Energy Harvesting From Bistable Systems Under Random Excitation

The transformation of otherwise unused vibrational energy into electric energy through the use of piezoelectric energy harvesting devices has been the subject of numerous investigations. The mechanical part of such a device is often constructed as a cantilever beam with applied piezo patches. If the harvester is designed as a linear resonator the power output relies strongly on the matching of the natural frequency of the beam and the frequency of the harvested vibration which restricts the applicability since most vibrations which are found in built environments are broad-banded or stochastic in nature. A possible approach to overcome this restriction is the use of permanent magnets to impose a nonlinear restoring force on the beam that leads to a broader operating range due to large amplitude motions over a large range of excitation frequencies. In this paper such a system is considered introducing a refined modeling with a modal expansion that incorporates two modal functions and a refined modeling of the magnet beam interaction. The corresponding probability density function in case of random excitation is calculated by the solution of the corresponding Fokker-Planck equation and compared with results from Monte Carlo simulations. Finally some measurements of ambient excitations are discussed.DFG, 253161314, Untersuchung des nichtlinearen dynamischen Verhaltens von stochastisch erregten Energy Harvesting Systemen mittels Lösung der Fokker-Planck-Gleichun

A moment-equation-copula-closure method for nonlinear vibrational systems subjected to correlated noise

We develop a moment equation closure minimization method for the inexpensive approximation of the steady state statistical structure of nonlinear systems whose potential functions have bimodal shapes and which are subjected to correlated excitations. Our approach relies on the derivation of moment equations that describe the dynamics governing the two-time statistics. These are combined with a non-Gaussian pdf representation for the joint response-excitation statistics that has i) single time statistical structure consistent with the analytical solutions of the Fokker-Planck equation, and ii) two-time statistical structure with Gaussian characteristics. Through the adopted pdf representation, we derive a closure scheme which we formulate in terms of a consistency condition involving the second order statistics of the response, the closure constraint. A similar condition, the dynamics constraint, is also derived directly through the moment equations. These two constraints are formulated as a low-dimensional minimization problem with respect to unknown parameters of the representation, the minimization of which imposes an interplay between the dynamics and the adopted closure. The new method allows for the semi-analytical representation of the two-time, non-Gaussian structure of the solution as well as the joint statistical structure of the response-excitation over different time instants. We demonstrate its effectiveness through the application on bistable nonlinear single-degree-of-freedom energy harvesters with mechanical and electromagnetic damping, and we show that the results compare favorably with direct Monte-Carlo Simulations

Vibrational energy harvesting for sensors in vehicles

The miniaturization of semiconductor technology and reduction in power requirements have begun to enable wireless self-sufficient devices, powered by ambient energy. To date the primary application lies in generating and transmitting sensory data. The number of sensors and their applications in automotive vehicles has grown drastically in the last decade, a trend that seems to continue still. Wireless self-powered sensors can facilitate current sensor systems by removing the need for cabling and may enable additional applications. These systems have the potential to provide new avenues of optimization in safety and performance.This thesis delves into the topic of vibrations as ambient energy source, primarily for sensors in automotive vehicles. The transduction of small amounts of vibrational, or kinetic, energy to electrical power, also known as vibrational energy harvesting, is an extensive field of research with a plethora of inventions. A short review is given for energy harvesters, in an automotive context, utilizing transduction through either the piezoelectric effect or magnetic induction. Two practical examples, for ambient vibration harvesting in vehicles, are described in more detail. The first is a piezoelectric beam for powering a strain sensor on the engines rotating flexplate. It makes combined use of centrifugal force, gravitational pull and random vibrations to enhance performance and reduce required system size. The simulated power output is 370 \ub5W at a rotation frequency of 10.5 Hz, with a bandwidth of 2.44 Hz. The second example is an energy harvesting unit placed on a belt buckle. It implements magnetic induction by the novel concept of a spring balance air gap of a magnetic circuit, to efficiently harvest minute vibrations. Simulations show the potential to achieve 52 \ub5W under normal road conditions driving at 70 km/h. Theoretical modeling of these systems is also addressed. Fundamental descriptions of the lumped and distributed models are given. Based on the lumped models of the piezoelectric energy harvester (PEH) and the electromagnetic energy harvester (EMEH), a unified model is described and analyzed. New insights are gained regarding the pros and cons of the two types of energy harvester run at either resonance or anti-resonance. A numerical solution is given for the exact boundary of dimensionless quality factor and dimensionless intrinsic resistance, at which the system begins to exhibit anti-resonance. Regarding the maximum achievable power, the typical PEH is favored when running the system in anti-resonance and the typical EMEH is favored at resonance. The described modeling considers all parameters of the lumped model and thus provides a useful tool for developing vibrational energy harvester prototypes

