Harvesting energy from ambient vibr

Harvesting energy from ambient vibrations by using the direct piezoelectric effect has received significant attention over the last two decades [1, 2, 3]. This focus is due to the need for low-power consumption devices, such as micro-electromechanical systems and sensors [4]. Many review papers have summarized the literature of piezoelectric energy harvesting [5, 6, 7, 8]. The most common configuration for piezoelectric energy harvesting has been either a unimorph or a bimorph piezoelectric cantilever beam. Many researchers have focused on the mathematical modeling of this harvester. A reliable mathematical model may allow studying different aspects of energy harvesting, predicting the electrical outputs, moreover, optimizing the harvester in order to obtain the maximum electrical output for a given input. The linear models of piezoelectric energy harvesters are available in many papers. For example, Erturk and Inman [3] presented a distributed parameter electromechanical model of cantilevered piezoelectric energy harvester with the Euler–Bernoulli beam assumptions. Closed-form expressions of the voltage, current, and power outputs, as well as the mechanical response were obtained under the base excitation. Some linear models have been validated experimentally and show good agreement between theory and experiment [9, 10, 11]. The study of Tang and Wang [12] presented a modified model of cantilevered piezoelectric energy harvester with tip mass offset and a dynamic magnifier by using the generalized Hamilton’s principle. The modified model was demonstrated by parametric studies. The results show that the harvesting power can be dramatically enhanced with proper selection of the design parameters of the dynamic magnifier and tip mass offset. However, these validations are very low levels of excitation and not necessarily valid in all applications. In practical application, it is likely that linear models of the energy harvester will be unable to predict accurately the resonance frequency, leading to inaccurate prediction for the performance of the harvester due to frequency shift. It is advisable to take into account the nonlinear behavior of energy harvesters in the design, particularly if the energy harvester is subjected to high levels of excitation. The paper by Daqaq et al. [13] identified the primary limitations associated with linear vibration harvesters and presented a critical review of recent research focused on the use of nonlinearity to improve the performance of vibration harvesters.