Remarks On the Use of Variational mode decomposition for Chaos and Nonlinear Dynamics Analysis in Fractional-Order Systems applications

Resumo

This study investigates the dynamics of an electromechanical device for energy generation. The device utilizes a motor with an unbalanced mass coupled to a piezoelectric substrate. The central focus of the analysis is measuring the average power generated by the piezoelectric material, which is stimulated by the motor's vibrations. We explore the fractional dynamics of the system, examining variables such as the parameter of the fractional derivative operator and the control parameter. Using techniques like bifurcation diagrams and recurrence analysis, we investigate the routes to chaos and their implications on the stability and behavior of the system. The study is enhanced by the implementation of Variational Mode Decomposition, a technique that allows us to decipher the complexities of the system's dynamics.