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

Abstract

Using the Lagrangian formulation, the equations of motion are set up for a damped extensible pendulum subjected to support excitation. The well established perturbation technique known as the Method of Multiple Scales is used to investigate steady states, with the outstanding feature that the original non-autonomous problem is reduced to an autonomous form, thus easing the analysis and the stability verification. The theory is thereafter correlated with an extensive experimental study.