Three-dimensional nonlocal-surface energy-based statics, dynamics, and divergence instability of movable cable-like nanostructures with arbitrary translational motion

Abstract

Previous studies were concerned with transverse vibrations of axially moving nanowires; however, their statics as well as lateral and transverse vibrations and potential instabilities for the most general form of the translational motion in the presence of axially, laterally, and transversely distributed and pointed loads have not been explained yet. To scrutinize this interesting problem simply, but effectively, the authors develop a fairly comprehensive cable-like model for three-dimensionally moving pretensioned wire-like nanostructures in vacuum under static loads accounting for both nonlocality and surface energy. By decomposing the total deformations into the statics and dynamics parts, the continuum-based governing equations pertinent to purely linear static and dynamic states are presented for the first time. The explicit expressions of static deformations and potential divergence instability of the movable nanowire with general translation motion are displayed and discussed. Subsequently, Galerkin methodology based on admissible modes is employed for dynamic analysis of laterally loaded nanowires in the movable manner. The influences of crucial factors on the free vibration response as well as dynamic instability are investigated for various types of motions.