Analytical Modeling of a Doubly Clamped Flexible Piezoelectric Energy Harvester with Axial Excitation and Its Experimental Characterization

With the rapid development of wearable electronics, novel power solutions are required to adapt to flexible surfaces for widespread applications, thus flexible energy harvesters have been extensively studied for their flexibility and stretchability. However, poor power output and insufficient sensitivity to environmental changes limit its widespread application in engineering practice. A doubly clamped flexible piezoelectric energy harvester (FPEH) with axial excitation is therefore proposed for higher power output in a low-frequency vibration environment. Combining the Euler–Bernoulli beam theory and the D’Alembert principle, the differential dynamic equation of the doubly clamped energy harvester is derived, in which the excitation mode of axial load with pre-deformation is considered. A numerical solution of voltage amplitude and average power is obtained using the Rayleigh–Ritz method. Output power of 22.5 μW at 27.1 Hz, with the optimal load resistance being 1 MΩ, is determined by the frequency sweeping analysis. In order to power electronic devices, the converted alternating electric energy should be rectified into direct current energy. By connecting to the MDA2500 standard rectified electric bridge, a rectified DC output voltage across the 1 MΩ load resistor is characterized to be 2.39 V. For further validation of the mechanical-electrical dynamical model of the doubly clamped flexible piezoelectric energy harvester, its output performances, including both its frequency response and resistance load matching performances, are experimentally characterized. From the experimental results, the maximum output power is 1.38 μW, with a load resistance of 5.7 MΩ at 27 Hz, and the rectified DC output voltage reaches 1.84 V, which shows coincidence with simulation results and is proved to be sufficient for powering LED electronics

Influence of combined fundamental potentials in a nonlinear vibration energy harvester

Ambient mechanical vibrations have emerged as a viable energy source for low-power wireless sensor nodes aiming the upcoming era of the ‘Internet of Things’. Recently, purposefully induced dynamical nonlinearities have been exploited to widen the frequency spectrum of vibration energy harvesters. Here we investigate some critical inconsistencies between the theoretical formulation and applications of the bistable Duffing nonlinearity in vibration energy harvesting. A novel nonlinear vibration energy harvesting device with the capability to switch amidst individually tunable bistable-quadratic, monostable-quartic and bistable-quartic potentials has been designed and characterized. Our study highlights the fundamentally different large deflection behaviors of the theoretical bistable-quartic Duffing oscillator and the experimentally adapted bistable-quadratic systems, and underlines their implications in the respective spectral responses. The results suggest enhanced performance in the bistable-quartic potential in comparison to others, primarily due to lower potential barrier and higher restoring forces facilitating large amplitude inter-well motion at relatively lower accelerations

Investigation of Nonlinear Piezoelectric Energy Harvester for Low-Frequency and Wideband Applications

This paper proposes a monostable nonlinear Piezoelectric Energy Harvester (PEH). The harvester is based on an unconventional exsect-tapered fixed-guided spring design, which introduces nonlinearity into the system due to the bending and stretching of the spring. The physical–mathematical model and finite element simulations were performed to analyze the effects of the stretching-induced nonlinearity on the performance of the energy harvester. The proposed exsect-tapered nonlinear PEH shows a bandwidth and power enhancement of 15.38 and 44.4%, respectively, compared to conventional rectangular nonlinear PEHs. It shows a bandwidth and power enhancement of 11.11 and 26.83%, respectively, compared to a simple, linearly tapered and nonlinear PEH. The exsect-tapered nonlinear PEH improves the power output and operational bandwidth for harvesting low-frequency ambient vibrations

Dynamic analysis and fabrication of a bi-stable structure designed for MEMS energy harvesting applications.

Thanks to the rapid growth in demand for power in remote locations, scientists’ attention has been drawn to vibration energy harvesting as an alternative to batteries. Over the past ten years, the energy harvesting community has focused on bistable structures as a means of broadening the working frequency range and, by extension, the effective efficiency of vibration-based power scavenging systems. In the current study, a new method is implemented to statically and dynamically analyze a bistable buckled, multi-component coupled structure designed specifically for low-frequency vibration energy harvesting systems in both macro and MEMS-scale sizes. Furthermore, several micro-fabrication steps using advanced manufacturing technology methods were applied to design and fabricate a micro-scale version of the energy harvester at the University of Louisville Micro/Nano Technology Center. First, previously efforts performed on different aspects of vibration energy harvesting systems are reviewed to show the current challenges associated with such devices. The coupled structure proposed in this project is then introduced and its equations of motion are developed based on nonlinear Euler-Bernoulli beam theory. These governing equations are discretized and solved using a Galerkin method in two different approaches: with some known shape functions which only satisfies the geometrical boundary conditions; with the exact shape functions obtained from solving the linearized coupled structure as a one single system. An experimental setup is also used to verify the advantages of designed structure in capturing bistable motion at low-frequency range. To validate the modeling approaches, the obtained results are compared with the ones captured from both FEA model and the experimental setup, which shows the superiority of the proposed approach in which exact shape functions of the system are used as the basis in the discretization process. After the validation of the proposed approach, it is applied on a micro-scale version of the system in which structural, piezoelectric, and electrode layers are all considered as they exist in an actual device. Furthermore, a different bistable system, which was previously studied by other researchers in the area, is analyzed by this method to show the reliability of the proposed model. For all these cases, the amplitude-frequency response of the system and snap-through regime with the variation of various parameters, including exciting frequency, base vibration, and buckling loads are investigated based on the developed model. It is shown that bisatble motion and other nonlinear phenomena such as super-harmonic behavior in the system can be captured under certain circumstances, which can significantly impact major system functionalities such as output voltage response and is crucial for the performance of energy harvesting devices. As mentioned above, various micro-fabrication techniques were also used to design and fabricate a micro-scale version of the proposed system, which eventually led to the successful fabrication of a MEMS device as a result of experimental efforts performed to overcome the challenges and issues associated with the designed manufacturing process

