Vibration analysis of rotating rods based on the nonlocal elasticity theory and coupled displacement field

TLDR: In this article, a linear proportional relation between axial and angular velocities is introduced to capture the effect of the rotational motion into analysis of the continuous system, and a variational approach is adopted to derive the equations of motion for clamped-clamped and clamped free boundary conditions.

Abstract: Free longitudinal vibration analysis of a rotating rod based on the Eringen’s nonlocal elasticity is studied in this paper. Rod is supposed to rotate around a fixed axis with a constant angular velocity. To capture the effect of the rotational motion into analysis of the continuous system, a linear proportional relation is introduced between axial and angular velocities. For the first time the mentioned relation is presented based on the internal motions of the infinitesimal element. This novelty makes the rotational displacement as a dependent function of axial displacement playing a significant role through the analysis. Variational approach is adopted to derive the equations of motion for clamped–clamped and clamped-free boundary conditions. For verification of the results obtained from the Galerkin approach, comparison with technical literature is reported. Finally current results illustrate the dependency of the dynamic-vibration analysis of the presented system on the nonlocality and the rotational velocity parameter. This dependency shows the decrement of the frequency with increment in both the angular velocity and the nonlocal parameter. As a result, the mentioned parameters are key factors in the design and analysis of such systems.