Fabrication and design of multi-layered radar absorbing structures of MWNT-filled glass/epoxy plain-weave composites
Sang-Eui Lee, Ji-Ho Kang, Chun-Gon Kim
*Department of Mechanical Engineering, Division of Aerospace Engineering, Korea Advanced Institute of Science and Technology (KAIST), 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
Available online 6 January 2006
Abstract
The object of this study is to design radar absorbing structures (RAS) with load-bearing ability in the X-band. Glass/epoxy plain- weave composites of excellent specific stiffness and strength, containing multi-walled carbon nanotubes (MWNT) to induce dielectric loss, were fabricated. Observations of the microstructure and the permittivity of the composites confirmed that the fabrics are suitable for use as RASs. A genetic algorithm and a theory of the reflection/transmission of electromagnetic waves in a multi-layered RAS were applied to design an optimal RAS composed of MWNT-filled composites. The thickness per ply was observed to vary, depending on the number of plies and the MWNT contents. A fabrication process was proposed that considered the variation. The proposed process was in the fabrication of a designed RAS, and the theoretical and measured reflection losses of the RAS were found to be in good agreement.
2005 Elsevier Ltd. All rights reserved.
Keywords: X-band frequency; Permittivity; Radar absorbing structure; Multi-walled carbon nanotube
1. Introduction
Radar cross section (RCS) reduction technology, which protects aircraft against radar detection, has become essen- tial in contemporary warfare high-tech high-performance equipment. This technology is categorized into: shaping of aircrafts, radar absorbing materials (RAMs) and radar absorbing structures (RASs). The shaping is to design the external features of the aircraft to reduce the electromag- netic (EM) waves backscattered to the radar source direc- tion. The RAM and RAS are developed to absorb the EM energy and thereby minimize reflected waves. In gen- eral, the shaping conflicts with the design to improve the aerodynamic performance. Therefore, the developments of RAM and RAS have become essential for RCS reduction.
In general, RAMs have been fabricated in the form of sheets that consist of insulating polymer, like rubber, and
magnetic or dielectric loss materials, such as ferrite, perm- alloy, carbon black, and short carbon fiber. RAMs have the strong advantage of being easily applied to the surfaces of existing structures; however, RAMs increase structure weights and have poor mechanical and environment-resis- tant properties. Thus, RAMs cannot be used as load-bear- ing structures and they require constant maintenance and repair[1].
A RAS is composed of continuous fiber–reinforced composites and lossy materials which are mixed and dis- persed into the matrix of the composites. The EM proper- ties of these composites can be also tailored by controlling the content of the lossy materials. Therefore, RASs avoid the disadvantages of RAMs due to the high stiffness and strength of the composites involved and they are also able to have the same EM energy dissipating ability of RAMs.
The characteristics of the composites to be stacked ply by ply facilitate multi-layered structures, which are necessary to broaden absorption bandwidth. On the other hand, each ply of the composite prepreg has a finite and discrete thick- ness, and its thickness per ply changes according to the
0263-8223/$ - see front matter 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruct.2005.11.036
* Corresponding author. Tel.: +82 42 869 3719; fax: +82 42 869 3710.
E-mail address:[email protected](C.-G. Kim).
www.elsevier.com/locate/compstruct
number of plies and the content of the lossy materials involved. Therefore, achieving the precise thickness of a designed RAS is difficult.
For a lossy filler to be highly effective, it should have a high conductivity for shielding by reflection, a high aspect ratio for a conductive network, and a small size relative to the skin depth [2,3]. In this study, multi-walled carbon nanotube (MWNT) satisfying those requirements [4,5]
was selected as a lossy filler. Moreover, the MWNT is expected to act as a mechanical reinforcement[5].
The absorption and reflection of a RAS depend on a number of variables, including frequency, incident angle, polarization, and the permittivity, permeability and thick- ness of each layer of the RAS. To address these variables and produce an optimal RAS, optimal design concept is necessary. In previous studies, Powell’s method or a genetic algorithm (GA) has been used, and several objective func- tions have been proposed[6–9].
