Vibration Simulation and Multivariate Statistical Analysis Method of Composite Structures

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

Abstract

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

CLC Number:

TP391.9

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.

Figures/Tables 20

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Table 1

Material structural parameters and their deviations

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

Table 1

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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