On Nonlinear Torsional Vibrations of Nanorod

In research, the nonlinear frequencies of nanorod exposed to torsional vibrations are investigated. The nanorod equations of torsional vibrations are obtained by using Hamilton’s principle, which can be reduced to the classical governing equation by putting a zero nonlocal parameter. The torsional frequencies and mode shapes are derived for two boundary conditions, namely, clamped-clamped and clamped-free. The approximate-analytical solution of the nonlocal nonlinear natural frequencies is extracted by using multiple scales method (MSM). Finally, the effects of nonlocal coefficient and mode number for two boundary conditions including clamped-clamped and clamped-free are calculated. It can be noted, by decreasing the mode number of the frequencies, the nonlinear frequencies of both boundary conditions increase. Moreover, by increasing the value of the nonlocal parameter, the nonlinear torsional frequencies decrease. Also, this reduction is more pronounced for nanorod with clamped-clamped boundary condition, while the nanorod with clamped-free has an increasing trend.