Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 295 a/h k ξ=0 ξ=0.1 ξ=0.2 SSDT Present SSDT Present SSDT Present 5 0 0.4494 0.4496 0.4576 0.4578 0.4668 0.4670 0.5 0.3984 0.3986 0.4024 0.4026 0.4068 0.4068 1 0.3702 0.3704 0.3700 0.3702 0.3688 0.3690 2 0.3464 0.3466 0.3408 0.3410 0.3318 0.3320 5 0.3314 0.3320 0.3230 0.3238 0.3084 0.3090 10 0.3246 0.3252 0.3170 0.3176 0.3084 0.3042 10 0 0.1214 0.1215 0.1236 0.1237 0.1260 0.1261 0.5 0.1067 0.1067 0.1076 0.1076 0.1085 0.1085 1 0.09884 0.09884 0.09846 0.09846 0.09778 0.09784 2 0.09250 0.09256 0.09064 0.09064 0.08772 0.08772 5 0.08932 0.08940 0.08672 0.08678 0.08212 0.08218 10 0.08766 0.08772 0.08536 0.08542 0.08120 0.08132 20 0 0.03108 0.03108 0.03164 0.03164 0.03224 0.03224 0.5 0.02722 0.02722 0.02742 0.02742 0.02766 0.02766 1 0.02518 0.02518 0.02508 0.02508 0.02488 0.02488 2 0.02360 0.02360 0.02308 0.02308 0.02230 0.02230 5 0.02288 0.02288 0.02218 0.02218 0.02096 0.02096 10 0.02246 0.02246 0.02186 0.02186 0.02078 0.02078 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 =100, K s =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). 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   .