Nonlocal forced vibrations of rotating cantilever nano-beams

This study presents a dynamic analysis of a single rotating nonlocal cantilever nano-beam under external excitations. The cases of undamped and damped forced vibrations are analyzed. By employing Eringen's nonlocal elasticity theory and based on Euler-Bernoulli's beam theory, the governing equation of motion of the forced vibration rotating nonlocal cantilever nano-beam is derived. The mentioned equation of motion is discretized by the Galerkin method. In the paper, the standard modal analysis procedure is used for determining the forced responses. The novelty of the study lies in the transient responses of the rotating cantilever nano-beams with the nonlocality magnitude effect taken into consideration. In the parametric study the influences of the varying angular velocity and varying hub radius effects are presented. The solutions for the natural frequencies of the rotating system are determined. For the undamped vibrations are carry out for two analysis of time histories. Time histories have clearly described the impact of contemplated effects for a longer time which causes periodical response. An interesting phenomenon can be noted in the case of higher values of an angular velocity effect. Only in this case, the periodical response has not been observed in the transverse deflection. The study also includes an influence of the axial extension load. Even though the qualitative impact of the axial external load is known, the quantitative effect will be shown here.