On the Dynamics of a Post-Buckled Vibrating Beam: An Experimental Study

Abstract

A beam is clamped at one of its ends and is subjected to a shear force at its other end which causes deformation in the principal plane with stiffest resistance to bending. Above a critical value of load, bifurcation occurs, the beam twists and experiences out-of-plane deformation which tends to transfer bending to the plane of weakest resistance. Here, attention is focused on an experimental study of dynamic lateral torsional buckling. The load is exerted, by a tip mass whose inertia provides the load-levels that lead to buckling. Specifically, in the experiment, a beam is attached to the shaft of a motor at one of its ends and a large mass is attached to its other end. Rotation of the motor causes deflection of the beam in its principal plane of stiffest bending resistance. By increasing the excitation frequency and/or amplitude of oscillation of the motor's shaft, the shear force applied by the mass on the beam's end exceeds a critical value which causes dynamic lateral torsional buckling of the beam. Buckling has been observed at several operating points with different spatial and temporal motions. The deformations in the post-buckled regime are large and often complex, for this reason non-standard experimental techniques need to be employed. Only with these techniques, comparison with numerical and analytical models can take place. This work focuses on experimental investigations using several sensing elements, a laser vibration sensor, a fast video camera and a shaft encoder whose signals have be processed simultaneously to provide sufficient information about the 3D dynamics. The paper describes the experimental system, the data and signal processing methods for the non-stationary system and the unique dynamical behavior the system under dynamic buckling conditions.