Thickness Equivalence Model Based on Serial Neural Network for Explosion Resistance of Radome

doi:10.12382/bgxb.2024.1001

Abstract

Abstract:

The thickness equivalence of composite radome under the far-field explosion loads is studied by taking the fiber-reinforced polymer (FRP) laminate as the research object.A serial artificial neural network (S-ANN) model based on the principle of deflection equivalence is proposed to predict the thickness equivalence relationship between glass fiber radomes with different performances.A finite element model for the dynamic response of FRP laminates under explosive loads is established.The maximum deflection of FRP laminates under the conditions of different detonation distances,laminate thicknesses,densities,and longitudinal elastic moduli is obtained by conducting batch calculations on this finite element model.Based on this,a S-ANN thickness equivalence model is established.The proposed model achieves the thickness equivalence for different types of FRP materials under far-field explosion loads.In addition,the frequency response characteristics of the glass fiber equivalent radome are analyzed using the $A ¯ B ¯ C ¯ D ¯$ transmission matrix and a numerical simulation method.The research results show that the longitudinal elastic modulus has the greatest influence on the explosion resistance and equivalent thickness of glass fiber radome under far-field explosion loads.The equivalent thickness has little influence on the amplitude of the radome’s transmission efficiency,but it changes the resonant frequency of the radome’s transmission efficiency.This study can provide reference for the thickness equivalence research and optimization design of radomes.

Key words: radome, fiber reinforced composite material, neural network, finite element, explosion load, thickness equivalence

CLC Number:

TB332

CHEN Changfa, WU Jun’an, GUO Rui, CUI Hao, YAN Shuaiyin, ZHOU Hao. Thickness Equivalence Model Based on Serial Neural Network for Explosion Resistance of Radome[J]. Acta Armamentarii, 2025, 46(9): 241001-.

Figures/Tables 23

Fig.1 The finite element model of FRP laminates

Table 1 Material properties[21]

参数	数值
密度ρ/(g·cm^-3)	1.6
纵向、横向弹性模量E₁₁,E₂₂/GPa	55
厚度方向弹性模量E₃₃/GPa	7
面内方向剪切模量G₁₂/GPa	4.5
厚度方向剪切模量G₁₃,G₂₃/GPa	1.8
泊松比v₁₂	0.25
纤维、基体拉伸强度X_t,Y_t/MPa	890
纤维、基体压缩强度X_c,Y_c/MPa	300

Fig.2 The comparison of reflected overpressure loading curve with experimental results

Fig.3 The center-point displacement-time curves for FRP laminates

Table 2 Comparison of the experimental and FEA calculated maximum deflections

爆距/m	冲量/ (Pa·s)	最大挠度/mm
爆距/m	冲量/ (Pa·s)	FEA结果	试验结果	误差%
1.0	109	12.22	12.90	5.3
0.8	154	15.55	16.68	6.8
0.6	219	20.61	21.10	2.3

Table 3 The results of sensitivity analysis

变量	数值	Pearson相关系数
E₁₁/GPa	45,50,55,60,65	-0.615
E₃₃/GPa	5,6,7,8,9	-0.001
ρ/(g·cm^-3)	1.2,1.4,1.6,1.8,2.0	-0.723
G₁₂/GPa	3,4,4.5,5,6	-0.303
XT/MPa	700,800,900,1000,1100	0

Fig.4 Architecture of ANN model

Fig.5 Architecture of S-ANN thickness equivalent model

Table 4 The values of input variables for FEA model

输入变量	数值
比例距离/(m·kg^-1/3)	1.2,1.6,2.0,2.4
密度/(g·cm^-3)	1.5,1.8,2.1,2.4
厚度/mm	2,4,6,8,10
面内方向弹性模量/GPa	40,60,80,100

Fig.6 The relative error of predicted results on training set

Fig.7 Verification of predicted results of S-ANN equivalent thickness model

Fig.8 Predicted results of maximum deflection

Table 5 Pearson correlation coefficient between input variables and maximum deflection

变量	D	E₁₁	ρ	T
Pearson系数	-0.2846	-0.2481	-0.0520	-0.8536

Fig.9 Predicted results of equivalent thickness

Table 6 Performance of different fiberglass radomes[8]

玻璃纤维类型	ρ/ (g·cm^-3)	E₁₁/ GPa	介电常数ε	损耗角正切 tanδ
E-glass	1.78	48.2	4.04	0.014
S-glass	1.74	54.7	3.44	0.014
M-glass	1.94	60.5	4.62	0.009
D-glass	1.47	31.7	3.22	0.006
石英玻璃	1.54	37.5	3.32	0.005
高硅氧玻璃	1.61	34.3	2.94	0.012

Fig.10 Thickness equivalence curves among different glass fiber radomes

Fig.11 Tensile test and explosion impact test

Fig.12 Tensile test and explosion impact test

Table 7 Comparison of the maximum deflections of E-glass and quartz glass laminates

编号	比例距离/ (m·kg^-1/3)	试件	W/mm
编号	比例距离/ (m·kg^-1/3)	试件	试验结果	仿真结果	误差/%
1	1.6	E-glass	24.0	22.3	7.1
2	1.6	石英玻璃	23.5	22.6	3.8
3	2.0	E-glass	18.5	17.6	4.9
4	2.0	石英玻璃	18.5	17.8	3.8

Fig.13 Schematic diagram of electromagnetic wave incident obliquely on glass fiber radome

Fig.14 Electromagnetic simulation model of glass fiber radome

Fig.15 Frequency response characteristics of transmission efficiency of quartz glass radome at oblique incidence (vertical polarization)

Fig.16 Frequency response characteristics of transmission efficiency of quartz glass radome at oblique incidence (parallel polarization)

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