Free Vibration Analysis of DWCNTs Using CDM and Rayleigh-Schmidt Based on Nonlocal Euler-Bernoulli Beam Theory

Table 9

First free frequencies of vibrations of DWCNTs with different boundary conditions between inner and outer tubes, (for 𝜂=0).

Boundary condition	Method	𝜔1	𝜔2	𝜔3	𝜔4	𝜔5	𝜔6	𝜔7
Fr-Fr inner	[15]	1.040	2.84	5.140	7.890	8.130	8.380	9.350
Cl-Cl outer	CDM	1.021	2.786	5.760	6.270	6.669	7.915	8.083
Fr-Fr inner	[15]	0.170	1.040	2.890	5.290	6.550	7.890	8.170
Cl-Fr outer	CDM	0.163	1.024	2.833	5.210	6.491	7.860	8.041
SS-SS inner	[15]	1.050	2.840	5.180	7.290	7.890	8.240	9.080
Cl-Cl outer	CDM	1.0219	2.789	5.104	7.212	7.914	8.243	9.010
Cl-Cl inner	[15]	1.080	2.940	5.490	7.900	8.130	8.240	—
Cl-Cl outer	CDM	1.058	2.881	5.394	7.925	8.00	8.255	9.400
	R-S	1.061	—	—	—	—	—	—