteristics of composite laminates under parametric uncertainties and the different degree of influence of these parameters on the natural frequency under different boundary conditions and different vibration orders, a two-dimensional anisotropic medium-thick plate material model and a three-dimensional anisotropic cylindrical thin-shell material vibration model are established. Aiming at the uncertainty of structural parameters of these composite materials, the composite material vibration simulation and multivariate statistical analysis software are developed to simulate the structural vibration of composite materials. A multivariate statistical analysis method for natural frequency uncertainty of composite materials is presented. Through principal component analysis and factor analysis methods, the data dimensionality is reduced, and the natural frequency of materials can be expressed by a few principal components or factor components, so as to finally achieve the purpose of analyzing and dealing with the uncertainty of natural frequency of composite materials more efficiently and accurately, and solve the complicated problem of the uncertainty analysis process of composite materials. This can improve the efficiency of composite structural design in various fields.

Key words: composite material, vibration simulation, uncertainty, natural frequency, principal component analysis, factor analysis

中图分类号:

TP391.9

郭博,铁鸣,范文慧 . 复合材料结构振动仿真及其多元统计分析方法[J]. 系统仿真学报, 2025, 37(3): 571-583.

Guo Bo,Tie Ming,Fan Wenhui . Vibration Simulation and Multivariate Statistical Analysis Method of Composite Structures[J]. Journal of System Simulation, 2025, 37(3): 571-583.

图/表 20

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图7

表1

材料结构参数及其偏差

参数	参数大小	偏差量
长 $a$ /mm	1 000	10
宽 $b$ /mm	1 000	10
厚度 $h$ /mm	200	2
弹性模量 $E$ ₁/GPa	40	4
弹性模量 $E$ ₂/GPa	1	0.1
剪切模量 $G$ ₁₂/GPa	0.6	0.06
剪切模量 $G$ ₁₃/GPa	0.6	0.06
剪切模量 $G$ ₂₃/GPa	0.5	0.05
泊松比 $μ$	0.25	0.025
密度 $ρ$ /(kg/m)³	200	20
铺设角 $θ$ ₁/(°)	0	3
铺设角 $θ$ ₂/(°)	90	3
铺设角 $θ$ ₃/(°)	0	3

表1

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图9

表2

表3

图10

表4

表5

表6

图11

表7

图12

图13

参考文献 18

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参数	RC₁	RC₂	RC₃	RC₅	RC₄	h₂	u₂	com
a	-0.13	0.34	-0.55	0.13	0	0.46	0.543	1.9
b	-0.19	0.10	0.63	0.12	0.27	0.52	0.475	1.7
h	0.18	0.69	-0.12	-0.13	-0.05	0.54	0.459	1.3
E₁	0.13	-0.03	0.63	0.08	-0.28	0.50	0.498	1.5
E₂	-0.12	0.52	-0.07	0	-0.56	0.61	0.394	2.1
G₁₂	0.98	0.10	0.04	0.01	0.02	0.96	0.036	1.0
G₁₃	0.98	0.10	0.04	0.01	0.02	0.96	0.036	1.0
G₂₃	-0.38	0.41	0.01	0.38	0.20	0.50	0.500	3.5
p	0.11	-0.19	0.12	-0.57	-0.02	0.39	0.613	1.4
μ	-0.11	-0.56	-0.12	-0.35	0.08	0.46	0.535	1.9
θ₁	-0.02	-0.01	-0.02	-0.01	0.86	0.74	0.258	1.0
θ₂	0.12	-0.06	0.24	0.72	0.01	0.60	0.405	1.3
θ₃	0.01	-0.26	-0.48	0.52	-0.21	0.61	0.391	2.8

参数	RC₁	RC₂	RC₃	RC₄	RC₅
SS loadings	2.20	1.48	1.44	1.43	1.31
Proportion var	0.17	0.11	0.11	0.11	0.10
Cumlative var	0.17	0.28	0.39	0.50	0.60
Proportion Explained	0.28	0.19	0.18	0.18	0.17
Cumlative Proportion	0.28	0.47	0.65	0.83	1.00

主成分	Estimate	Error	value	Pr(>\|t\| )
intercept	-0.134 49	0.913 27	-0.147	0.883 57
RC₁	0.129 53	0.032 02	4.045	0.000 20
RC₄	0.018 61	0.005 86	3.177	0.002 66
RC₅	0.038 05	0.013 50	2.818	0.007 10

参数	PA₁	PA₂	PA₃	PA₄	PA₅	h₂	u₂	com
a	-0.13	0.33	0.04	0.11	0.38	0.28	0.7213	2.4
b	-0.09	-0.19	-0.08	0.27	-0.34	0.24	0.7599	2.8
h	0.15	0.27	-0.10	0.15	0.16	0.15	0.8475	3.2
E₁	0.14	-0.08	-0.17	0.09	-0.26	0.13	0.8662	2.9
E₂	-0.03	0.46	-0.33	0.09	0.15	0.35	0.6480	2.2
G₁₂	1.00	0.03	0.08	0.05	0.02	1.00	-0.0039	1.0
G₁₃	1.00	0.03	0.08	0.05	0.02	1.00	-0.0039	1.0
G₂₃	-0.28	0.24	0.12	0.35	-0.07	0.28	0.7202	3.1
p	0.11	-0.25	-0.09	-0.26	-0.01	0.15	0.8532	2.6
μ	-0.10	-0.34	0.08	-0.32	0.11	0.25	0.7533	2.5
θ₁	-0.08	-0.50	0.44	0.42	0.28	0.70	0.3011	3.6
θ₂	0.05	0.11	0.10	0.27	-0.26	0.17	0.8325	2.7
θ₃	-0.09	0.50	0.62	-0.29	-0.19	0.77	0.2337	2.7

参数	PA₁	PA₂	PA₃	PA₄	PA₅
SS loadings	2.17	1.18	0.78	0.76	0.58
Proportion var	0.17	0.09	0.06	0.06	0.04
Cumulative var	0.17	0.26	0.32	0.38	0.42
Proportion Explained	0.40	0.22	0.14	0.14	0.11
Cumulative Proportion	0.40	0.61	0.76	0.89	1.00