Analysis of Nonlinear Nonlocal Axial Free Vibrations of Gold Nanoscale Rod

In the current research, the nonlinear frequencies of gold nanoscale rod exposed to axial vibrations are investigated. The gold nanorod equations of axial vibrations are obtained by using Hamilton’s principle, which can be reduced to the classical governing equation by putting a zero nonlocal parameter. The axial frequencies and the mode shapes are derived for clamped-clamped (CC) boundary condition. 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 CC boundary condition is calculated. The results obtained are useful for mechanical and medical sciences.

Keywords:

Nonlinear vibrations , Nonlocal vibrations , Gold nanoscale rod