Nonlinear Vibrations of a Beam With a Tip Mass Attached to a Rotating Hub

Abstract

A model of a light beam mounted to a rigid hub and forced by an external torque has been analysed in the paper. An additional loading caused by a small mass attached to the end of the beam and the influence of mass moment of inertia of the hub have been also taken into account. The motion of a flexible light beam is a composition of slewing motion and undesired vibrations, which can be crucial if the stiffness of the structure is not high, comparing to the external dynamical load. The nonlinear model of the beam proposed in [2], [3] have been applied to explain behaviour of the system. That model has taken into account bending, tension and a non-linear curvature, which differs the system from the classical approach [4] or the approach presented in [5] for large displacement of a beam model. The influence of the mass moment of inertia of the hub and the tip-mass is investigated in the paper. Differential equation of motion and dynamical boundary conditions are derived by applying the Hamilton’s principle whilst the reduced model have been obtained by virtue of the Galerkin’s procedure.