Defects in flexoelectric solids

A solid is said to be flexoelectric when it polarizes in proportion to strain gradients. Since strain gradients are large near defects, we expect the flexoelectric effect to be prominent there and decay away at distances much larger than a flexoelectric length scale. Here, we quantify this expectation by computing displacement, stress and polarization fields near defects in flexoelectric solids. For point defects we recover some well known results from strain gradient elasticity and non-local piezoelectric theories, but with different length scales in the final expressions. For edge dislocations we show that the electric potential is a maximum in the vicinity of the dislocation core. We also estimate the polarized line charge density of an edge dislocation in an isotropic flexoelectric solid which is in agreement with some measurements in ice. We perform an asymptotic analysis of the crack tip fields in flexoelectric solids and show that our results share some features from solutions in strain gradient elasticity and piezoelectricity. We also compute the energy release rate for cracks using simple crack face boundary conditions and use them in classical criteria for crack growth to make predictions. Our analysis can serve as a starting point for more sophisticated analytic and computational treatments of defects in flexoelectric solids which are gaining increasing prominence in the field of nanoscience and nanotechnology.     

Power extraction from aeroelastic limit cycle oscillations

Nonlinear limit cycle oscillations of an aeroelastic energy harvester are exploited for enhanced piezoelectric power generation from aerodynamic flows. Specifically, a flexible beam with piezoelectric laminates is excited by a uniform axial flow field in a manner analogous to a flapping flag such that the system delivers power to an electrical impedance load. Fluid–structure interaction is modeled by augmenting a system of nonlinear equations for an electroelastic beam with a discretized vortex-lattice potential flow model. Experimental results from a prototype aeroelastic energy harvester are also presented. Root mean square electrical power on the order of 2.5 mW was delivered below the flutter boundary of the test apparatus at a comparatively low wind speed of 27 m/s and a chord normalized limit cycle amplitude of 0.33. Moreover, subcritical limit cycles with chord normalized amplitudes of up to 0.46 were observed. Calculations indicate that the system tested here was able to access over 17% of the flow energy to which it was exposed. Methods for designing aeroelastic energy harvesters by exploiting nonlinear aeroelastic phenomena and potential improvements to existing relevant aerodynamic models are also discussed.     

Damping in a parametric pendulum with a view on energy harvesting

The present article addresses the quantification of damping in a parametric pendulum, with a view on further applications in the design of energy harvesting devices. Detailed new experimental data is obtained for such purpose, and a novel mathematical model is presented. Linear and quadratic viscous damping and also dry friction are taken into account. To introduce the dry friction component, the pendulum axis is mounted on ball bearings. This is considered as a very realistic situation of a harvester. Damping parameters are determined by minimizing the difference between numerical and experimental time histories. It is shown that the damping model here presented is more adequate to replicate experiments than commonly used linear models, which consider only a linear viscous damping term characterized by means of free decay tests. It is also pointed that linear models are not adequate for refined studies, since they can lead to erroneous predictions of rotation zones, and consequently to wrong considerations in the design of pendulum harvesters.     

Interplay between phononic bandgaps and piezoelectric microstructures for energy harvesting

The paper introduces a multifunctional structural design combining superior mechanical wave filtering properties and energy harvesting capabilities. The proposed concept is based on the ability of most periodic structures to forbid elastic waves from propagating within specific frequency ranges known as phononic bandgaps. The bandgap density and the resulting filtering effect are dramatically enhanced through the introduction of a microstructure consisting of stiff inclusions which resonate at specific frequencies and produce significant strain and energy localization. Energy harvesting is achieved as a result of the conversion of the localized kinetic energy into electrical energy through the piezoelectric effect featured by the material in the microstructure. The idea is illustrated through the application to hexagonal truss-core honeycombs featuring periodically distributed stiff cantilever beams provided with piezoelectric electrodes. The multifunctional capability results from the localized oscillatory phenomena exhibited by the cantilevers for excitations falling in the neighborhood of the bending fundamental frequencies of the beams. This application is of particular interest for advanced aerospace and mechanical engineering applications where distinct capabilities are simultaneously pursued and weight containment represents a critical design constraint. The scalability of the analysis suggests the possibility to miniaturize the design to the microscale for microelectromechanical systems (MEMS) applications such as self-powered microsystems and wireless sensors.     

