Nonlinear dynamic behavior of carbon nanotubes incorporating size effects

Abstract

This research endeavors to investigate the geometrically nonlinear dynamic characteristics of Carbon Nanotubes (CNTs) while incorporating size effects based on the Second Strain Gradient (SSG) elasticity theory. To this end, the nonlinear governing equations and its corresponding boundary conditions are deduced in alignment with the Green–Lagrange strain tensor and Hamilton’s principle. Concurrently, the weak form is expounded through the utilization of the C3 continuum Hermite interpolation functions, which ensure the continuity and smoothness of higher-order strain and displacement fields. Subsequently, a perturbation methodology is introduced, incorporating nonlinear phenomena into the context of linear wave propagation within the framework of periodic structures theory. The wave propagation characteristics manifest a pronounced disparity between the models based on linear SSG theory and those through nonlinear SSG theory with stiffness hardening phenomenon. In contrast to the zigzag CNTs, armchair CNTs evince an elevated aptitude for wave control. The application of nonlinear SSG theory in combination with the wave finite element method is significant for comprehending the wave propagation characteristics of complex CNTs.