Porosity dependent torsional vibrations of restrained fg nanotubes using modified couple stress theory

Abstract

In the present study, size-dependent static and free torsional vibration responses of functionally graded porous nanotubes are examined using Fourier sine series and Stokes' transformation for the first time. The boundary conditions of functionally graded porous nano-sized tubes are defined by the two elastic torsional springs at the both ends. A power law rule is utilized to describe the distribution of functionally graded material and this distribution is considered through the radius of nanotube. The governing equations of the mechanical response of porous nanotubes with elastic boundary conditions and subjected to torsion are accomplished via the modified couple stress theory. The purpose of the presented work is to construct an eigen value solution including the small scale parameter based on the modified couple stress theory, torsional spring coefficients representing the boundaries of the porous nanotubes, functionally graded index caused by power law rule and porosity volume fraction.