Investigations on Vibration and Buckling of Carbon Nanotubes with Small Initial Curvature by Nonlocal Elasticity Theory

Many experimental observations have shown that in most nanostructures such as nanocomposites, carbon nanotubes (CNTs) are often characterized by a certain degree of waviness along their axial dimension. This geometrical imperfection has a profound effect on the mechanical behavior of CNTs. In the present work, the effects of initial curvature, shear deformation and influence of surrounding medium that are modeled as Winkler-Pasternak elastic foundation on behavior of slightly curved carbon nanotubes are investigated. It is shown that the initial curvature has an important role on mechanical behavior of curved carbon nanotubes. To capture the small size effects, nonlocal elasticity theory is implemented. Timoshenko beam theory (TBT) is used to model the behavior of CNTs and the governing equations are solved analytically. The effects of initial height and shear deformation on vibration frequencies and buckling loads are studied. It is found that these effects considerably contribute to mechanical behavior ...