In this study, a program was coded to predict the reflec- tion loss of a multi-layered RAS for normal incident EM waves in the X-band (8.2–12.4 GHz); the code was linked with a GA to design the RAS. A fabrication process of the RAS was proposed that considered the nonlinear mea- sure of thickness per ply, depending on the number of plies and the content of MWNT. The practical applicability of the process was confirmed by the excellent agreement between the theoretical and measured reflection loss of a designed RAS.
2. Fabrication of MWNT-filled glass/epoxy plain-weave composites
2.1. Material and fabrication
The MWNTs used in this study, purchased from ILJIN nanotech Co. (South Korea), were synthesized via a chemical vapor deposition method with a carbon mass fraction of about 95%. The MWNTs were 10–25 nm in diameter and 10–50lm in length. A transmission electron microscopy (TEM) image of the MWNTs is shown in Fig. 1.
Glass/epoxy plain-weave composites, K618, were sup- plied by Hankuk Fiber Co. (South Korea). First, the MWNTs were dispersed in epoxy matrix. The fabric com- posites were impregnated by the mixture of the matrix and the MWNTs. Then, The MWNT-filled fabric composites were dried for 5–7 min at 100C. Drying times increased with MWNT contents. As the viscosity of the premixture increased rapidly over the 3.0 weight percent (wt.%), it
was difficult to maintain the uniformity of MWNTs in the matrix. The weight fraction of MWNTs to the total weight of the fabric, the epoxy system and the MWNTs is shown in Table 1. Specimens were cured and vacuum- bagged in an autoclave first for 30 min at 80C and then for 2 h at 130C. While the specimens were being cured, the pressure was stabilized at 3 atm.
2.2. Microstructure
The microstructure of the fabricated composites was captured by scanning electron microscopy (SEM).Figs. 2 and 3 show the SEM images of MWNT 1.0. Images of the matrix rich region and the interface between the glass
Fig. 1. TEM image of MWNT used.
Table 1
Denotation of MWNT-filled glass/epoxy plain-weave composites Denotation
MWNT 0.0 MWNT 0.4 MWNT 0.7 MWNT 1.0 MWNT 1.3 MWNT 1.6 MWNT 3.0 MWNT 5.0
MWNT content (wt.%) 0.0 0.4 0.7 1.0 1.3 1.6 3.0 5.0
Fig. 2. SEM image of MWNT 1.0.
fiber yarns in the warp and fill directions, shown inFig. 2, are enlarged inFig. 3(a) and (b). It can be observed from Fig. 3 that the MWNTs were distributed mainly in the matrix rich region and in the interface between the yarns;
in addition, the MWNTs did not penetrate far into the yarns. The uneven distribution of MWNT and glass fiber yarns is expected to induce a high dielectric loss by multi-reflection in the composites. Fig. 4 shows the microstructure of MWNT 3.0. It can be observed from Fig. 4 that porosity increases as the wt.% of the MWNT increases. This porosity also affects the permitti- vity, because it can enable multiple reflections in the materials.
3. Permittivity of MWNT-filled glass/epoxy plain-weave composites
3.1. Measurement
The cured composites were cut precisely to the dimensions of an X-band rectangular waveguide, 22.86· 10.16 mm, and were then inserted into the waveguide.
The S-parameter was measured by using a network ana- lyzer, HP 8722ES. The permittivities were calculated by using the phase change ofS21 in the composites[10]. The phase change should be more than 90in a specimen, which is why a specimen with low loss is required to be thick.
However, the high thickness caused the magnitude of S21 to be reduced to measurement limit, resulting in an mea- surement error. Thus, each specimen had a range of thick- ness that enabled precise permittivity calculation. The thickness, shown in Table 2, was determined considering as explained above. Thus, the thickness of MWNT 1.3 and MWNT 1.6 decreased compared to the other speci- mens. The air gap between the waveguide and the specimen affected the signal of S21, so that the gap was perfectly sealed up with silver paste.
