Chaotic Behavior of a Cantilever Beam Subjected to Magnetic Force

Abstract

The chaotic vibration of a cantilever beam with a permanent magnet and an additional mass on its free tip was studied experimentally. The beam was installed vertically and its clamped end was excited by harmonic force. Another permanent magnet was fixed under the free tip of the beam. Experimental evidence for the existence of a strange attractor in this deterministic dynamic system was presented. It is found that chaotic responses of the beam are much larger than its resonant ones. The range of chaotic vibrations changes obviously with the decrease in the distance between two magnets. The bifurcation diagram shows that the response of the beam suddenly comes into chaos from the regular vibration with the increase in the exciting amplitude. Experimental Poincare maps agree well with the numerical results.