PSI - Issue 14

12

R. Saini, S. Saini, R. Lal, and I. V. Singh / Structural Integrity Procedia 00 (2018) 000–000

Rahul Saini et al. / Procedia Structural Integrity 14 (2019) 362–374

373

Fig. 6. C - plate - ‘────’, S - plate - ‘- - - - - -’; (a) Ω vs � ∗ � : ‘○’- � , ‘ △ ’- � � , ‘□’- � � , ‘⁎’- � � ; (b) First three mode shapes.  Ω � � Ω � , for same set of the values of parameters.  For both C and S-plates, the frequency parameter Ω for fully ceramic plate ( Ω ��� � is always higher than that for the corresponding FGM plate ( Ω ��� ).  The value of Ω decreases with the increase in the value of temperature difference and it is found that Ω ∆��� � Ω ∆��� , whatever be the values of other parameters. The percentage decrease in the value of Ω for � �� ∗ � � with the change in temperature difference ∆ to 400 are 6.58, 7.86 for C, S-plates, respectively, with TD material properties, when the plate is vibrating in the first mode. These variations are differing only at the first place of decimal for fully ceramic plate. In view of the TI material properties, the percentage variation in Ω with varying values of ∆ from to 400, for � � � ∗ � � are -3.81 and -5.69 for C and S-plates, respectively. However, for ∗ � �� , values do not exist due to buckling.  The behaviour of Ω with the change in the nature of temperature distribution from NTD to LTD and then to UTD is found in the order of Ω ��� � Ω ��� � Ω ��� . The percentage variation in the values of Ω with varying values of ∆ from to 400 for � �� for UTD, LTD and NTD are (-15.39, -7.50, -6.58) and (-18.35, -9.06, -7.86) for ∗ � � while values do not exist due to buckling for ∗ � �� for both the plates vibrating in the first mode of vibration.  The value of critical buckling load � ∗ � decreases as the nature of the plate changes from ceramic to metallic i.e. changes from 0 to 5 for both the plates. The above analysis will be of great practical use to a design engineer dealing with FGM plates in obtaining the desired frequency by controlling one or more parameters involved in the present study.