3.2. Permittivity
Five specimens per MWNT content were used to mea- sure permittivity, as shown in Figs. 5 and 6. These figures revealed that the permittivities of all the specimens were nearly constant, regardless of frequency, and that they increased exponentially with the weight fraction of MWNT. The latter tendency was also found in the
Fig. 4. SEM image of MWNT 3.0.
Table 2
Thickness of specimen used for permittivity measurement Denotation
MWNT 0.0 MWNT 0.4 MWNT 0.7 MWNT 1.0 MWNT 1.3 MWNT 1.6
Thickness (mm) 15.0 15.0 15.0 15.0 5.0 3.0
Fig. 3. Enlarged SEM image of MWNT 1.0: (a) matrix rich region and (b) interface between yarns in warp and fill direction.
previous research[1,11], and it is believed to originate from a rapid buildup of the conductive network and the forming of porosities with increasing MWNT contents. From the above results, although MWNT 3.0 and MWNT 5.0 with
high filler contents were expected to have very high dielec- tric losses, they had low reproducibility of EM properties.
This result was due to the viscosity increase of the mixture of the epoxy matrix and the MWNT, leading to the poor impregnation of glass fiber yarns. Therefore, MWNT 3.0 and MWNT 5.0 were excluded from use as RAS materials.
4. Optimal design of a multi-layered RAS
4.1. Reflection and transmission of a multi-layered RAS
The condition that the whole incident energy is absorbed requires that the effective input impedance of a multi-layered RAS be identical to that of the free space.
Considering the entire multi-layered RAS shown in Fig. 7, the generalized reflection coefficient eRi;iþ1 at the interface between regioniandi+ 1 can be written as e
Ri;iþ1¼ Ri;iþ1þReiþ1;iþ2e2ikiþ1;zðdiþ1;diÞ
1þRiþ1;iReiþ1;iþ2e2ikiþ1;zðdiþ1;diÞ ð1Þ
Ri;iþ1¼liþ1ki;zlikiþ1;z
liþ1ki;zþlikiþ1;z ð2Þ
where Ri,i+1 is the reflection coefficient between region i and region i+ 1, considering only the reflection between the two regions. For a case in which the last layer consists of a metal or a carbon fiber reinforced composite with elec- trical conductivity corresponding to metals, the generalized reflection coefficient in the first layer is obtained by putting e
RN¼ 1 in Eq.(1)and calculating the reflection coefficient between each region sequentially.
4.2. Genetic algorithm
A genetic algorithm [12]is a search algorithm based on the mechanics of natural selection and genetics. It simulates natural evolution so that multiple design points evolve to converge to a global optimum. A GA combines the sur- vival of the fittest among string structures having a struc- tured, yet randomized, information exchange to form a search algorithm with some of the innovative flair of a
9 10 11 12
0 2 4 6 8 10 12 14 16 18 20
Real permittivity,ε r'
8.2 12.4
MWNT1.3 MWNT1.6 MWNT0.7
MWNT1.0
Frequency (GHz) MWNT0.0
MWNT0.4
9 10 11 12
0 2 4 6 8 10 12 14 16 18 20
MWNT1.3 MWNT1.6 MWNT0.7
MWNT1.0 MWNT0.0
MWNT0.4
8.2 12.4
Imaginary permittivity,εr''
Frequency (GHz)
Fig. 5. Relative permittivity of MWNT-filled composites with frequency.
0 4 8 12 16 20
1.6 1.0 1.3
0.0 0.4 0.7
Permittivity at 10.3 GHz
Wt% of MWNT εr'
εr''
Fig. 6. Relative permittivity of MWNT-filled composites with weight fraction of MWNT at 10.3 GHz.
