Influence of Behavior of a Coupled Dynamic System on an Energy Harvester

This paper examines the behavior of a two-degrees-of-freedom (2DOF) kinematic system of the spring pendulum coupled to a harvester. The harvester is the electromagnetic device that is reliant on a magnet's oscillation within a coil. Using the Lagrangian, the governing equations of motion (GEOM) are generated. The multiple-time-scales approach (MTSA) is employed to provide the analytical solutions (AS) for these equations up the third-order of approximations. To ascertain these solutions, we juxtapose them with numerical ones. The modulation equations are set up, and the principal external resonance instances are investigated concurrently upon the solvability constraints. A schematic representation of the dynamical system's behavior is provided by the time histories, phase portraits, and nonlinear stability analysis of the modulation equations. Moreover, the time histories of the electromagnetic harvester's current, power, and voltage are shown to illustrate how various parameters impact the generation of electrical energy. According to the Routh-Hurwitz stability criteria (RHSC), stability/instability regions exist wherein the behavior of the examined system is stable over a large range of applied parameters. In addition, stable/unstable fixed points within the scenario of steady-state are distinguished. This work's relevance is confined to the practical implementations of its findings in daily life, including energy sources for the industrial, electronic and medical devices.