A solution method for longitudinal vibrations of functionally graded nanorods

Abstract

In the present study, a nonlocal finite element formulation of free longitudinal vibration is derived for functionally graded nano-sized rods. Size dependency is considered via Eringen’s nonlocal elasticity theory. Material properties, Young’s modulus and mass density, of the nano-sized rod change in the thickness direction according to the power-law. For the examined FG nanorod finite element, the axial displacement is specified with a linear function. The stiffness and mass matrices of functionally graded nano-sized rod are found by means of interpolation functions. Functionally graded nanorod is considered with clamped-free boundary condition and its longitudinal vibration analysis is performed.