Piezoelectric energy harvesting and synchronization of excited and modified Huygens’s pendulums

We consider a model of modified Huygens pendulums in order to be able to study the dynamics of such a system and carry out piezoelectric energy harvesting and the effects of phenomena encountered on this energy harvesting. The modifications made to the system here are the use of compound pendulums, a parametric force, and the addition of a piezoelectric transducer for energy harvesting. Thanks to the Lagrangian formalism, the governing equations were established and the numerical resolution was made using the fourth-order Runge-Kutta algorithm. We observed the presence of several types of synchronization (in-phase, anti-phase, quadrature-phase) and the existence of periodic, multi-periodic, or chaotic dynamics. Also, synchronization plays an important role in energy harvesting, in particular, in-phase synchronization, which promises much better performance than anti-phase synchronization. The effects of system parameters (amplitude and frequency of parametric force, stiffness coefficient, electromechanical coupling coefficient, etc.) are also studied on synchronization and energy harvesting. These results have applications in the manufacture of sensors and actuators, the power supply of electronic devices, and the manufacture of autonomous devices.