Dynamic properties of flexural beams using a nonlocal elasticity model

Abstract

In this paper, a nonlocal Bernoulli-Euler beam model is established based on the theory of nonlocal elasticity. Frequency equations and modal shape functions of beam structures with some typical boundary conditions are derived based on the model. The corresponding dynamic properties are presented and discussed in detail, which are shown to be very different from those predicted by classic elasticity theory when nonlocal effects are significant. The results can be applied to modeling and characterization of size-dependent mechanical properties of micro- or nanoelectromechanical system (MEMS or NEMS) devices.

Virus sensor based on single-walled carbon nanotube: improved theory incorporating surface effects

“…Note that the model of Lu et al [6] or Lu et al [7] is valid for a surface elasticity loading modelled as a conservative loading. The reader is referred also to the recent study of Challamel & Elishakoff [12] for a discussion on conservative versus non-conservative modelling of surface elasticity effects.…”

“…Considerable interest has been demonstrated recently in the application of non-local continuum mechanics for proper modelling of microbeams and nanobeams. Lu et al [6,7] proposed a generalization of the Bresse-Timoshenko equations for flexural beams to be analysed by the non-local theory. However, they did not include surface effects.…”

Nonlinear Dynamic Analysis of Electrostatically Actuated Single-walled Carbon Nanotubes Using Nonlocal Elasticity

“…The dynamic properties of the beams using the NLE model were investigated by Lu et al (2006). They established a nonlocal Euler-Bernoulli beam model based on this theory and presented the frequency equations and shape modes of the beam structures with some typical boundary conditions based on the derived model.…”

Large amplitude free vibration of micro/nano beams based on nonlocal thermal elasticity theory

“…Up to now, many research works correlated to nonlocal elasticity theory have been reported trying to develop nonlocal continuum models and apply them to analyze the general behavior of structures in micro/nano scale, see Refs. (Lu et al, 2006;Wang et al, 2008;Murmu and Pradhan, 2009;Civalek and Akgöz, 2010;Civalek and Demir, 2011;Setoodeh et al, 2011;Thai, 2012;Eltaher et al, 2013;Rahmani and Pedram, 2014) and the references therein. It has been clear from these available surveys that nonlocal effects play a significant role both for static and dynamic issues exhibited by micro/nano structures.…”