PSI - Issue 45

Oscar Zi Shao Ong et al. / Procedia Structural Integrity 45 (2023) 140–147 O.Z.S. Ong et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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0.25 4 b a   .

Fig. 3. Fundamental natural frequencies of a simply supported UD CNT reinforced plate, with /

Now, focusing on the effects of the reinforcement and mass imperfection magnitude, the dimensionless fundamental natural frequency of the SSSS CNT reinforced square plate with mass imperfection, while varying the mass imperfection, M , between 0 to 7 kg, with CNT distribution of UD, FG-O, and FG-X, are tabulated in Tables 1, 2, and 3, respectively. The mass imperfection is situated at the middle of the plate ( x 0 = 0.5 & y 0 = 0.5). As demonstrated in Table 1, the introduction of mass imperfection leads to a decrease in natural frequency, for all cases, however, more evident for the cases of lower CNT volume fractions. This is due to higher CNT volume fractions leads to stiffer plate, making the CNT reinforced plate less likely to be influenced by the mass imperfection. As presented in the tables, these results indicate that FG-X CNT reinforced plate has the highest natural frequency, followed by UD, and FG-O having the lowest natural frequency. Finally yet importantly, the effects of the position of the mass imperfection needs to be understood. Setting M = 7 kg and y 0 = 0.5, the fundamental dimensionless natural frequency of the UD CNT reinforced square plate, while varying x 0 between 0.1 and 0.9, is tabulated in Table 4. A symmetrical result of natural frequency is obtained, about the center of the plate ( x 0 = 0.5). Moving the mass imperfection along the x axis in either direction results in higher natural frequency, showing the decreasing effect of mass imperfection. Similar results are achieved varying y 0 while maintaining x 0 = 0.5 because of the square shape nature of the plate. Not much changes are visible for the case of higher CNT volume fraction, demonstrating the effect of UD CNT reinforcements dampening the effect of the mass imperfection. Table 1. Fundamental dimensionless natural frequencies of a simply supported UD CNT reinforced square plate, with M = 0 – 7 kg. * CNT V M (kg) Natural frequency * CNT V M (kg) Natural frequency * CNT V M (kg) Natural frequency 0.11 0 63.8056 0.14 0 71.3588 0.17 0 78.6044 1 63.5752 1 71.3477 1 78.6039 2 63.3473 2 71.3366 2 78.6034 3 63.1218 3 71.3255 3 78.6028 4 62.8987 4 71.3144 4 78.6023 5 62.6779 5 71.3033 5 78.6018 6 62.4595 6 71.2923 6 78.6013 7 62.2433 7 71.2812 7 78.6007