Axial vibration analysis of a Rayleigh nanorod with deformable boundaries

Abstract

In this study, the free axial vibration of Rayleigh nanorods with axial restraints is studied via Eringens' nonlocal elasticity theory. This higher order elasticity theory takes into account the size effect into the formulation due to dealing with micro and nanostructures. The boundary conditions and equation of motion are obtained using Hamilton's principle. Two symmetrical axial elastic springs are attached to a nanorod at both ends. The novelty of the present study is that it seeks to obtain a general eigen value algorithm for the angular frequencies subjected to the rigid or restrained boundary conditions in a nanorod for the first time. A Fourier sine series is used to work Stokes' transformation for the Rayleigh nanorods with elastic springs at the ends. Afterward, the effect of the spring coefficient on the the eigen-frequency is investigated. Also, the effects of the nonlocal parameter and the elastic springs on the eigen-frequency is reported.