On the efficiency of energy harvesting using vortex-induced vibrations of cables

Many technologies based on fluid–structure interaction mechanisms are being developed to harvest energy from geophysical flows. The velocity of such flows is low, and so is their energy density. Large systems are therefore required to extract a significant amount of energy. The question of the efficiency of energy harvesting using vortex-induced vibrations (VIV) of cables is addressed in this paper, through two reference configurations: (i) a long tensioned cable with periodically-distributed harvesters and (ii) a hanging cable with a single harvester at its upper extremity. After validation against either direct numerical simulations or experiments, an appropriate reduced-order wake-oscillator model is used to perform parametric studies of the impact of the harvesting parameters on the efficiency. For both configurations, an optimal set of parameters is identified and it is shown that the maximum efficiency is close to the value reached with an elastically-mounted rigid cylinder. The variability of the efficiency is studied in light of the fundamental properties of each configuration, i.e. body flexibility and gravity-induced spatial variation of the tension. In the periodically-distributed harvester configuration, it is found that the standing-wave nature of the vibration and structural mode selection plays a central role in energy extraction. In contrast, the efficiency of the hanging cable is essentially driven by the occurrence of traveling wave vibrations.     

Design of piezoelectric energy harvesting devices subjected to broadband random vibrations by applying topology optimization

Converting ambient vibration energy into electrical energy by using piezoelectric energy harvester has attracted a lot of interest in the past few years.In this paper,a topology optimization based method is applied to simultaneously determine the optimal layout of the piezoelectric energy harvesting devices and the optimal position of the mass loading.The objective function is to maximize the energy harvesting performance over a range of vibration frequencies.Pseudo excitation method (PEM) is adopted to analyze structural stationary random responses,and sensitivity analysis is then performed by using the adjoint method.Numerical examples are presented to demonstrate the validity of the proposed approach.     

Energy harvesting of a heaving and forward pitching wing with a passively actuated trailing edge

This study experimentally investigates the energy harvesting capabilities of an oscillating wing with a passively actuated trailing edge. The oscillation kinematics are composed of a combined heaving and forward pitching motions, where the pitching axis is well behind the wing center of mass. Passive actuation is attained by connecting the trailing edge with the wing body using a torsion rod. The degree of flexibility of the trailing edge is represented by the Strouhal number based on the trailing edge natural frequency. The trailing edge passive response is studied for oscillation Strouhal numbers of 0.017, 0.025 and 0.033. Instantaneous aerodynamic forces are measured in a closed loop wind tunnel at a Reynolds number of 40 000, based on the free stream velocity and the wing chord length. Measured results include the effective angle of attack induced by the trailing edge actuation as well as the lift and moment during the oscillation cycle. For the imposed kinematics in this study, the pitching motion has a positive contribution to the mean power output whereas the heaving motion has a relatively small but negative contribution. Additionally, by decreasing the natural frequency of the trailing edge closer to that of the imposed oscillation frequency, the magnitude of the lift and moment forces and hence the mean power output, increases. It is found that there exists a strong correlation between mean power output and the effective angle of attack, shown through the passive trailing edge response, resulting in an increase in energy harvesting potential.     

Optimal electromagnetic energy extraction from transverse galloping

A fully coupled electro-fluid-elastic model for electromagnetic energy harvesting from Transverse Galloping is presented here. The model considers a one degree-of-freedom galloping oscillator where fluid forces are described resorting to quasi-steady conditions; the electromagnetic generator is modelled by an equivalent electrical circuit where power is dissipated at an electrical load resistance; the galloping oscillator and the electromagnetic model are coupled appropriately. Two different levels of simplification have been made depending on the comparison between the characteristic electrical and mechanical timescales. The effect of the electrical resistance load on the energy harvested is studied theoretically. For fixed geometry and mechanical parameters, it has been found that there exists an optimal electrical resistance load for each reduced velocity. On the practical side, this result can be helpful to design tracking-point strategies to maximize energy harvesting for variable flow velocity conditions.     

