On the Positioning of a Piezoelectric Material in the Energy Harvesting From a Nonideally Excited Portal Frame

Abstract

In this paper, we consider the application of the piezoelectric energy harvesting using a portal frame structure of two-degrees-of-freedom. The piezoelectric material is considered as a linear device using a capacitive mathematical model. The portal structure is of two-degrees-of-freedom considering with quadratic coupling between the first and second modes of vibration. 2:1 internal resonance between the first and second modes is set, which is a particular condition of this type of system due to the appearance of a saturation phenomenon. As this phenomenon causes the system to start vibrating from the second mode and, at steady-state, vibrates at the first mode, the objective of this work is to verify the energy uptake, considering the different positioning of a piezoelectric material, which is coupled to the supported beam and/or to the column. In addition, the structure is excited by a nonideal DC motor with a limited power supply. The results show a considerably nonlinear behavior due to the nonideal motor, and, with the saturation phenomenon, it is more efficient to collect energy by coupling the PZT to the column. The investigation of the stability of the system due to the piezoelectric coefficient Θ is also taken into account, which is carried out by numerical tools as phase planes, Poincare maps, bifurcation diagrams, and 0–1 test.