Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 293 Thai and Choi [54] as shown in Tab.2. It can be observed that the results are in very good agreement with those predicted by Thai and Choi [54]. / a b / a h Theory Power law index ( k ) 0 0.5 1 2 5 10 0.5 5 Ref (49) 11.3952 11.2331 11.1780 11.2018 11.3593 11.4558 Present 11.3959 11.2335 11.1783 11.2019 11.3587 11.4557 10 Ref (49) 11.7257 11.4992 11.4270 11.4530 11.6243 11.7093 Present 11.7259 11.4993 11.4271 11.4529 11.6239 11.7092 20 Ref (49) 11.8246 11.5780 11.5005 11.5273 11.7054 11.7886 Present 11.8246 11.5781 11.5005 11.5272 11.7053 11.7885 1 5 Ref (49) 15.3904 14.8757 14.6305 14.5004 14.5843 14.6636 Present 15.3923 14.8768 14.6313 14.5006 14.5830 14.6635 10 Ref (49) 16.1728 15.4895 15.1887 15.0455 15.1497 15.2045 Present 16.1735 15.4898 15.1890 15.0455 15.1488 15.2043 20 Ref (49) 16.4249 15.6851 15.3663 15.2209 15.3414 15.3929 Present 16.4251 15.6852 15.3663 15.2209 15.3411 15.3928 2 5 Ref (49) 28.6467 26.8009 25.7640 24.9077 24.5036 24.4352 Present 28.6591 26.8086 25.7703 24.9109 24.4983 24.4367 10 Ref (49) 32.3893 29.7133 28.3322 27.2931 26.8741 26.6994 Present 32.3937 29.7163 28.3346 27.2932 26.8675 26.6951 20 Ref (49) 33.8869 30.8606 29.3467 28.2628 27.9294 27.7426 Present 33.8882 30.8614 29.3474 28.2627 27.9267 27.7419 Table 2 : Dimensionless fundamental frequency  of rectangular plates ( 100) w s k k   , 2 ˆ ( ) / m m a E h     In order to analyse the effect of porosity on the natural frequency of FGM plates, numerical results are presented in Tabs. 2-6 and graphically plotted in Figs. 2-4. a/h k ξ=0 ξ=0.1 ξ=0.2 SSDT Present SSDT Present SSDT Present 5 0 0.4150 0.4152 0.4208 0.4210 0.4274 0.4276 0.5 0.3550 0.3552 0.3548 0.3550 0.3544 0.3546 1 0.3204 0.3206 0.3144 0.3146 0.3062 0.3062 2 0.2892 0.2895 0.2754 0.2756 0.2550 0.2554 5 0.2665 0.2674 0.2470 0.2480 0.2158 0.2170 10 0.2554 0.2563 0.2352 0.2364 0.2026 0.2042 10 0 0.1134 0.1134 0.1149 0.1149 0.1167 0.1167 0.5 0.0963 0.0963 0.09616 0.09616 0.09592 0.09598 1 0.0868 0.0868 0.08498 0.08504 0.08256 0.08256 2 0.0788 0.0788 0.07480 0.07480 0.06896 0.06896 5 0.07398 0.07410 0.06858 0.06870 0.05978 0.05988 10 0.07144 0.07150 0.06616 0.06628 0.05738 0.05754 20 0 0.02908 0.02908 0.02948 0.02948 0.02992 0.02992 0.5 0.02464 0.02464 0.02460 0.02460 0.02454 0.02454 1 0.02222 0.02222 0.02174 0.02174 0.02110 0.02110 2 0.02018 0.02018 0.01915 0.01915 0.01762 0.01763 5 0.01910 0.01910 0.01770 0.01771 0.01541 0.01542 10 0.01847 0.01848 0.01715 0.01715 0.01491 0.01492 Table 3 : The first non-dimensional frequencies ෝ 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 =K s =0)