An eigenvalue solution for torsional vibrations of restrained porous nanorods using doublet mechanics theory

Abstract

This study focuses on an effective analytical eigenvalue solution for the torsional vibration of porous nanorods using small-scale-dependent doublet mechanics theory. This analytical solution, unlike other studies, provides solutions to both rigid boundary conditions and non-rigid (deformable) boundary conditions. For this, the porous nanorod is considered with torsional springs at both ends. The varying stiffness values of these torsion springs allow the provision of a rigid boundary condition on the one hand and the examination of deformable boundary conditions on the other. In this study, the effects of different porosity values, spring stiffness, and size dependency on the porous nanorod's torsional vibration response are examined in detail via the proposed solution.