Bending, Buckling, and Vibration of Micro/Nanobeams by Hybrid Nonlocal Beam Model

Abstract

The hybrid nonlocal Euler-Bernoulli beam model is applied for the bending, buckling, and vibration analyzes of micro/nanobeams. In the hybrid nonlocal model, the strain energy functional combines the local and nonlocal curvatures so as to ensure the presence of small length-scale parameters in the deflection expressions. Unlike Eringen’s nonlocal beam model that has only one small length-scale parameter, the hybrid nonlocal model has two independent small length-scale parameters, thereby allowing for a more flexible and accurate modeling of micro/nanobeamlike structures. The equations of motion of the hybrid nonlocal beam and the boundary conditions are derived using the principle of virtual work. These beam equations are solved analytically for the bending, buckling, and vibration responses. It will be shown herein that the hybrid nonlocal beam theory could overcome the paradoxes produced by Eringen’s nonlocal beam theory such as vanishing of the small length-scale effect in the deflection expression or the surprisingly stiffening effect against deflection for some classes of beam bending problems.