Region N Region N-1 Region 3 Region 2 Region 1
z x
–d1 –d2 –d3
–dN–1
1 1,ε μ
2,ε2
μ
3 3,ε μ
4 4,ε μ
1 1, –
– N
N ε
μ
N N ε μ ,
Region 4
Fig. 7. Reflection and transmission in multi-layered RAS.
human search. In every generation, a new set of artificial strings is created using bits and pieces from the fittest of the old strings (which is called ‘crossover’ in the algorithm);
while an occasional new part is added for good measure (which is called ‘mutation’ in the algorithm). Its calculation process uses a nondeterministic scheme and exclusive of differentiability or convexity. The most useful advantage of this algorithm is that it uses discrete design variables by nature. Therefore, it is simple to use discrete values as design variables, such as the thickness of each layer and the stacking sequence of a multi-layered RAS. For this rea- son, a GA was selected as an optimal algorithm in this study.
4.3. Application of the GA
The optimal design algorithm was established by linking a GA with a reflection loss analysis of multi-layered RAS.
Fig. 8 shows the flow chart of the optimal design algo- rithm. The parameters used to solve the optimal design problem were set up through a number of optimizations and are shown inTable 3.
In this study, the thickness and permittivity of each layer were selected as design variables. The number of layers and the sweeping thickness to be simulated were specified as constraints to limit the design space, and the thickness per ply was fixed as 0.1 mm. The optimal design was per- formed 10 times by varying random number seeds and the distribution of the initial populations before the fittest of 10 cases was selected as an optimal solution.
The objective function was defined as follows.
F ¼ Z fmax
fmin
jCij2df ¼ XNF
i¼1
jCij2 fmaxfmin
NF1
ð3Þ If jCij2<20 dB, jCij2¼ 20 dB ð4Þ
where jCij2 in Eq. (3) refers to the ratio of the reflected power to incident one and NF represents the number of the points at which reflection loss is calculated. The objec- tive function refers to the area between the frequency axis and the reflection loss curve. By adding Eq. (4), the only area within 20 dB absorption, that means 99% absorp- tion of incident power, was maximized.
Generate initial population
Calculate Reflection Loss
Read Reflection Loss
Calculate fitness
Selection & reproduction
Crossover
Mutation
Converge ? Make input for R.L.
Assign constraints - maximum thickness - the n umber of la yer - stand ard of abso rp tio n
START
END
- Transmi ssion l ine m eth od
yes no
Fig. 8. Flow chart of genetic algorithm linked with calculation program of reflection loss.
Table 3
Parameters of genetic algorithm
Parameters Value
Population size 200
Probability of crossover 0.7
Probability of mutation 0.05
Convergence limit
# of successive same best designs 50
Error of the average value 0.01%
Selection parameter
Tourney size 10
Table 4
Optimal results of two-layered RAS
Case Material Thickness (mm) Fitness
1st layer 2nd layer 1st layer 2nd layer
1 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
2 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
3 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
4 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
5 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
6 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
7 MWNT 1.6 MWNT 0.0 0.3 2.5 62.2
8 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
9 MWNT 0.4 MWNT 1.6 1.9 1.4 64.9
10 MWNT 1.3 MWNT 0.0 0.9 1.5 59.9
9 10 11 12
-50 -40 -30 -20 -10 0
8.2 12.4
Reflection loss (dB)
Frequency (GHz)
Fig. 9. Reflection loss of the optimal RAS of MWNT 0.4 (1.9 mm) and MWNT 1.6 (1.4 mm).
4.4. Result of the optimal design
Optimal design was performed for a two-layered RAS.
The maximum thickness to be simulated was limited to 3.5 mm. The back surface of the RAS was assumed to be a perfect conductor. Table 4 shows the design results. Of 10 simulated cases, the RAS with the largest absorption bandwidth was composed of MWNT 0.4, with a thickness of 1.9 mm, and MWNT 1.6, with a thickness of 1.4 mm.
