DYNAMICS OF A FLEXIBLE BEAM CARRYING A MOVING MASS USING PERTURBATION, NUMERICAL AND TIME-FREQUENCY ANALYSIS TECHNIQUES

The dynamic behaviour of a flexible cantilever beam carrying a moving mass-spring is investigated. This system is an idealization of an important class of problems that are characterized by interaction between a continuously distributed mass and stiffness sub-system (the beam), and a lumped mass and stiffness sub-system (the moving mass-spring). Inertial non-linearities form the coupling between the two, resulting in internal resonance behavior under certain parametric conditions. The dynamics of the system are described by coupled non-linear partial differential equations, where the coupling terms have to be evaluated at the position of the moving mass. The equations of motion are solved numerically using the Galerkin method and an automatic ODE solver. The numerical results are compared with a closed-form analytical solution obtained using a perturbation method and a parametric analysis of the system is performed using the perturbation solution. The spectral behavior of the system is investigated using time-frequency analysis.