Propagation of electromagnetic waves in laminated periodic composite structures

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138.6 Propagation

of

Electromagnetic Waves in Laminated

Periodic Composite Structures

Huann-Ice Chiu, Hsiao-Ckang Chu. and Chun Hsiung Chen Department of Electrical Engineering, National Taiwan University.

Taipei, Taiwan 10617

A b s t r a c t

A new model based on filament-current and thin-current assumptions

together with suitable phase correction is proposed for discussing the electromagnetic fields in a multi-layered and lossy periodic composite structure which has circular conductiIig fibers embedded in a dielectric matrix. In this

study, numcrical results for graphitc/cpoxy

(G/E)

composites are presented

and compared with previous investigation. This new model is useful in char-

acterizing the composite materials even up to the higher frequency range. I n t r o d u c t i o n

Advanced composite materials have recently been suggested as substi- tutes for metals in modern aircraft systems due to their superior mechanical properties. But the shieldiiig and reflection properties of advanced composite

materials are significantly different from those of metals, making the study

of their electromagnetic characteristics an important issue in electromagnetic

compatibility

(EPIC).

Previous electromagnetic investigations of composite materials were mostly in the lower frequency range in which the fiber spacing is much less than the wavelength. Under such a condition, the composite material may be modeled as a laminated anisotropic medium and bulkily represented by a

complex permittivity tensor

[l].

But this bulk tensor model is inadequate in

analyzing the reflection and transmission characteristics in higher frequency range in which the fiber spacing is comparable to the wavelength.

In higher frequency range, the composite material should be modeled as a lossy periodic structure of having conducting fibers embedded in a di-

electric matrix. Recently, a filament-current phase-correction model

[a]

has

been proposed to analyze its higher frequency effect for the

T M

case. Hovv- ever, only single-layer composite structures are analyzed. In this study, a simplified model is proposed to analyze the plane-wave shielding and reflection properties of a laminated periodic fiber-matrix composite structure.

Formulation

Consider an electromagnetic propagation problem in which a plane

wave i s obliquely incident upon an N-ply laminated periodic composite struc-

ture as shown in Fig. 1. Each individua.1 lamina has conducting fibers of radius a and conductivity D embedded in a dielectric matrix of thickness

t

0-7803-4178-3/97/$10.00

0

1997

IEEE

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and dielectric. constant e,. The periodic spacing is d and the strilcture is uniform in Q’ direction.

LVe first use the filament-current model [2] to discuss the induced current along the fiber direction in each fiber and assume that the fiber current is concentrated along the fiber center. We then use the thin-current model to treat the induced current perpendicular to the fiber direction and assume that the induced current is concentrated on the plane z’ =

0.

Next, the scat- tering effect of the fibers is dealt with by calculating the scattered field from the induced currents both parallel and perpendicular to the fiber direction. Finally, by including the effect of the dielectric matrix. multiple reflection and transmission at the air-matrix interfaces, as well as the phase correction across the fiber grating [2], one may obtain the reflected and transmitted Floquet mode fields from which the shielding effectiveness

( S E )

and reflection loss

( R )

may be calculated.

Results

.A

comparison of our results for a single-layer

G/E

composite with those of Lin [I] is shown in Fig. 2. The effect of varing the layer number :V is presented in Fig. 3 , where the results of Lin [l] are also included. Good agreement between both results again supports the superiority of the bulk tensor model [l] in the lower frequency range

(f

<

10’ Hz). Fig. 4 shows the effect of varing the incident angle 8 for 4-ply

G/E

composite. Results of the

bulk tensor model and the approximate model which only takes the filament current into consideration ace also included for comparison. It is found that there is no evident distinction for the incident angle 8

<

70”.

Conclusion

A new model based on filament-current and thin-current assumptions

together with suitable phase correction has been proposed to analyze the

propagation chaxacteristics of a multilayer composite material. This model

can efficiently handle the complicated laminated periodic structure with re-

duced

CPU

time in computation even up t o the higher frequency range.

Acknowledgment

Republic of China under Grant NSC 56-2213-E-002-020.

References

[I]

&I.-S.

Lin and C.

H.

Chen, “Plane-wave shielding characteristics of

anisotropic laminated composites,”

IEEE

Trans. Electromagn. Compat.,

[2]

H.-C.

Chu arid

C. H.

Chen, “Shielding and Reflection Properties

of Periodic Fiber-Matrix Composite Structures,’IEEE Trans. Electromagn.

Compat., vol. 35. no. 1, pp. 1-6, Feb. 1996.

This study was supported by the National Science Council of Taiwan,

vol. 35, no. 1, pp. 21-27, Feb. 1993.

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(dB)

8=0°.E,=3.3 , a = 6 . 6 7 ~ 1 d S / m

300r---l

1 = d , a=0.337 d , d = 1.016 ,' X

t

I

1 reflected

(Bi

,

Bb)

wave

incident

wave

c

d,-

(A'~,A:)

I \

I

&- I Z' Y x

Fig.

1. Geometry of N-ply laminated periodic composite structures. Lin [ i l 200

.

-

Thistheorj

_ _ - -

100. O t - - - l 40

Fig.

2. Comparison of shielding effectiveness

(SE)

and reflection loss

(R)

for single-layer GIE composite

with those of Lin [l].

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(dB)

i 3= ,'O E,= 3.4 , U = 6.67xI&S/m t = d ~ a.0.437 d , d =0.127 mm

2.

_ _ - - -

_ _ _ _ _ _ _ _ _ - - -

SE

100

R

* o .

10

'

,

'.

\.

15C 1

oc

SE

50 0 40 20 0 f = 1 0 6 H z , Er=3.1, U =6.67xl$S/m t = d , a=0.137 d , d = 0.127

- - .

Lin [ I 1

-

Thistheory Only filament-current

'A

O0

30' 60' goo

e

Fig. 3.

SE

and

R of

G/E

composite

with

N

(number

of

layers) as parameters. Also included are results of Lin

[l]

for

comparison. comparison.

Fig.

4.

SE

and

R of

4-ply

G/E

composite

with

different incident angle 0. Results of Lin

[l]

are also included for