Carbon nanocones have quite fascinating elec- tronic and structural properties, whose axial vibration is sel- dom investigated in previous studies. In this paper, based on a nonlocal elasticity theory, a nonuniform ro...Carbon nanocones have quite fascinating elec- tronic and structural properties, whose axial vibration is sel- dom investigated in previous studies. In this paper, based on a nonlocal elasticity theory, a nonuniform rod model is ap- plied to investigate the small-scale effect and the nonuniform effect on axial vibration of nanocones. Using the modified Wentzel-Brillouin-Kramers （WBK） method, an asymptotic solution is obtained for the axial vibration of general nonuni- form nanorods. Then, using similar procedure, the axial vi- bration of nanocones is analyzed for nonuniform parameters, mode number and nonlocal parameters. Explicit expressions are derived for mode frequencies of clamped-clamped and clamped-free boundary conditions. It is found that axial vi- bration frequencies are highly overestimated by the classical rod model because of ignorance of the effect of small length scale.展开更多
基金supported by the National Natural Science Foundation of China (11072157 and 10932006)the Program for Changjiang Scholars and Innovative Research Team in University(IRT0971)
文摘Carbon nanocones have quite fascinating elec- tronic and structural properties, whose axial vibration is sel- dom investigated in previous studies. In this paper, based on a nonlocal elasticity theory, a nonuniform rod model is ap- plied to investigate the small-scale effect and the nonuniform effect on axial vibration of nanocones. Using the modified Wentzel-Brillouin-Kramers （WBK） method, an asymptotic solution is obtained for the axial vibration of general nonuni- form nanorods. Then, using similar procedure, the axial vi- bration of nanocones is analyzed for nonuniform parameters, mode number and nonlocal parameters. Explicit expressions are derived for mode frequencies of clamped-clamped and clamped-free boundary conditions. It is found that axial vi- bration frequencies are highly overestimated by the classical rod model because of ignorance of the effect of small length scale.
