Controlling the kinematics of a spring-pendulum system using an energy harvesting device

Abstract

This work focuses on vibration alleviation and energy harvesting in a dynamical system of a spring-pendulum. The structure of the pendulum is modified using an independent electromagnetic harvesting system. The harvesting depends on the oscillation of a magnet in a coil. An endeavor has been made to get both the energy harvesting and mitigation of vibration efficacy of the harvester. The governing kinematics equations are derived using Lagrange’s equations and are solved asymptotically using the multiple scales method to achieve the intended outcome as new and precise results. The resonance states are classified, and the influence of various parameters of the studied system is analyzed. Fixed points at steady states are categorized into stable and unstable. The time behavior of the solutions, the modified amplitudes, and phases are examined and interpreted in the light of their graphical plots. Zones of stability and instability are concerned, in which the system’s behavior is stable for a wide range of used parameters. This model has become essential in recent times as it uses control sensors in industrial applications, buildings, infrastructure, automobiles, and transportation.