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Nonlinear coupled transversal-longitudinal vibrations of a thin rotating beam attached to a rigid hub are investigated in the paper. The analytical model is based on Euler–Bernoulli beam theory, extended to accommodate a moderately large displacement field and modest geometrical nonlinearities. The governing partial differential equations (PDEs) of motion are derived from Hamilton’s principle for clamped-free boundary conditions. The complete set of three PDEs involving transversal and longitudinal vibrations and angular velocity is expanded up to the third perturbation order. Then, the longitudinal motion, which includes effects arising from the structure’s rotation, has been reduced to the transverse motion. Moreover, the assumption of constant angular velocity is made, and finally a new original reduced (condensed) single d.o.f. model of the rotating beam is proposed. Next, the PDEs are reduced to ODEs by means of the Galerkin method, and the final form of the condensed transversal-longitudinal dynamics of the rotating beam is obtained. The effect of angular velocity and nonlinear coupling terms on the softening or hardening of the resonance curves is demonstrated. Moreover, the importance of the preset angle in contributing to the Coriolis force in system dynamics is studied.
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