Modelling and Analysing of a Spring Pendulum Motion in the Presence of Energy Harvesting Devices

Abstract

Energy harvesting will become more and more essential mechanical vibration applications of many devices. The vibrations can be converted by appropriate devices into electrical energy, which can be used as a power supply instead of ordinary ones. This paper investigates a dynamical system associated with two devices: a piezoelectric device and an electromagnetic one. These devices are connected with a nonlinear damping spring pendulum with 2DOF, in which its supported point moves in a circular path. The equations of motion are obtained using Lagrange’s equations of the second kind. The asymptotic solutions of these equations are obtained up to the third approximation utilizing the perturbation approach of multiple scales. The comparison between these solutions and the numerical ones reveals high consistency between them. The steady-state solutions are obtained, and their stabilities are tested. The influences of the excitation amplitudes, the damping coefficients, and the different frequencies on energy harvesting devices outputs are examined and discussed. The work is essential due to its significance in real-life applications. The developed methodology and obtained results can be useful in various applications like power supply of sensors and charging electronic devices.