Issue 50

H. Saidi et alii, Frattura ed Integrità Strutturale, 50 (2019) 286-299; DOI: 10.3221/IGF-ESIS.50.24 296 As the material power index increases for FGM plates, the dimensionless frequency will decrease. The variation curves of the natural frequency of the first mode of various functionally graded plates as a function of material power index parameter ‘’k’’, for different values of porosity was presented in Fig. 2. It can be seen that the increase of porosity parameter leads to an increase of the frequency of the first mode. Fig. 3 shows the influence of thickness ratio, on the natural frequency of FGM plates (ξ=0), the elastic foundation parameters are taken equal to ( 100) w s K K   . It can be seen that the ratio (a/h) has a considerable effect on the frequency of the FGM plate, (The later decreases with the increase of this ratio). Figure 4 : Effect of Pasternak shear modulus parameter on dimensionless frequency of FGM plates, a/h=10, k=2. Fig. 4 shows the effect of Pasternak parameters on the variation of the dimensionless frequency of FGM plate for different values of porosity. The results show that the frequency increases with the increase of Pasternak parameter and porosity index. C ONCLUSION his work proposes a new higher-order shears deformation theory for free vibration response of FG plates with porosity embedded in elastic medium. In this investigation the FGM plate are assumed to have a new distribution of porosity according to the thickness of the plate. The elastic medium is modeled as Winkler-Pasternak two parameter model to express the interaction between the FGM plate and elastic foundation. The four unknown shear deformation theory is employed to deduce the equations of motion from Hamilton’s principle. The Hamilton’s principle is used to derive the governing equations of motion. The accuracy of this theory is verified by compared the developed results with those obtained using others plate theory. Some examples are performed to demonstrate the effect of changing gradient material, elastic parameters, porosity index, and length to thickness ratios on the fundamental frequency of functionally graded plate. It has been demonstrated that the present analytical formulation can accurately predict natural frequencies of FG plates with porosity resting on elastic foundation. Also it can be concluded that the effect of volume fraction distributions, slenderness ratio and porosity on the non-dimensional frequency is significant . R EFERENCES [1] Koizumi, M. (1997), FGM activities in Japan, Compos Part B, 28, pp. 1–4. DOI: 10.1016/S1359-8368(96)00016-9. [2] Akbaş, Ş. D. (2015), Wave propagation of a functionally graded beam in thermal environments, Steel and Composite Structures, 19(6), pp. 1421-1447. DOI: 10.12989/scs.2015.19.6.1421. T