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Free vibration and response of a variable speed rotating cantilever beam with tip mass

The study shows a new nonlinear model of a rotating cantilever beam with tip mass. The nonlinear model is built with considering axial geometric nonlinear and large curvature. On the basis of the nonlinear Green strain–displacement relations, the nonlinear motion equations are derived using the Hamilton principle. Applying the proposed dynamic model, the effect of various parameters on the natural frequency and stability is performed. The angular velocity value of frequency veer is obtained under different parameters. The dynamical response is calculated with variable rotating velocity. The comparison of numerical results shows good consistency with the other literature.