Maximal Lyapunov Exponent and Smaller Alignment Index Computation Characterization of an Electrodynamic Electromechanical System Powered by Sine, Square and Triangle Waves Electrical Signals

Abstract

The goal of this work is first to compare the bifurcation diagrams of an electrodynamic electromechanical system when it is subjected to sine, square and triangular periodic excitations. The example considered is the electromechanical pendulum. Then the task is to analyze the dynamical states of the same system using the computation of the Smaller Alignment Index (SALI) along with the Poincaré Surface of Section (PSS). The bifurcation diagrams present abrupt and period-doubling transitions to chaos. It is found that the triangle form of the excitation gives the larger range of the signal amplitude in which the system behaves chaotically. For the SALI and PSS analyses, they are plotted both for the conservative and nonconservative systems with the impact of the monostability and bistability taken into account. It was found that the conservative system with bistable potential is mainly characterized by chaotic dynamics while regular dynamics are predominant in the system with monostable potential. The evolution of the percentage of chaotic orbits based on SALI was represented to support this result. In the nonconservative case, it was noted that when switching from bistability to monostability, the system can undergo a change of dynamics or keep its chaotic dynamics as seen for triangle excitation. The SALI method was successfully used to determine the dynamics of the system driven by the different forms of excitations as predicted by other tools.