Modeling of the vibration and stability of a dynamical system coupled with an energy harvesting device

Abstract

This paper studies the vibrational motion of a dynamical system connected to an electromagnetic device, which is one of the energy harvesting (EH) devices that transform the vibrational motion into electric energy. This system has three degrees-of-freedom (DOF) and consists of two linked parts attached together; one is a nonlinear Duffing oscillator, and the other is a nonlinear damping spring pendulum. The regulating equations of motion (EOM) are achieved utilizing Lagrange’s equations and solved analytically applying the approach of multiple scales (AMS) till the third order of approximation. The accuracy of the attained solutions has been examined by comparing them with the numerical ones of the EOM. The time histories of the solutions and the nonlinear stability analysis of the modulation equations are represented graphically in various plots. The Poincaré maps and phase portraits diagrams displayed the stable behavior of the studied dynamical system. In addition, the different ranges of the stabilities are examined and discussed. In the electromagnetic device, the output power and current time series are depicted as a function of different values of the damping coefficients, excitation amplitudes, and load resistance. It is noted that the output current and power are dropped when the damping coefficient is raised. On the other hand, the increment of the excitation has a positive effect on the electrical generation and produces increment of the output power and current. Furthermore, the output power grows when the total resistance increases to accommodate the applied load. The EH device generates high output current and power at low-frequency values. The significance of this work is limited to the numerous uses of its outcomes in everyday life, such as powering medical devices, serving as a power supply for sensors, and serving as a backup energy source for some electronic devices.