Surface Effects on Free Vibration Analysis of Nanobeams Using Nonlocal Elasticity: A Comparison Between Euler-Bernoulli and Timoshenko
Subject Areas : EngineeringSh Hosseini – Hashemi 1 , M Fakher 2 , R Nazemnezhad 3
1 - School of Mechanical Engineering, Iran University of Science and Technology---
Center of Excellence in Railway Transportation, Iran University of Science and Technology
2 - School of Mechanical Engineering, Iran University of Science and Technology
3 - School of Mechanical Engineering, Iran University of Science and Technology
Keywords: Free vibration, Surface effects, Nonlocal elasticity, Nanobeam, Euler-Bernoulli theory, Timoshenko theory,
Abstract :
In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress through the nanobeam thickness. The governing equations are obtained and solved for Silicon and Aluminum nanobeams with three different boundary conditions, i.e. Simply-Simply, Clamped-Simply and Clamped-Clamped. The results show that the influence of the surface effects on the natural frequencies of the Aluminum nanobeams follows the order CC
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