Performance enhancement of wing-based piezoaeroelastic energy harvesting through freeplay nonlinearity

We investigate experimentally how controlled freeplay nonlinearity affects harvesting energy from a wing-based piezoaeroelastic energy harvesting system. This system consisits of a rigid airfoil which is supported by a nonlinear torsional spring (freeplay) in the pitch degree of freedom and a linear flexural spring in the plunge degree of freedom. By attaching a piezoelectric material (PSI-5A4E) to the plunge degree of freedom, we can convert aeroelastic vibrations to electrical energy. The focus of this study is placed on the effects of the freeplay nonlinearity gap on the behavior of the harvester in terms of cut-in speed and level of harvested power. Although the freeplay nonlinearity may result in subcritical Hopf bifurcations (catastrophic for real aircrafts), harvesting energy at low wind speeds is beneficial for designing piezoaeroelastic systems. It is demonstrated that increasing the freeplay nonlinearity gap can decrease the cut-in speed through a subcritical instability and gives the possibility to harvest energy at low wind speeds. The results also demonstrate that an optimum value of the load resistance exists, at which the level of the harvested power is maximized.     

Energy harvesting of monostable Duffing oscillator under Gaussian white noise excitation

Energy harvesting of monostable Duffing oscillator with piezoelectric coupling under Gaussian white noise excitation is investigated. Based on the Fokker–Plank–Kolmogorov equation of piezoelectric coupling systems, the statistical moments of the response are derived from the Van Kampen expansion. The effects of the spectral density of the random excitation and the coefficient of cubic nonlinearity on the expected response moments are analyzed. Some numerical examples are presented to demonstrate the effects of excitation spectral density, coefficient of cubic nonlinearity and initial conditions on the output voltage.     

Piezoelectric energy harvesting from morphing wing motions for micro air vehicles

Wing flapping and morphing can be very beneficial to managing the weight of micro air vehicles through coupling the aerodynamic forces with stability and control. In this letter, harvesting energy from the wing morphing is studied to power cameras, sensors, or communication devices of micro air vehicles and to aid in the management of their power. The aerodynamic loads on flapping wings are simulated using a three-dimensional unsteady vortex lattice method. Active wing shape morphing is considered to enhance the performance of the flapping motion. A gradient-based optimization algorithm is used to pinpoint the optimal kinematics maximizing the propellent efficiency. To benefit from the wing deformation, we place piezoelectric layers near the wing roots. Gauss law is used to estimate the electrical harvested power. We demonstrate that enough power can be generated to operate a camera. Numerical analysis shows the feasibility of exploiting wing morphing to harvest energy and improving the design and performance of micro air vehicles.     

A review of nonlinear piezoelectric energy harvesting interface circuits in discrete components

Piezoelectric energy harvesting is considered as an ideal power resource for low-power consumption gadgets in vibrational environments. The energy extraction efficiency depends highly on the interface circuit, and should be highly improved to meet the power requirements. The nonlinear interface circuits in discrete components have been extensively explored and developed with the advantages of easy implementation, stable operation, high efficiency, and low cost. This paper reviews the state-of-the-art progress of nonlinear piezoelectric energy harvesting interface circuits in discrete components. First, the working principles and the advantages/disadvantages of four classical interface circuits are described. Then, the improved circuits based on the four typical circuits and other types of circuits are introduced in detail, and the advantages/disadvantages, output power, efficiency, energy consumption, and practicability of these circuits are analyzed. Finally, the future development trends of nonlinear piezoelectric energy harvesting circuits, e.g., self-powered extraction, low-power consumption, and broadband characteristic, are predicted.

