Research Article
On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory
Table 1
The first two natural frequencies (Hz) of the piezoelectric FGM, S-S (
, ).
| | Source | Number of elements | Computational time (s) | Mode 1 | Mode 2 | | | | | | |
| | CBT-Exact [12] | — | — | 435.309 | 374.916 | 349.683 | 1691.218 | 1453.180 | 1353.334 | | FBT-Exact [12] | — | — | 428.399 | 368.360 | 339.793 | 1600.435 | 1368.370 | 1230.287 | | PBT-Exact [12] | — | — | 427.996 | 368.151 | 337.747 | 1594.783 | 1365.460 | 1207.247 | | SBT-Exact [12] | — | — | 427.979 | 368.172 | 337.624 | 1594.517 | 1365.688 | 1205.928 | | EBT-Exact [12] | — | — | 427.974 | 368.205 | 337.529 | 1594.398 | 1366.072 | 1204.915 | | This work | 4 | 0.869 | 424.300 | 368.400 | 345.600 | 1683.70 | 1458.00 | 1264.400 | | 6 | 0.874 | 423.100 | 367.400 | 344.700 | 1656.10 | 1434.20 | 1263.200 | | 8 | 0.884 | 422.600 | 367.200 | 344.600 | 1648.700 | 1427.500 | 1262.800 | | 10 | 0.941 | 422.500 | 367.000 | 344.300 | 1645.900 | 1425.400 | 1262.600 | | 12 | 0.995 | 422.500 | 366.900 | 343.500 | 1644.200 | 1423.800 | 1262.400 |
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