On the influence of an energy harvesting device on a dynamical system

Abstract

This article studies the motion of a three degrees-of-freedom (DOF) dynamical system, which consists of two parts, a dynamic part, and an electromagnetic harvesting device. The composition of the system depends on the magnet oscillating in the coil of this device. An electric potential is exerted because of the electromotive force to obtain energy harvesting (EH). Lagrange's equations (LE) are used to derive the system’s equations of motion (EOM), which are solved analytically up to a third-order of approximation using the multiple-scales method (MSM). These solutions are considered novel, in which the mentioned method is applied to a novel dynamical system. The gained are confirmed through comparison with the numerical solutions of the EOM to reveal a high degree of consistency. To establish the system’s solvable conditions and modulation equations (ME), three scenarios of primary external resonance are investigated simultaneously. Certain diagrams of time histories for the amplitudes and phases of the examined dynamical system are plotted to show their behaviors at any given instance of time. The Routh–Hurwitz criteria (RHC) are used to establish the stability and instability regions in light of the graphs of resonance response curves. The presence of an energy harvester in dynamic devices helps us to convert vibrational motion into electrical energy that can be exploited in several applications in a variety of daily tasks, including structural and environmental monitoring, military applications, space exploration, and remote medical sensing.