Effect of axial rotation on free transverse vibration analysis of two-phase nanobeams

In this study the transverse free vibration behavior of spinning nanobeams along their axis is investigated, employing a novel approach: the local/nonlocal two-phase elasticity, for the first time. Initially, the nanobeam is modeled using the Euler–Bernoulli theory. Subsequently, with the assistance of the Hamilton principle and the local/nonlocal two-phase elasticity theory, the boundary conditions (BCs) and governing equations of motion are derived. The solution of the equation of motion is obtained through the generalized differential quadratic numerical method, which significantly reduces the cost of calculations. This study concludes with an analysis of how various parameters, such as boundary conditions (BCs), nonlocal parameters, rotation direction, geometry of nanobeam, rotation speed, and phase fraction factors, influenced the free vibrations of rotating nanobeams. Furthermore, a satisfactory validation is achieved by comparing the results of this work with previous investigations. Overall, this study contributes valuable insights into the impact of rotation speed and local/nonlocal parameters on the vibration response of nanobeams.