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

This paper reviews energy harvesting technology from mechanical vibration. Recent advances on ultralow power portable electronic devices and wireless sensor network require limitless battery life for better performance. People searched for permanent portable power sources for advanced electronic devices. Energy is everywhere around us and the most important part in energy harvesting is energy transducer. Piezoelectric materials have high energy conversion ability from mechanical vibration. A great amount of researches have been conducted to develop simple and efficient energy harvesting devices from vibration by using piezoelectric materials. Representative piezoelectric materials can be categorized into piezoceramics and piezopolymers. This paper reviews key ideas and performances of the reported piezoelectric energy harvesting from vibration. Various types of vibration devices, piezoelectric materials and mathematical modeling of vibrational energy harvestings are reviewed.

A Review of Piezoelectric Energy Harvesting Based on Vibration

Cantilevered beams with piezoceramic (PZT) layers are the most commonly investigated type of vibration energy harvesters. A frequently used modeling approach is the single-degree-of-freedom (SDOF) modeling of the harvester beam as it allows simple expressions for the electrical outputs. In the literature, since the base excitation on the harvester beam is assumed to be harmonic, the well known SDOF relation is employed for mathematical modeling. In this study, it is shown that the commonly accepted SDOF harmonic base excitation relation may yield highly inaccurate results for predicting the motion of cantilevered beams and bars. First, the response of a cantilevered Euler-Bernoulli beam to general base excitation given in terms of translation and small rotation is reviewed where more sophisticated damping models are considered. Then, the error in the SDOF model is shown and correction factors are derived for improving the SDOF harmonic base excitation model both for transverse and longitudinal vibrations. The formal way of treating the components of mechanical damping is also discussed. After deriving simple expressions for the electrical outputs of the PZT in open-circuit conditions, relevance of the electrical outputs to vibration mode shapes and the electrode locations is investigated and the issue of strain nodes is addressed.

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On Mechanical Modeling of Cantilevered Piezoelectric Vibration 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)

Piezoelectric materials (PZT) have shown the ability to convert mechanical forces into an electric field in response to the application of mechanical stresses or vice versa. This property of the materials has found extensive applications in a vast array of areas including sensors and actuators. The study presented in this paper targets the modeling of a PZT bender for voltage and power generation by transforming ambient vibrations into electrical energy. This device can potentially replace the battery that supplies the power in a microwatt range necessary for operating sensors and data transmission. One of the advantages is that it is maintenance-free over a long time span. The feasibility of this application has been repeatedly demonstrated in the literature, but a real demonstration of a working device is partially successful because of the various design parameters necessary for a construction of the PZT bender. According to a literature survey, the device can be modeled using various approaches. This paper focuses on the analytical approach based on Euler–Bernoulli beam theory and Timoshenko beam equations for the voltage and power generation, which is then compared with two previously described models in the literature: the electrical equivalent circuit and energy method. The three models are then implemented in a Matlab/Simulink/Simpower environment and simulated with an AC/DC power conversion circuit. The results of the simulation and the experiment have been compared and discussed.

https://iopscience.iop.org/article/10.1088/0964-1726/16/2/024/pdf

D Shen

Papers

Modeling and analysis of a bimorph piezoelectric cantilever beam for voltage generation