Vibrations of double-nanorod-systems with defects using nonlocal-integral-surface energy-based formulations

Abstract

We report suitable surface energy-nonlocal-integral and -differential models for investigating mechanical behavior of a nanosystem consists of double parallel nanorods with defects. By visualizing the locally caused defects by appropriate linear springs, the equations of motion that display longitudinal vibrations of the defected nanosystem are derived accounting for nonlocality and surface energy effects. For the nanosystem at hand with a single defect in each nanorod, there would exist four coupled-integro-partial differential equations with eight boundary conditions. By evaluating the exact nonlocal-surface energy-based modes associated with fixed–fixed and fixed-free defected nanorods according to the nonlocal-differential-based model, Galerkin method is implemented to assess the longitudinal frequencies. The capabilities of the nonlocal-integral-based model in capturing the natural frequencies of the nonlocal-differential-based model for the defected nanosystem with fixed–fixed and fixed-free ends are revealed. The roles of the nonlocality, surface energy, nanorod diameter and length, location and mechanical constants of defects as well as the constant of the elastic interface layer on the free vibration are explained.