Analytical investigation on free torsional vibrations of noncircular nanorods

Abstract

This paper is devoted to the free torsional behavior of the nanorods containing noncircular cross sections. The rectangular cross section is chosen to be the case of the study. Three various boundary conditions, namely the clamped–clamped (C–C), clamped–free (C–F), and clamped–torsional spring (C–T) boundary conditions, are used to model the nanorod. Hamilton’s principle is utilized to derive the equation of motion along with associated boundary conditions. The derived equation is reformulated by Eringen’s nonlocal elasticity approach to exhibit the small-scale effect. An analytical method is established to discretize and analyze the equation of motion. The novelty of this work is the analysis of the torsional vibration in rectangular nanorods, which are not observed in previous works. For the results, the influences of the horizontal and vertical aspect ratios ( $$a/b$$ and $$b/a$$ ) (for C–C and C–F boundary conditions) and the influences of the nonlocal parameter and stiffness of the boundary spring (for C–T boundary condition) are illustrated schematically and tabularly.