Experimental Observations of Nonlinear Nonplanar Oscillations of a Cantilever Beam

Abstract

The dynamics of a thin cantilever beam undergoing combined torsion and bending vibrations are examined experimentally. The beam’s fundamental natural frequencies in the two orthogonal bending motions and in torsion are fv1 = 5.719 Hz, fw1 = 189.730 Hz, and fφ1 = 138.938 Hz, respectively. A base-excitation shaker imparts a harmonic load that acts parallel to the width of the beam. First, the response of the beam is examined when the excitation frequency is equal to the fundamental torsion natural frequency (i.e., f = 138.9 Hz). For low levels of excitation, the motion consists mainly of hardly noticeable twisting vibrations. For high levels of excitation, the energy of the first torsion mode excites the first out-of-plane bending mode. In this case, the beam responses exhibit modulated vibrations containing both high-frequency and low-frequency components. Second, the beam is excited at the frequency f = 132.0 Hz, which is in the neighborhood the difference of these two natural frequencies. For large excitation levels, the beam vibrates with large-amplitude out-of-plane bending motions that exhibit chaotically intermittent behaviors.