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.
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.
This letter introduces a piezomagnetoelastic device for substantial enhancement of piezoelectric power generation in vibration energy harvesting. Electromechanical equations describing the nonlinear system are given along with theoretical simulations. Experimental performance of the piezomagnetoelastic generator exhibits qualitative agreement with the theory, yielding large-amplitude periodic oscillations for excitations over a frequency range. Comparisons are presented against the conventional case without magnetic buckling and superiority of the piezomagnetoelastic structure as a broadband electric generator is proven. The piezomagnetoelastic generator results in a 200% increase in the open-circuit voltage amplitude (hence promising an 800% increase in the power amplitude).
The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature's attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting.
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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