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

A two-step hybrid approach for modeling the nonlinear dynamic response of piezoelectric energy harvesters

An effective hybrid computational framework is described here in order to assess the nonlinear dynamic response of piezoelectric energy harvesting devices. The proposed strategy basically consists of two steps. First, fully coupled multiphysics finite element (FE) analyses are performed to evaluate the nonlinear static response of the device. An enhanced reduced-order model is then derived, where the global dynamic response is formulated in the state-space using lumped coefficients enriched with the information derived from the FE simulations. The electromechanical response of piezoelectric beams under forced vibrations is studied by means of the proposed approach, which is also validated by comparing numerical predictions with some experimental results. Such numerical and experimental investigations have been carried out with the main aim of studying the influence of material and geometrical parameters on the global nonlinear response. The advantage of the presented approach is that the overall computational and experimental efforts are significantly reduced while preserving a satisfactory accuracy in the assessment of the global behavior

On Mechanical and Electrical Coupling Determination at Piezoelectric Harvester by Customized Algorithm Modeling and Measurable Properties

Piezoelectric harvesters use the actuation potential of the piezoelectric material to transform mechanical and vibrational energies into electrical power, scavenging energy from their environment. Few research has been focused on the development and understanding of the piezoelectric harvesters from the material themselves and the real piezoelectric and mechanical properties of the harvester. In the present work, the authors propose a behavior real model based on the experimentally measured electromechanical parameters of a homemade PZT bimorph harvester with the aim to predict its Vrms output. To adjust the harvester behavior, an iterative customized algorithm has been developed in order to adapt the electromechanical coupling coefficient, finding the relationship between the harvester actuator and generator behavior. It has been demonstrated that the harvester adapts its elongation and its piezoelectric coefficients combining the effect of the applied mechanical strain and the electrical behavior as a more realistic behavior due to the electromechanical nature of the material. The complex rms voltage output of the homemade bimorph harvester in the frequency domain has been successfully reproduced by the proposed model. The Behavior Real Model, BRM, developed could become a powerful tool for the design and manufacturing of a piezoelectric harvester based on its customized dimensions, configuration, and the piezoelectric properties of the smart materials.This research was funded by the Basque Government, grant number KK-2021/00082-µ4IIoT, and by the European Commission, grant number 869884- RECLAIM

SUSTAINABLE ENERGY HARVESTING TECHNOLOGIES – PAST, PRESENT AND FUTURE

Chapter 8: Energy Harvesting Technologies: Thick-Film Piezoelectric Microgenerato

High-fidelity simulation of an ultrasonic standing-wave thermoacoustic engine with bulk viscosity effects

We have carried out boundary-layer-resolved, unstructured fully-compressible Navier--Stokes simulations of an ultrasonic standing-wave thermoacoustic engine (TAE) model. The model is constructed as a quarter-wavelength engine, approximately 4 mm by 4 mm in size and operating at 25 kHz, and comprises a thermoacoustic stack and a coin-shaped cavity, a design inspired by Flitcroft and Symko (2013). Thermal and viscous boundary layers (order of 10 $\mathrm{\mu}$m) are resolved. Vibrational and rotational molecular relaxation are modeled with an effective bulk viscosity coefficient modifying the viscous stress tensor. The effective bulk viscosity coefficient is estimated from the difference between theoretical and semi-empirical attenuation curves. Contributions to the effective bulk viscosity coefficient can be identified as from vibrational and rotational molecular relaxation. The inclusion of the coefficient captures acoustic absorption from infrasonic ($\sim$10 Hz) to ultrasonic ($\sim$100 kHz) frequencies. The value of bulk viscosity depends on pressure, temperature, and frequency, as well as the relative humidity of the working fluid. Simulations of the TAE are carried out to the limit cycle, with growth rates and limit-cycle amplitudes varying non-monotonically with the magnitude of bulk viscosity, reaching a maximum for a relative humidity level of 5%. A corresponding linear model with minor losses was developed; the linear model overpredicts transient growth rate but gives an accurate estimate of limit cycle behavior. An improved understanding of thermoacoustic energy conversion in the ultrasonic regime based on a high-fidelity computational framework will help to further improve the power density advantages of small-scale thermoacoustic engines.Comment: 55th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201