The reflection loss of this RAS is shown inFig. 9. It had a 10 dB absorbing bandwidth over the entire X-band, and had a20 dB absorbing bandwidth of 1.0 GHz (9.1–
10.1 GHz).
5. Fabrication of a multi-layered RAS and measurement of reflection loss
5.1. Free space measurement system
The free space technique system used in this study for measuring the reflection loss of transverse electromagnetic (TEM) waves is shown inFig. 10. The system consists of a pair of spot-focusing horn lens antennas, a sample holder, an HP 8510C network analyzer and a computer for data acquisition. The width and length of the aluminum table are 1.83 m and 1.83 m, respectively, and the standard size of the sample specimens for holder is 150 mm·150 mm.
This system used the spot-focusing horn lens antennas for minimizing diffraction effects, the TRL (through- reflect-line) calibration technique and the time-domain gat- ing of the HP 8510C network analyzer for minimizing mul- tiple reflection[13].
5.2. Fabrication and measurement
The fabrication method of RAS is categorized into; the co-curing method and secondary bonding method. The lat- ter method requires an additional process to bond together the materials with different filler contents by using an adhe- sive film. Thus, the co-curing process is more advantageous in terms of cost, and so it was used to fabricate the multi- layered RAS.
A number of fabrications of MWNT-filled composites with various thicknesses revealed that the thickness per ply (TPP) decreased with an increase in the number of plies and that the TPP increased with the weight fraction of MWNT; the dependence of the TPP on the number of plies is due to the increase in compaction of composites with the number of plies, and the dependence of the TPP on the MWNT concentration results from the support of curing pressure by MWNTs. This nonlinear behavior of TPP, shown inTable 5, makes the precise thickness of a designed RAS difficult to be achieved. Therefore, the fabrication process in this study was established, based on the assump- tion that the TPP of each material in a designed multi-lay- ered RAS is similar to that of the material with the same thickness of the RAS.Fig. 11shows a schematic of fabrica- tion process that considers the nonlinearity of TPP. For a case in which a RAS,tRASin thickness, was designed com- posed of MWNT 0.4, with a thickness oft1, and MWNT 1.6, with a thickness of t2, it is difficult to determine the number of plies of each material (STEP 1). First, the sin- gle-layered RAS of each material is fabricated tRAS in thickness before its TPP is calculated (STEP 2). Then, the number of plies of each material, n1 and n2, is obtained by dividing the designed thickness, t1 and t2, by the TPP calculated in the previous step, TPP3 and TPP4
(STEP 3).
The above process was applied to the two-layered RAS of Section4. First, MWNT 0.4 and MWNT 1.6 was fab- ricated with a thickness of 3.3 mm, respectively. The MWNT 0.4 with 21 plies was 0.149 mm in TPP and 3.28 mm in total thickness. The MWNT 1.6 with 20 plies was 0.169 mm in TPP and 3.38 mm in total thickness (STEP 2). As the designed thicknesses of MWNT 0.4 and MWNT 1.6 was 1.9 mm and 1.4 mm, respectively,
Fig. 10. Free space measurement system.
Table 5
Ply thickness according to the number of plies and MWNT contents Material No. of plies Thickness (mm) Thickness/ply (mm)
MWNT 0.4 13 2.17 0.167
21 3.28 0.149
MWNT 1.6 9 1.47 0.184
20 3.38 0.169
MWNT 0.0 10 1.62 0.162
16 2.44 0.153
MWNT 1.3 6 1.11 0.185
15 2.39 0.159
the RAS was expected to have a thickness of 3.29 mm by using 13 plies for MWNT 0.4 (1.94 mm) and nine plies for MWNT 1.6 (1.35 mm) (STEP 3). As the TPP of each material was finite and discrete, not continuous, it was difficult to realize precisely the designed thicknesses of each material. However, the fabricated RAS had a thickness of 3.27 mm, which has only 0.02 mm
thickness difference compared to the predicted thickness of 3.29 mm.
