Nonlinear structural, inertial and damping effects in an oscillating cantilever beam

Abstract

The nonlinear oscillations of a cantilever beam are studied with a theoretical computational model and the results are compared to experimental results obtained in a previous study. In order to explore the various possible nonlinear effects, the cantilevered beam is oscillated by the clamped base in a harmonic motion. Frequency sweeps are conducted in the vicinity of the first and second resonance frequencies of the beam to produce tip displacements of the order of the beam’s length. Three types of nonlinear effects are included in the model and discussed: Inertial, structural, and fluid damping nonlinearities. Comparison of results from the computational model to previously conducted experiments near the first natural frequency shows reasonable to good agreement, suggesting that this model could be effective in describing large amplitude oscillations. Based on the success of this experimental/computational correlation, a computational study near the second resonant mode suggests that nonlinear inertial effects at a higher resonance frequency have a greater effect on both peak amplitude and the frequency at which it is achieved. For the first resonant mode the effects of nonlinear inertia and nonlinear stiffness are offsetting and hence the peak resonant frequency is little changed from that predicted by linear theory and only a very modest hysteresis is observed. However for the second resonant mode, because the nonlinear inertia effect dominates relative to the nonlinear stiffness effect, there is a greater shift in the peak resonant frequency from its linear value and a more substantial hysteresis is observed.