Piezoelectric transduction has received great attention for vibration-to-electric energy conversion over the last five years. A typical piezoelectric energy harvester is a unimorph or a bimorph cantilever located on a vibrating host structure, to generate electrical energy from base excitations. Several authors have investigated modeling of cantilevered piezoelectric energy harvesters under base excitation. The existing mathematical modeling approaches range from elementary single-degree-of-freedom models to approximate distributed parameter solutions in the sense of Rayleigh–Ritz discretization as well as analytical solution attempts with certain simplifications. Recently, the authors have presented the closed-form analytical solution for a unimorph cantilever under base excitation based on the Euler–Bernoulli beam assumptions. In this paper, the analytical solution is applied to bimorph cantilever configurations with series and parallel connections of piezoceramic layers. The base excitation is assumed to be translation in the transverse direction with a superimposed small rotation. The closed-form steady state response expressions are obtained for harmonic excitations at arbitrary frequencies, which are then reduced to simple but accurate single-mode expressions for modal excitations. The electromechanical frequency response functions (FRFs) that relate the voltage output and vibration response to translational and rotational base accelerations are identified from the multi-mode and single-mode solutions. Experimental validation of the single-mode coupled voltage output and vibration response expressions is presented for a bimorph cantilever with a tip mass. It is observed that the closed-form single-mode FRFs obtained from the analytical solution can successfully predict the coupled system dynamics for a wide range of electrical load resistance. The performance of the bimorph device is analyzed extensively for the short circuit and open circuit resonance frequency excitations and the accuracy of the model is shown in all cases.

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An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations

Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are also presented for excitations around the modal frequencies. Finally, the model proposed is used in a parametric case study for a unimorph harvester, and important characteristics of the coupled distributed parameter system, such as short circuit and open circuit behaviors, are investigated in detail. Modal electromechanical coupling and dependence of the electrical outputs on the locations of the electrodes are also discussed with examples.

A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters

Energy harvesting technologies have been explored by researchers for more than two decades as an alternative to conventional power sources (e.g. batteries) for small-sized and low-power electronic devices. The limited life-time and necessity for periodic recharging or replacement of batteries has been a consistent issue in portable, remote, and implantable devices. Ambient energy can usually be found in the form of solar energy, thermal energy, and vibration energy. Amongst these energy sources, vibration energy presents a persistent presence in nature and manmade structures. Various materials and transduction mechanisms have the ability to convert vibratory energy to useful electrical energy, such as piezoelectric, electromagnetic, and electrostatic generators. Piezoelectric transducers, with their inherent electromechanical coupling and high power density compared to electromagnetic and electrostatic transducers, have been widely explored to generate power from vibration energy sources. A topical review of piezoelectric energy harvesting methods was carried out and published in this journal by the authors in 2007. Since 2007, countless researchers have introduced novel materials, transduction mechanisms, electrical circuits, and analytical models to improve various aspects of piezoelectric energy harvesting devices. Additionally, many researchers have also reported novel applications of piezoelectric energy harvesting technology in the past decade. While the body of literature in the field of piezoelectric energy harvesting has grown significantly since 2007, this paper presents an update to the authors' previous review paper by summarizing the notable developments in the field of piezoelectric energy harvesting through the past decade.

https://iopscience.iop.org/article/10.1088/1361-665X/ab36e4/pdf

A review of energy harvesting using piezoelectric materials: state-of-the-art a decade later (2008–2018)

The idea of vibration-to-electric energy conversion for powering small electronic components by using the ambient vibration energy has been investigated by researchers from different disciplines in the last decade. Among the possible transduction mechanisms, piezoelectric transduction has received the most attention for converting ambient vibrations to useful electrical energy. In the last five years, there have been a considerable number of publications using various models for the electromechanical behavior of piezoelectric energy harvester beams. The models used in the literature range from elementary single-degree-of-freedom (SDOF) models to approximate distributed parameter models as well as analytical distributed parameter solution attempts. Because of the diverse nature of researchers working in energy harvesting (including electrical, mechanical and materials engineers), several oversimplified and incorrect physical assumptions have been propagated in the literature. Issues of the correct formulation for piezoelectric coupling, correct physical modeling, use of low fidelity models, incorrect base motion modeling, and the use of static expressions in a fundamentally dynamic problem are discussed and clarified here. These common indiscretions, which have been repeated in the existing piezoelectric energy harvesting literature, are addressed and clarified with improved models, and examples are provided. This paper aims to provide corrections and necessary clarifications for researchers from different engineering disciplines interested in electromechanical modeling of piezoelectric energy harvesters.

https://iopscience.iop.org/article/10.1088/0964-1726/17/6/065016/pdf

Issues in mathematical modeling of piezoelectric energy harvesters

With the increasing requirements for microelectromechanical systems (MEMS) regarding stability, miniaturization and integration, novel materials such as wide band gap semiconductors are attracting more attention. Polycrystalline SiC has first been implemented into Si micromachining techniques, mainly as etch stop and protective layers. However, the outstanding properties of wide band gap semiconductors offer many more possibilities for the implementation of new functionalities. Now, a variety of technologies for SiC and group III nitrides exist to fabricate fully wide band gap semiconductor based MEMS. In this paper we first review the basic technology (deposition and etching) for group III nitrides and SiC with a special focus on the fabrication of three-dimensional microstructures relevant for MEMS. The basic operation principle for MEMS with wide band gap semiconductors is described. Finally, the first applications of SiC based MEMS are demonstrated, and innovative MEMS and NEMS devices are reviewed.

http://iopscience.iop.org/article/10.1088/0022-3727/40/20/S19/pdf

Shih-Nung Chen

Papers

Analytical modeling of piezoelectric vibration-induced micro power generator