A Solution Method for Longitudinal Vibrations of Functionally Graded Nanorods

Year 2020, Volume: 12 Issue: 2, 78 - 87, 14.10.2020

Büşra Uzun , Mustafa Özgür Yaylı

https://doi.org/10.24107/ijeas.782419

Cited By: 7

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.

Keywords

Nonlocal elaticity theory, Functionally graded materials, Nanorod, Finite element method, Vibration

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