Short comments on chaotic behavior of a double pendulum with two subharmonic frequencies and in the main resonance zone

Abstract

The parametric pendulum and others different pendular mechanisms were extensively analyzed in current literature because of the chaotic motions. Recently, practical reasons, like energy harvesting, motivated the study of some pendular systems. The resonance and the chaos may occur in multiple and submultiple frequencies based on the natural frequency of the pendulum. In the present paper, a double pendulum is analyzed with two subharmonic frequencies and in the main resonance zone. The results found demonstrate high similarities of the double pendulum with the parametric pendulum when compared the bifurcation diagrams based on varying the amplitude. The conditions in the numerical simulation include a variation in the viscous friction in the joints and different amplitudes and frequency of excitation. The differential equations used dimensionless parameters representing time, frequency, amplitude, friction, position and velocities. Concerning the results, all tests performed have pointed that the same type of motion takes place in the two pendulums after the transient time have already elapsed.