A Theoretical and Experimental Analysis of Support-excited Non-linear Vibrations of the Extensible Pendulum

Using the Lagrangian formulation, the equations of motion areset up for a damped extensible pendulum subjected to supportexcitation. The well established perturbation technique knownas the Method of Multiple Scales is used to investigate steadystates, with the outstanding feature that the original non-autonomousproblem is reduced to an autonomous form, thus easing the analysisand the stability verification. The theory is thereafter correlatedwith an extensive experimental study.