     

Wide spectrum solar energy harvesting through an integrated photovoltaic and thermoelectric system

This paper proposes a power system concept that integrates photovoltaic （PV） and thermoelectric （TE） technologies to harvest solar energy from a wide spectral range. By introduction of the ＇spectrum beam splitting＇ technique, short wavelength solar radiation is converted directly into electricity in the PV cells, while the long wavelength segment of the spectrum is used to produce moderate to high temperature thermal energy, which then generates electricity in the TE device. To overcome the intermittent nature of solar radiation, the system is also coupled to a thermal energy storage unit. A systematic analysis of the integrated system is carried out, encompassing the system configuration, material properties, thermal management, and energy storage aspects. We have also attempted to optimize the integrated system. The results indicate that the system configuration and optimization are the most important factors for high overall efficiency.     

Analytical and finite-element study of optimal strain distribution in various beam shapes for energy harvesting applications

Owing to the increasing demand for harvesting energy from environmental vibration for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted considerable interest from various parties and has become one of the most common approaches to converting redundant mechanical energy into electrical energy. As the output voltage produced from a piezoelec-tric material depends largely on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beam that have not yet been discussed in any prior literature. Both analytical and finite-element models are derived and the resultant strain distributions in the beam are computed based on a MATLAB solver and ANSYS finite-element analysis tools. An optimum geome-try for a vibration-based energy harvesting system is verified. Finally, experimental results comparing the power density for triangular and rectangular piezoelectric beams are also pre-sented to validate the findings of the study, and the claim, as suggested in the literature, is verified.     

Recent advancement of flow-induced piezoelectric vibration energy harvesting techniques: principles,structures, and nonlinear designs

Energy harvesting induced from flowing fluids (e.g., air and water flows) is a well-known process, which can be regarded as a sustainable and renewable energy source. In addition to traditional high-efficiency devices (e.g., turbines and watermills), the micro-power extracting technologies based on the flow-induced vibration (FIV) effect have sparked great concerns by virtue of their prospective applications as a self-power source for the microelectronic devices in recent years. This article aims to conduct a comprehensive review for the FIV working principle and their potential applications for energy harvesting. First, various classifications of the FIV effect for energy harvesting are briefly introduced, such as vortex-induced vibration (VIV), galloping, flutter, and wake-induced vibration (WIV). Next, the development of FIV energy harvesting techniques is reviewed to discuss the research works in the past three years. The application of hybrid FIV energy harvesting techniques that can enhance the harvesting performance is also presented. Furthermore, the nonlinear designs of FIV-based energy harvesters are reported in this study, e.g., multi-stability and limit-cycle oscillation (LCO) phenomena. Moreover, advanced FIV-based energy harvesting studies for fluid engineering applications are briefly mentioned. Finally, conclusions and future outlook are summarized.

     

Energy harvesting by two magnetopiezoelastic oscillators with mistuning

We examine an energy harvesting system of two magnetopiezoelastic oscillators coupled by electric circuit and driven by harmonic excitation. We focus on the effects of synchronization and escape from a single potential well. In the system with relative mistuning in the stiffness of the harvesting oscillators, we show the dependence of the voltage output for different excitation frequencies.     

Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency

This paper investigates the energy harvested from the flutter of a plate in an axial flow by making use of piezoelectric materials. The equations for fully coupled linear dynamics of the fluid–solid and electrical systems are derived. The continuous limit is then considered, when the characteristic length of the plate's deformations is large compared to the piezoelectric patches' length. The linear stability analysis of the coupled system is addressed from both a local and global point of view. Piezoelectric energy harvesting adds rigidity and damping on the motion of the flexible plate, and destabilization by dissipation is observed for negative energy waves propagating in the medium. This result is confirmed in the global analysis of fluttering modes of a finite-length plate. It is finally observed that waves or modes destabilized by piezoelectric coupling maximize the energy conversion efficiency.