Modeling and Analyzing a Spring Pendulum Motion in the Presence of Energy Harvesting Devices

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 governing system of motion is derived using Lagrange’s equations of the second kind. The analytic solutions of this system are obtained up to the second approximation using the 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 ranges 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 developed methodology and obtained results can be useful in various applications like power supply of sensors and charging electronic devices.