A Hardening Nonlocal Elasticity Approach to Axial Vibration Analysis of an Arbitrarily Supported FG Nanorod

The present work is aimed at analyzing free longitudinal vibrations of nanorods composed a functionally graded (FG) material with deformable boundaries within hardening nonlocal elasticity approach. For this purpose, FG nanorod the ceramic and metal constituents considered to be elastically supported by means axial springs both ends. Then analytical method based on association Fourier sine series Stokes transformation developed solve vibration problem nondeformable boundaries. Free restrained first studied elasticity. To show validity profitability proposed method, presented used for analysis rigidly homogeneous setting appropriate spring stiffness values. main superiority new approach in its power dealing numerous boundary conditions determine frequencies nanorods. Using solution various numerical applications are given different small-scale parameters, gradient index, length.