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

Table 3

Numerical comparison among R-R, R-S, and CDM of clamped-clamped DWCNTs: in columns 3 and 5, the first two dimensionless fundamental frequencies 𝜆₁ and 𝜆₂, with 𝑐₁₂=0, are reported, while in column 4 the first frequency 𝜆, with 𝑐₁₂=0.0694 TPa, is listed.

𝜂0	Method	𝜆1	𝜆	𝜆2
0	R-R	22.793	36.394	41.628
	R-S	22.410	35.783	—
	CDM	22.373	35.722	40.859
0.1	R-R	21.427	34.212	39.132
	R-S	21.137	33.750	—
	CDM	21.109	33.704	38.551
0.2	R-R	18.449	29.458	33.694
	R-S	18.303	29.225	—
	CDM	18.289	29.202	33.402
0.3	R-R	15.422	24.625	28.166
	R-S	15.359	24.525	—
	CDM	15.353	24.515	27.001
0.4	R-R	12.934	20.652	23.622
	R-S	12.907	20.609	—
	CDM	12.905	20.605	21.139
0.5	R-R	11.005	17.571	20.098
	R-S	10.992	17.552	—
	CDM	10.991	17.550	17.273