Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen’s theory using differential quadrature method

This study investigates the small scale effect on the nonlinear bending vibration of a rotating cantilever and propped cantilever nanobeam. The nanobeam is modeled as an Euler–Bernoulli beam theory with von Kármán geometric nonlinearity. 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 Euler–Bernoulli beam based on Eringen’s nonlocal elasticity theory. The differential quadrature method as an efficient and accurate numerical tool in conjunction with a direct iterative method is adopted to obtain the nonlinear vibration frequencies of nanobeam. The effect of nonlocal small–scale, angular speed, hub radius and nonlinear amplitude of rotary nanobeam is discussed.