Rayleigh-Ritz Vibrational Analysis of Multiwalled Carbon Nanotubes Based on the Nonlocal Flügge Shell Theory
Table 2
Comparison between the present shell model and the beam model given in [30] for the first three natural frequencies of a double-walled CNT with different boundary conditions ().
Frequencies (THz)
Length (nm)
14
16
18
20
24
26
28
30
CC/SS
0.8760
0.6876
0.5531
0.4539
0.3208
0.2750
0.2383
0.2084
1.05
0.81
0.64
0.52
0.36
0.31
0.27
0.23
2.2109
1.7654
1.4385
1.1925
0.8548
0.7365
0.6407
0.5623
2.84
2.20
1.75
1.43
1.00
0.85
0.73
0.64
3.8679
3.1476
2.6038
2.1848
1.5944
1.3828
1.2098
1.0666
5.18
4.17
3.36
2.76
1.94
1.66
1.43
1.25
CC/FF
0.9290
0.7276
0.5843
0.4790
0.3381
0.2897
0.2509
0.2194
1.04
0.8
0.53
0.51
0.36
0.31
0.26
0.23
2.3230
1.8484
1.5027
1.2437
0.8898
0.7661
0.6662
0.5844
2.84
2.2
1.75
1.42
0.99
0.85
0.73
0.64
4.0609
3.2857
2.7080
2.2666
1.6491
1.4290
1.2493
1.1008
5.14
4.16
3.36
2.76
1.94
1.66
1.43
1.25
CC/CC
0.9277
0.7269
0.5839
0.4788
0.3380
0.2896
0.2509
0.2193
1.08
—
—
—
—
—
—
—
2.3176
1.8455
1.5010
1.2427
0.8893
0.7658
0.6660
0.5842
2.94
—
—
—
—
—
—
—
4.0420
3.2756
2.7021
2.2630
1.6475
1.4279
1.2484
1.1002
5.49
—
—
—
—
—
—
—
Based on the present shell model. Based on the beam model given by Xu et al. [30].
