Phase portrait analysis of a cantilevered piezoelectric-electromagnetic energy harvester

Abstract

This paper investigates a piezoelectric-electromagnetic hybrid energy harvester (PEM-HEH) which has only been developed recently where a linear electromagnetic harvester is attached to the free end of a cantilevered piezoelectric bimorph. First, the electromechanical model of PEM-HEH is introduced based on Euler–Bernoulli theory and Lagrange’s equations. It is demonstrated the coupling between the linear transverse motion of the piezoelectric bimorph and the nonlinear axial motion of the magnet inside the electromagnetic harvester. It turns out that the combination of two linear harvesters leads to a frequency-doubling effect in a nonlinear system. Next, a sample test is implemented to verify the characteristics of the nonlinearity of the system in phase portrait. Finally, relevant conclusions could be drawn.