Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method

Abstract

This study investigates the small-scale effect on the flapwise bending vibrations of a rotating nanoplate that can be the basis of nano-turbine design. The nanoplate is modeled as classical plate theory (CPT) with boundary conditions as the cantilever and propped cantilever. The axial forces are also included in the model as the true spatial variation due to the rotation. Hamilton’s principle is used to derive the governing equation and boundary conditions for the classic plate based on Eringen’s nonlocal elasticity theory and the differential quadrature method is employed to solve the governing equations. The effect of the small-scale parameter, nondimensional angular velocity, nondimensional hub radius, setting angle and different boundary conditions in the first four nondimensional frequencies is discussed. Due to considering rotating effects, results of this study are applicable in nanomachines such as nanomotors and nano-turbines and other nanostructures.