Nonlocal elastic beam models in small size structures

Abstract

Vibration dynamics of elastic beams,that are used inanotechnology,such as atomic force microscope modeling, carbon nanotubes and micro/nanoelectromechanical devices, is considered in terms of a fundamental response within a matrix framework. The modeling equations with nonlocal effects are written as a matrix differential equation subject to boundary conditions. Eigenanalysis isperformed for Eringen’s nonlocal elasticity, strain gradient and couple stress nonlocal models. This lead to higher-order regular and singular differential systems nonlinearly depending upon frequency.Simply supported beams are discussed in terms of plane waves. Simulations were performed for Timoshenko and Euler-Bernoulli models that include nonlocal effects. It was observed that nonlocal effects can decrease or increase natural frequencies, in comparison to classical case, depending of nonlocal model in use. Also, strain gradient and couple stress models have more influence in natural frequencies when thickness h is comparable to characteristic internal length l.