The analytical and experimental reflection losses and the resonance frequency of the RAS are shown in Fig. 12 and Table 6. The analytical reflection loss of the designed RAS was identical to the reflection loss calculated with the thickness value that considered fabrication pro- cess. The results were found to be in good agreement, except that the resonance frequency shifted down by 0.3 GHz and that the 20 dB bandwidth became wider.
A high value of reflection loss over 30 dB is almost meaningless as it means the EM energy absorption of 99.9%.
5.3. Discrepancy between analysis and measurement
The main reasons behind the discrepancy between the analysis and the measurement are as follows: the MWNT transfer in the interface between composites with different filler contents; the difference between the specimen thick- nesses in permittivity measurement and those of materials in the designed RAS.
To observe the MWNT transfer in an interface, 10th RAS in Table 4 was fabricated including MWNT 0.0.
The inclusion of MWNT 0.0 facilitated the observation, because MWNT 0.0 has no MWNTs. The RAS was also obtained by conducting optimal design using a constraint on the sweeping thickness of 2.6 mm.
The RAS was expected to have a thickness of 2.49 mm by using six plies of MWNT 1.3 with 0.96 mm and 10 plies of MWNT 1.6 with 1.53 mm. The fabricated RAS had a thickness of 2.55 mm, having the reasonable thickness dif- ference of 0.06 mm, compared to the predicted thickness of 2.49 mm.
Fig. 13shows the cutting plane of the RAS. Although a distinct interface between MWNT 0.0 and MWNT 1.3 was observed, as shown in Fig. 13(b), the sinusoidal function- like pattern observed in Fig. 13(a) indicates the mixing of the matrices of the two layers and the MWNT transfer in the interface. There was little difference in frequency between both cases to observe. The ambiguity of the inter- face may lead to a resonance frequency shift and an absorbing bandwidth change.
The reflection loss and the absorbing bandwidth of the RAS are shown in Fig. 14 and Table 7. The analytical reflection losses for the designed thickness and for the thickness considering the fabrication process are shown with the measured reflection loss in Fig. 14. The
9 10 11 12
-70 -60 -50 -40 -30 -20 -10 0
Simulation: 3.30 (mm) [1.90 |MWNT0.4 + 1.40|MWNT1.6 ] Simulation: 3.29 (mm) [1.94 |MWNT0.4 + 1.35|MWNT1.6 ] Experiment: 3.27 (mm)
8.2 12.4
Reflection loss (dB)
Frequency (GHz)
Fig. 12. Comparison of reflection loss between simulation and experiment for the RAS of MWNT 0.4 and MWNT 1.6.
Table 6
Comparison between analysis and experiment for the RAS of MWNT 0.4 and MWNT 1.6
Thickness (mm) fr(GHz) 10 dB BW (GHz) 20 dB BW (GHz)
Simulation (using designed thickness) 3.30 9.5 4.2 (8.2–12.4) 1.0 (9.1–10.1)
Simulation (considering fabrication process) 3.29 9.5 4.2 (8.2–12.4) 1.0 (9.1–10.1)
Experiment 3.27 9.8 4.1 (8.3–11.6) 1.2 (9.2–10.4)
Fig. 11. Schematic of fabrication process considering nonlinearity of thickness per ply.
comparison between the simulation considering fabrication process and the experiment showed that the resonance fre- quency shifted about 0.3 GHz (9.6–9.9 GHz) and that the 10 dB absorbing bandwidth became broader 2.8–
3.1 GHz.
6. Conclusion
In this study, a MWNT was selected as a lossy filler with consideration for geometry and electrical conductivity. The MWNT was added into glass/epoxy plain-weave compos- ites to fabricate the materials used for RASs. The observa- tion of the microstructure of the composites revealed that the uneven distribution of MWNTs could induce a high dielectric loss, which was confirmed through the measure- ment of permittivity.
The optimal design of two-layered RAS, consisting of the MWNT-added glass/epoxy fabric composites, was per- formed by linking a GA with a program for the reflection/
transmission of electromagnetic waves in a multi-layered RAS. As a result, a two-layered RAS was designed having 90% absorption of EM energy for the entire X-band.
