PSI - Issue 14

Rahul Saini et al. / Procedia Structural Integrity 14 (2019) 362–374 R. Saini, S. Saini, R. Lal, and I. V. Singh / Structural Integrity Procedia 00 (2018) 000–000

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4.2. Parametric discussion To analyze the effect of various parameters on frequency parameter Ω , the results have been presented in Figs. 3-6, however for selected data the numerical values are also given in Table 3. From the results, it has been noticed that the values of Ω for S-plate are smaller than that for the corresponding C-plate. The value of Ω is found to decrease with the increasing value of i.e. as the nature of plate changes from ceramic to metallic for both the boundary conditions for the same set of the values of other parameters. The effect of temperature difference ∆ on Ω for an FGM plate with � � for two type of plate materials: (i) when the material properties are taken as TI; (ii) when the material properties are TD and varying nonlinearly in thickness direction for ∗ � ���� ��� has been shown in Fig. 3. Ω is found to decrease with the increasing values of ∆ for both the C and S-plates, whatever be the values of other parameters. It can be seen that the values of Ω for TD material are less than those for TI material for the same set of the values of other parameters. This effect is more pronounced for C-plate as compared to S-plate and increases with the increase in the number of modes. It has been noticed that the rate of decay in the value of Ω increases as the nature of in-plane force changes from tensile to compressive for both the plates. This rate of decay decreases with the increase in the number of modes. As a special case, a study for uniform temperature distribution (UTD): � � � � � � � ∆ as well as linear temperature distribution (LTD): � � � � � ∆ �� � ������ ∗ in equation (5) have been made. These numerical results together with non-linear temperature distribution (NTD) have been plotted in Fig. 4 for varying value of ∆ , for ∗ � ���� �� and fixed value of � � . It has been noticed that Ω decreases with the increase in the values of ∆ for all the three types of temperature distributions in the order UTD > LTD > NTD for both C and S-plates. The rate of decay for UTD is much higher as compared to LTD as well as NTD for the same set of the values of other parameters. This decay is higher for compressive force as compared to the tensile for both the plates and more pronounced in case of S-plate as compared to C-plate, keeping other parameters fixed. Fig. 5 presents the behaviour of Ω for varying values of ∗ for two values of � �� �� and ∆ � ��� for C and S-plates. It can be seen that the value of Ω increases with the increase in the value of ∗ for both the values of , keeping other parameters fixed. The rate of increase for � � is higher than that for � � .

Fig. 3. Ω vs ∆T, ∗ � ��� : ‘○’- TI, ‘ △ ’- TD; ∗ � ��� : ‘●’- TI, ‘ △ ’- TD; C - plate - ‘────’, S - plate - ‘- - - - - -’. The numerical results for critical buckling load � ∗ � have been plotted in Fig. 6a for � �� � and ∆ � ��� when the plate is vibrating in first mode of vibration. It has been noticed that the values of � ∗ � for C-plate are higher than that for the corresponding S-plate. The values of � ∗ � decrease with the increase in the value of from 0 to 5 i.e. as the nature of plate changes from fully ceramic (isotropic) to metallic. Two-dimensional mode shapes for a specified plate with � �� ∗ � �������∆ � ��� have been presented in