On torsional vibrations of triangular nanowire

The fundamental torsional vibration of the triangular nanowire for three different boundary conditions, including clamped-clamped (C-C), clamped-free (C-F), and clamped-torsional spring (C-T) boundary conditions are analyzed in this study. The equation of motion is derived by Hamilton's principle first, and then the nonlocal elasticity theory based on Eringen model is selected to cover the size-dependent behavior of the nanowire. An analytical method is utilized to solve the governing equation. This work is original and completely novel due to the analysis of vibration of the nanostructures, which possess the noncircular cross-sections. Accordingly, in this study, the effects of the value of the triangle edge and the nonlocal parameter on the variation of the natural frequencies are evaluated. The first three nondimensional natural frequencies are assessed by setting the warping function to zero and comparison with another work. Furthermore, the effect of the stiffness of the boundary torsional spring for C-T boundary condition, and influences of the aspect ratio and nonlocal parameter on the responses are studied.