Dynamics of a flexible cantilever beam carrying a moving mas-spring is investigated. The system is an idealisation of an important dass of problems characterised by nonlinear interaction between a continuously distributed mass and stifhess subsystem and a lumped mass and stiffness sub-system. Two models are developed, one with the beam undergoing small oscillations under the presence of kinematic nonlinearities arising fkom the coupled mas-beam behaviour ard a second mode1 for large oscillations where geometric nonlinearities are also considered.

A dosed form solution is obtained using the perturbation method of multiple scales and a parametric analysis is conducted. System response is investigated under interna1 resonance conditions between the moving mass and the beam. A new technique, based on the hite dement method is presented for numerical solution of nonlinear partial differential equations. Using this method the dynamics of the mas-beam system is investigated numerically for both the smd osdation and the large oscillation models. Motion of a catilever beam without the moving mass, undergoing large oscillations is also analysed. Time-Requency analysis is used to investigate the spectral behaviour of the system.