Torsional and longitudinal vibration analysis of a porous nanorod with arbitrary boundaries

Abstract

In the present study, free torsional and axial vibrations of porous nanorods with torsional, axial elastic boundary conditions are presented via Eringen's nonlocal elasticity theory. This theory takes into account the small size effect into the differential formulation due to dealing with nano-sized structures. Even though free axial and torsional vibrations based analysis of nanorod is a widely investigated topic, there are only few researches which exist in the scientific literature pertaining to the vibration analysis of porous nanostructures with nonrigid (deformable) boundary conditions. This study brings a contribution to the literature by presenting both porosity and small size effects with deformable boundary conditions. It is also planned to examine the effects of porosity and small size in detail. A model that allows to examine all of these effects within the framework is created within the scope of this study. To this end two torsional and axial springs are attached to the porous nanorod at both ends separately. Present model bridges the gap between deformable and non-deformable (rigid) boundary conditions. An eigen-value problem is constructed including torsional and axial coefficients by using Stoke transformation and the Fourier sine series. The novelty of this work is that it seeks to construct a general eigen value algorithm for the torsional and axial vibration frequencies of the porous nanorods subjected to the deformable and rigid boundary conditions for the first time. Moreover, the effects of some parameters such as porosity index, axial and torsional restraints on the free vibration frequencies are investigated and some conclusions are drawn.