Axial Vibration of a Nanoring Rod Using Nonlocal Finite Element Method

This paper provides a thorough analysis of the axial vibration behavior of nanoring rods based on nonlocal elasticity theory, highlighting its relevance to nanoscale systems. The equation governing the axial vibration of nanoscale rods under nonlocal effects is formulated. By applying appropriate transformations to this equation, the frequency equation is derived. Additionally, a nonlocal finite element formulation for the rod is developed using the weighted residual method.