@Article{cmc.2006.004.011,
AUTHOR = {G. Q.  Xie, S. Y.  Long},
TITLE = {Elastic Vibration Behaviors Oof Carbon Nanotubes Based on Micropolar Mechanics},
JOURNAL = {Computers, Materials \& Continua},
VOLUME = {4},
YEAR = {2006},
NUMBER = {1},
PAGES = {11--20},
URL = {http://www.techscience.com/cmc/v4n1/23404},
ISSN = {1546-2226},
ABSTRACT = {The concept of the micropolar theory is employed to investigate vibration behaviors of carbon nanotubes. The constitutive relation has been deduced from the two-dimensional analysis of the microstructure of the carbon nanotube. Van der Waals interactions are simulated by a weak spring model. Hamilton's principle is employed to obtain dynamics equations of the multi-walled carbon nanotube. Numerical examples for both single-walled and double-walled carbon nanotubes are presented and the significant difference in vibration behaviors between them has been distinguished. Numerical results show that fundamental frequencies for the cantilever single-walled carbon nanotube decreases with increase of the aspect ratio of them, and the fundamental frequencies of the double-walled carbon nanotube are lower than those of the single-walled carbon nanotube with the same inner diameter and length. The first four natural frequencies for the double-walled carbon are coaxial.},
DOI = {10.3970/cmc.2006.004.011}
}