Finite Element Model of Functionally Graded Nanobeam for Free Vibration Analysis

Abstract

In the present study, free vibration of functionally graded (FG) nanobeam is investigated. The variation of material properties is assumed in the thickness direction according to the power law. FG nanobeam is modeled as Euler-Bernoulli beam with different boundary conditions and investigated based on Eringen’s nonlocal elasticity theory. Governing equations are derived via Hamilton principle. Frequency values are found by using finite element method. FG nanobeam is composed of silicon carbide (SiC) and stainless steel (SUS304). The effects of dimensionless small-scale parameters (e₀a/L), power law exponent (k) and boundary conditions on frequencies are examined for FG nanobeam.

Keywords

• Functionally graded nanobeam,nonlocal elasticity theory,free vibration,finite element method

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