Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24

a/h k

ξ=0

ξ=0.1

ξ=0.2

SSDT 0.4494 0.3984 0.3702 0.3464 0.3314 0.3246 0.1214 0.1067 0.09884 0.09250 0.08932 0.08766 0.03108 0.02722 0.02518 0.02360 0.02288 0.02246

Present 0.4496 0.3986 0.3704 0.3466 0.3320 0.3252 0.1215 0.1067 0.09884 0.09256 0.08940 0.08772 0.03108 0.02722 0.02518 0.02360 0.02288 0.02246

SSDT 0.4576 0.4024 0.3700 0.3408 0.3230 0.3170 0.1236 0.1076 0.09846 0.09064 0.08672 0.08536 0.03164 0.02742 0.02508 0.02308 0.02218 0.02186

Present 0.4578 0.4026 0.3702 0.3410 0.3238 0.3176 0.1237 0.1076 0.09846 0.09064 0.08678 0.08542 0.03164 0.02742 0.02508 0.02308 0.02218 0.02186

SSDT 0.4668 0.4068 0.3688 0.3318 0.3084 0.3084 0.1260 0.1085 0.09778 0.08772 0.08212 0.08120 0.03224 0.02766 0.02488 0.02230 0.02096 0.02078

Present 0.4670 0.4068 0.3690 0.3320 0.3090 0.3042 0.1261 0.1085 0.09784 0.08772 0.08218 0.08132 0.03224 0.02766 0.02488 0.02230 0.02096 0.02078

0

0.5

5

1 2 5

10

0

0.5

10

1 2 5

10

0

0.5

20

1 2 5

10

Table 6 : The first non-dimensional frequencies ˆ  of Al/Al 2 O 3

square plate for various porosity parameters, power law indices and

thickness ratios (a=10h, n=m=1, K w =10). Tab. 3-6 present the natural frequencies of FGM plates resting on elastic foundation for different values of porosity parameter ( 0,   0.1,   0.2)        , and elastic foundation parameters. It can be seen that the results are in excellent agreement with those of Sinusoidal plate theory given by Zenkour, it is also concluded that the increase of porosity parameter leads to increase of natural frequency. It can be shown that the frequencies are increasing with the existence of (Winkler and Pasternak parameters). =100, K s

Figure 2 : Variation of the natural frequency of the FGM plates according to the material power index k, mode1, a=b.

Figure 3 : Influence of thickness ratio on the frequency of the plate FGM, mode 2, ξ=0, ( 100) w s K K   .

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