Nonlinear vibrations of an extensional beam with tip mass in slewing motion

Dynamics of a rotor composed of a flexible beam attached to a slewing rigid hub is presented in the paper. Dynamics of the structure is studied for a slender beam model, based on extended Bernoulli-Euler theory, which takes into account a nonlinear curvature, coupled transversal and longitudinal oscillations and non-constant angular velocity of the hub. Moreover, to demonstrate a general case for dynamical boundary conditions, lumped mass fixed at the beam tip is added. The partial differential equations (PDEs) are derived from Hamilton principle of the least action. The analytical solutions of the PDEs are obtained by the multiple time scale method applied directly to PDEs. Forced vibrations around selected resonance zones are studied and the influence of beam rotation, preset angle, hub radius, tip mass is presented. Hardening and softening phenomena, respectively for the first and the second mode, are obtained for various angular velocity values.