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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Table 2. Fundamental dimensionless natural frequencies of a simply supported FG-O 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 46.9908 0.14 0 52.1355 0.17 0 57.6289 1 46.8211 1 52.1274 1 57.6286 2 46.6532 2 52.1193 2 57.6282 3 46.4872 3 52.1112 3 57.6278 4 46.3228 4 52.1031 4 57.6274 5 46.1603 5 52.095 5 57.627 6 45.9994 6 52.0869 6 57.6266 7 45.8402 7 52.0788 7 57.6263 Table 3. Fundamental dimensionless natural frequencies of a simply supported FG-X 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 77.0617 0.14 0 86.4449 0.17 0 95.1415 1 76.7834 1 86.4315 1 95.1409 2 76.5082 2 86.418 2 95.1402 3 76.2358 3 86.4046 3 95.1396 4 75.9664 4 86.3912 4 95.139 5 75.6997 5 86.3778 5 95.1383 6 75.4359 6 86.3644 6 95.1377 7 75.1748 7 86.351 7 95.1371

Table 4. Fundamental dimensionless natural frequencies of a simply supported UD CNT reinforced square plate, with x 0

* = 0.1 - 0.9.

* CNT V

* CNT V

* CNT V

* CNT V

Natural frequency

Natural frequency

Natural frequency

Natural frequency

*

*

*

*

x 0

x 0

x 0

x 0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

18.686 16.5786 14.7514 13.6464 13.2854 13.6464 14.7514 16.5786 18.686

0.11

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

63.6513 63.2526

0.14

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

71.3513 71.3319 71.308 71.2886 71.2812 71.2886 71.308 71.3319 71.3513

0.17

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

78.6041 78.6031 78.602 78.6011 78.6007 78.6011 78.602 78.6031 78.6041

62.77

62.3875 62.2433 62.3875

62.77

63.2526 63.6513

5. Conclusion In this investigation, the aim was to assess the dynamical behaviour of a CNT reinforced plates with mass imperfections by utilising the Kirchhoff plate theory, the Hamilton principle and the modal decomposition method. The CNT distributions of UD, FG-O, and FG-X are employed in the thickness direction of the CNT reinforced plate. This study has identified that:  The introduction of CNT into the PmPV plate as reinforcement increases the natural frequency in all cases.  The thicker the CNT reinforced/non-reinforced plate is, the higher the dimensional natural frequency is.