An RAS fabrication process was proposed that consid- ered the nonlinearity of thickness per ply with MWNT con- tents and the number of plies. The comparison between the theoretical and experimental reflection loss confirmed that the process is applicable to the fabrication of multi-layered RASs.
A study in progress aims to broaden the absorbing bandwidth of a RAS which is composed of a multi-layered RAS and a frequency selective surface.
Fig. 13. Cutting planes of the RAS of MWNT 1.3 and MWNT 0.0: (a) sinusoidal function-like interface and (b) distinct interface.
9 10 11 12
-70 -60 -50 -40 -30 -20 -1
0
8.2 12.4
Reflection loss (dB)
Frequency (GHz)
Simulation 1: 2.40 (mm) [0.90|MWNT1.3 + 1.50|MWNT0.0 ] Simulation 2: 2.49 (mm) [0.96|MWNT1.3 + 1.53|MWNT0.0 ] Experiment: 2.55 (mm)
0
Fig. 14. Comparison of reflection loss between simulation and experi- ment; for the RAS of MWNT 1.3 and MWNT 0.0.
Table 7
Comparison between analysis and experiment for the RAS of MWNT 1.3 and MWNT 0.0
Material Thickness (mm) fr(GHz) 10 dB BW (GHz) 20 dB BW (GHz)
Simulation (using designed thickness) 2.40 10.2 3.1 (8.9–12.0) 0.9 (9.7–10.6)
Simulation (considering fabrication process) 2.49 9.6 2.8 (8.4–11.2) 0.8 (9.2–10.0)
Experiment 2.55 9.9 3.1 (8.5–11.6) 0.9 (9.5–10.4)
References
[1] Oh JH. Design of electromagnetic wave absorbing structure using layered composite plates. PhD thesis (KAIST), 2003.
[2] Chung DDL. Electromagnetic interference shielding effectiveness of carbon materials. Carbon 2001;39:279–85.
[3] Shui X, Chung DDL. Submicron diameter nickel filaments and their polymer–matrix composites. J Mater Sci 2000;35:1773–85.
[4] Thess A, Lee R, et al. Crystalline ropes of metallic carbon nanotubes.
Science 1996;273(5274):483–7.
[5] Allaoui A, Bai S, Cheng HM, Bai JB. Mechanical and electrical properties of a MWNT/epoxy composite. Compos Sci Technol 2002;62:1995–8.
[6] Nam GJ, Lee SS. Optimum design of broadband RAM (radar absorbing material)’s using multi-layer dielectrics. J—Kor Inst Telemat Electron Ser A 1995;32(1):70–8.
[7] Guan JG, Gan ZP, Gao GH, Zhang QJ. Optimized design of multi- ingredient radar absorbing materials using genetic algorithms. Key Eng Mater 2003;249:367–72.
[8] Perini Jose, Cohen LS. Design of broad-band radar-absorbing materials for large angles of incidence. IEEE Trans Electromag Comp 1993;35(2):223–30.
[9] Kim JB, Kim TW, Kim CG. Optimizing design technique of broad band microwave absorbing composite laminates. In: Proceedings of 2004 annual conference, vol. II, the Korea Institute of Military Science and Technology, Daejeon, South Korea, August 2004. p.
489–92.
[10] Lee HS. Measurement of radar cross section of a coated cylinder with two plates. MS thesis (KAIST), 2002.
[11] Achour ME, Malhi ME, Miane JL, Carmona F, Lahjomri F.
Microwave properties of carbon black–epoxy resin composites and their simulation by means of mixture laws. J Appl Polym Sci 1999;73:969–73.
[12] Goldberg DE. Genetic algorithm in search, optimization, and machine learning. Addison-Wesley Publishing Company; 1989.
[13] Seo IS, Chin WS, Lee DG. Characterization of electromagnetic properties of polymeric composite materials with free space method.
Compos Struct 2004;66:533–42.