Modeling an elastic beam with piezoelectric patches by including magnetic effects

Models for piezoelectric beams using Euler-Bernoulli small displacement theory predict the dynamics of slender beams at the low frequency accurately but are insufficient for beams vibrating at high frequencies or beams with low length-to-width aspect ratios. A more thorough model that includes the effects of rotational inertia and shear strain, Mindlin-Timoshenko small displacement theory, is needed to predict the dynamics more accurately for these cases. Moreover, existing models ignore the magnetic effects since the magnetic effects are relatively small. However, it was shown recently \cite{O-M1} that these effects can substantially change the controllability and stabilizability properties of even a single piezoelectric beam. In this paper, we use a variational approach to derive models that include magnetic effects for an elastic beam with two piezoelectric patches actuated by different voltage sources. Both Euler-Bernoulli and Mindlin-Timoshenko small displacement theories are considered. Due to the magnetic effects, the equations are quite different from the standard equations.Comment: 3 figures. 2014 American Control Conference Proceeding

MEMS Technologies for Energy Harvesting

The objective of this chapter is to introduce the technology of Microelectromechanical Systems, MEMS, and their application to emerging energy harvesting devices. The chapter begins with a general introduction to the most common MEMS fabrication processes. This is followed with a survey of design mechanisms implemented in MEMS energy harvesters to provide nonlinear mechanical actuations. Mechanisms to produce bistable potential will be studied, such as introducing fixed magnets, buckling of beams or using slightly slanted clamped-clamped beams. Other nonlinear mechanisms are studied such as impact energy transfer, or the design of nonlinear springs. Finally, due to their importance in the field of MEMS and their application to energy harvesters, an introduction to actuation using piezoelectric materials is given. Examples of energy harvesters found in the literature using this actuation principle are also presented

The design of low-frequency, low-g piezoelectric micro energy harvesters

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 107-112).A low-frequency, low-g piezoelectric MEMS energy harvester has been designed. Theoretically, this new generation energy harvester will generate electric power from ambient vibrations in the frequency range of 200~30OHz at excitation amplitude of 0.5g. Our previous energy harvester successfully resolved the gain-bandwidth dilemma and increased the bandwidth two orders of magnitude. By utilizing a doubly clamed beam resonator, the stretching strain triggered at large deflection stiffens the beam and transforms the dynamics to nonlinear regime, and increases the bandwidth. However, the high resonance frequency (1.3kHz) and the high-g acceleration requirement (4-5g) shown in the testing experiments limited the applications of this technology. To improve the performance of the current energy harvesters by lowering the operating frequency and excitation level, different designs have been generated and investigated. Moreover, a design framework has been formulated to improve the design in a systematic way with higher accuracy. Based on this design framework, parameter optimization has been carried out, and a quantitative design with enhanced performance has been proposed. Preliminary work on fabrication and testing setup has been done to prepare for the future experimental verification of the new design.by Ruize Xu.S.M

A Flexible Doubly Clamped Beam Energy Harvester with a Standard Rectifier Electric Circuit

While wearable electronics are rapidly developing nowadays, it is greatly limited by the power solutions. Flexible piezoelectric energy harvester presents advantages of high energy density, compact architecture, and easy integration with MEMS, which provides an attractive prospect to power these next generation electronics. Since the flexible devices are usually devised with wavy, island-bridge, and precisely controlled buckling structures, the doubly clamped beam structure for energy harvesting application is analytically studied in this paper. Combine with Euler-Bernoulli beam theory and separation variable method, the analytical expression for output voltage is derived. By conducting the analytical simulation, it is found that the output power is related with the geometry dimensions, external excitation and load resistances. For further validation, experiment is systematically studied. By connecting the standard rectifier electric circuit with the energy harvesting device, it is found that a 0.1uF capacitor can be fully charged in 0.15 s, and the charged output voltage is about 2.5 V, which are successfully used for powering LEDs