RETRACTED: Spatial vibrations and instability of axially loaded–torqued beam-like nanostructures via surface elasticity theory

To date, different features of elasto-dynamics of elastically embedded nanowires (NWs) have been investigated using advanced elasticity-based theories; however, their free vibrations in the presence of simultaneous action of axial force and torque have not been explored. The first objective of this work is to formulate the problem appropriately under the umbrella of the surface elasticity theory of Gurtin–Murdoch (SETGM). The main aspect of exertion of torque on the NW is the appearance of additional terms in the geometrical stiffness of the nanostructure such that spatial vibration analysis should be performed instead of the planar one. Using various beam models, the spatial equations of motion are established and then analyzed via a meshless technique. The interactional role of axial force and torque on the fundamental frequency is discussed. The influences of the NW’s aspect ratio, as well as interactions of the NW with elastic matrix, on the dominant frequencies are displayed methodically. The critical values of the slenderness ratio and NW’s radius are graphically illustrated. The most crucial roles of both shear deformation and surface effect on free vibration are observed at these critical levels.