Free transverse vibration analysis of spinning Timoshenko–Ehrenfest nano-beams through two-phase local/nonlocal elasticity theory

The present research aims to study the free transverse vibration of spinning nano-beams. Indeed, this research has conducted a numerical analysis through the generalized differential quadrature method, Timoshenko–Ehrenfest theory and the two-phase local/nonlocal elasticity theory as a size-dependent theory. First, comprehensive results have been validated, and then the effects of the local phase fraction coefficient and nonlocal factor on the natural frequencies and critical speed have been discussed.