Investigation on the Dynamic Behavior of Multistable Piezoelectric Energy Harvesters: Numerical Modeling and Experimentation

Abstract

The main goal of this research project is to study theoretically and experimentally a multistable piezoelectric energy harvesting system through the introduction of intentional nonlinear magnetic effects, which, in association with the piezoelectric effect, seek to enhance the harvester's energy generation capacity, either concerning the operating frequency range and also the electrical power generated by the piezoelectric generator. The research project falls in the general area of intelligent structures using piezoelectric materials, which presents a wide range of applications, including the topic of piezoelectric energy harvesting, widely investigated in recent years, and aims at designing electrome- chanical devices capable of converting generally wasted structural vibration signals into usable electrical energy. The cantilever beam model, partially or fully covered with a thin layer of piezoelectric ceramic and carrying a lumped mass at its free end has been widely used in the design of energy harvesting devices. Although very useful, this model presents some limitations, the main one being the electromechanical conversion frequency range, since, to maximize energy conversion, the harvester must operate in a very narrow frequency range, in the vicinity of its natural frequency. A second limitation concerns the adaptability of the operating frequency of the device since, in practical applications, it is common to have changes in the frequency of the external disturbance. A possible solution to increase the frequency range of the device is the introduction of intentional nonlinear effects, for example through non-contact magnetic field forces, which introduce nonlinear effects on the dynamic behavior of the harvester. In this sense, the so-called multi-stable piezoelectric harvesters have been the subject of many investigations in recent years, since they have interesting dynamic characteristics for the purposes not only of guaranteeing a wider operating frequency range but also of generating a greater amount of electrical energy, when compared to the corresponding linear model. Thus, this research project aims to study a multi-stable piezoelectric energy harvester, using the cantilever beam model associated with the bimorph configuration (a layer of piezoelectric material on each of the beam surfaces), and employing intentional magnetic effects by positioning neodymium magnets close to the free end (and magnetic) of the cantilever beam. From a chosen geometric configuration, a non-linear electromechanical model will be formulated that is essentially composed of two differential equations, one of them for the beam structure and the other for the voltage of the piezoelectric material. These coupled equations according to the generalized coordinates of absolute displacement and electrical voltage, will be used in a numerical study to investigate the key parameters that influence the dynamic behavior of the model regarding the generation of electrical energy from a given mechanical input. A physical prototype will be designed and built to perform experimental tests whose data will later be used to verify the analytical model. Both the model and the experimental apparatus will allow the study of several piezoelectric energy harvesting configurations, among them the classical linear configuration and the mono-stable and bi-stable configurations, which have been deserving great attention in the current literature on the subject. From the analytical-numerical and experimental studies, it is sought to obtain geometric configurations, mainly regarding the linear and angular positioning of the magnets, which allow the maximization of the electrical output power of the device. Additional multi-stable configurations to mono and bistable configurations will also be investigated, for example, the tristable configuration.