Numerical Simulation of the Vibration Behavior of Curved Carbon Nanotubes

Table 1

Material and geometric properties of C–C covalent bonds [14].

Corresponding force field constants	𝑘𝑟=651.97 nN/nm
	𝑘𝜃=0.8758 nN nm/rad^2
	𝑘𝜑=0.2780 nN nm/rad^2
𝐸= Young’s modulus =𝑘𝑟^2𝑏4𝜋𝑘𝜃	5.484×10^−6 N/nm^2
𝐺= shear modulus =𝐸2(𝜐+1)	2.159×10^−6 N/nm^2
𝑅𝑏= bond radius =2𝑘𝜃𝑘𝑟	0.0733 nm
𝐼𝑥𝑥=𝐼𝑦𝑦= second moments of area =𝜋𝑅𝑏^44	2.2661×10^−5 nm^4