Bending Vibration Analysis of Nanobeams using the Nonlocal Motion Equations Solved by an Integral Approach

Abstract

This paper deals with the dynamic characteristics for bending vibrations of Euler-Bernoulli type nanobeams taking into account the scale effects via the nonlocal motion equations. An integral method, based on the use of Green’s functions, has been used in order to obtain the corresponding eigenvalue problem. The proposed integral approach is an approximate matrix method. Effects of different boundary conditions and of an elastic foundation have been also included. The presented numerical examples show good agreement when compared to results from literature. The proposed method can be used in the case of nanodevices analysis modeled as beams (MEMS, NEMS).

Keywords

• nanobeams
• scale effects
• vibrations
• green’s functions
• winkler foundation