Adam M. Wickenheiser

Broadband vibration-based energy harvesting improvement through frequency up-conversion by magnetic excitation

Traditional vibration-based energy harvesters are designed for a specific base excitation frequency by matching its fundamental natural frequency. This work presents the modeling and analysis of a nonlinear, magnetically excited energy harvester that exhibits efficient broadband, frequency-independent performance utilizing a passive auxiliary structure that remains stationary relative to the base motion. This system is especially effective in the regime of driving frequencies well below its fundamental frequency, thus enabling a more compact design solution over traditional topologies. A model based on Euler–Bernoulli beam theory is coupled to a linear circuit and a model of the nonlinear, magnetic interaction to produce a distributed parameter magneto-electromechanical system. This model is used in both harmonic and stochastic base excitation case studies. The results of these simulations demonstrate multiple-order-of-magnitude power harvesting performance improvement at low driving frequencies and an insensitivity to time-varying base excitation. Furthermore, the proposed system is shown to outperform an optimally designed, standard energy harvester in the presence of broadband, random base excitation.

Optimization of Perching Maneuvers Through Vehicle Morphing

This paper discusses the development and optimization of trajectories designed to bring a long endurance unmanned aerial vehicle from a loitering state to a planted landing referred to as a perching maneuver. These trajectories are developed for attached, partially stalled, and fully stalled flow regimes. The effects of nonlinear aerodynamics and vehicle shape reconfiguration are shown to lessen the initial distance from the landing site required to initiate the maneuver, reduce the spatial bounds on the trajectory, and decrease the required thrust for the maneuver. The aerodynamics are modeled using empirical and analytical methods in both attached and separated flow regimes. Optimal solutions of varying thrust-to-weight ratio and center-of-gravity location are compared. Additionally, perching trajectories that compare morphing versus fixed configuration and stalled versus unstalled aircraft are presented to demonstrate the effects of relaxed constraints on vehicle geometry and flight envelope. Control effort is also evaluated in these simulations; specifically, the available control for disturbance rejection is compared for morphing versus fixed-configuration aircraft. The results of these comparisons show that morphing increases the controllability of the aircraft throughout the maneuver as well as decreases the cost of the optimal perching trajectory.

Modeling and experimental verification of synchronized discharging techniques for boosting power harvesting from piezoelectric transducers

This paper presents analytical models for studying the transient behavior of several power harvesting circuit topologies for use with piezoelectric bending transducers. Specifically, the problem of charging a large storage capacitor, which is inherently a time-varying process, is considered. Three circuit designs are studied?direct charging, synchronized switching and discharging to a storage capacitor, and synchronized switching and discharging to a storage capacitor through an inductor (SSDCI)?and they are compared to a matched resistive load case. Analytical models are developed for these cases to predict the charging rates and output power for various values of storage capacitance and quality factor. Experimental circuit designs are given and their results are compared to the theoretical predictions. It is shown that these predictions are accurate when the losses in the circuit are considered in the model. In spite of these losses, it is demonstrated that the SSDCI design can produce about 200% the output power of the idealized, matched resistive load case throughout the charging process and substantially reduce the charging time of the storage capacitor.

Power Optimization of Vibration Energy Harvesters Utilizing Passive and Active Circuits

This article presents the maximum power operating conditions for piezoelectric energy harvesters when connected to several different circuit topologies. Four circuits are studied herein for comparison: a simple resistive load, the standard rectifier circuit, and parallel and series synchronized switch harvesting on inductor. A single-mode model of a vibration-based energy harvester under base excitation is developed to capture the important dynamics near its fundamental resonance while providing a simple basis for performing design optimization. Relevant dimensionless parameters are given to provide a scale-free context for discussing the optimal operating points. For a prescribed vibration energy harvester, the base excitation frequency and load impedance for maximum power generation are provided by the results of this study. Furthermore, the effects of mechanical damping, electromechanical coupling, circuit quality factor, and rectifier forward voltage are presented. These effects are discussed in order to cite the salient parameters in the design of these energy harvesting systems.

Modeling the Effects of Electromechanical Coupling on Energy Storage Through Piezoelectric Energy Harvesting

This paper focuses on comparing the effects of varying degrees of electromechanical coupling in piezoelectric power harvesting systems on the dynamics of charging a storage capacitor. In order to gain an understanding of the behavior of these dynamics, a transducer whose vibrational dynamics are impacted very little by electrical energy extraction is compared to a transducer that displays strong electromechanical coupling. Both transducers are cantilevered piezoelectric beams undergoing base excitation whose harvested electrical energy is used to charge a storage capacitor. The transient dynamics of the coupled system are studied in detail with an emphasis on their charging power curves and the time to charge the storage capacitor to a specified voltage. An analytic model for the system is derived that takes into consideration the reduction in vibration amplitude of the beam caused by the removal of electrical energy. Although this model makes the typical assumption that the beam is vibrating at its open-circuit resonance, it is shown to predict the charging behavior of the system accurately when compared to experimental results and a complete, nonlinear simulation without this simplification. Finally, the simplifications and discrepancies created by several types of modeling assumptions for a highly coupled energy harvesting system are discussed.

Longitudinal dynamics of a perching aircraft

This paper introduces a morphing aircraft concept whose purpose is to demonstrate a new bioinspired flight capability: perching. Perching is a maneuver that uses primarily aerodynamics, as opposed to thrust generation, to achieve a vertical or short landing. The flight vehicle that will accomplish this is described herein with particular emphasis on its addition levels of actuation beyond the traditional aircraft control surfaces. The dynamics of this aircraft are examined with respect to changing vehicle configuration and flight condition. The analysis methodologies include an analytical and empirical aerodynamic analysis, trim and stability analyses, and flight simulation.Forthisstudy,theaircraft’smotionsarelimitedtothelongitudinalplaneonly.Specifically,cruiseandthe perching maneuver are examined, and comparisons are drawn between maneuvers involving vehicle reconfiguration and those that do not.

A Timoshenko beam model for cantilevered piezoelectric energy harvesters

Piezoelectric bimorph cantilevered beams are often used as energy harvesting devices. These devices are desired for, among other applications, remote sensing and animal tracking due to their potential for eliminating the need for battery replacement. Existing models of piezoelectric bimorph cantilevered beams have proved to describe the dynamics of slender beams at high frequencies accurately. In this paper, a Timoshenko model of transverse piezoelectric beam vibration is developed to address these limitations. Exact expressions for the voltage, current, power, and tip deflection of the piezoelectric beam are derived. Subsequently, several case studies are presented that examine the frequency response of vibration-based energy harvesters using this model. It is shown that the predicted responses converge towards previously derived Euler–Bernoulli beam models under certain limiting conditions. The Timoshenko model shows that the Euler–Bernoulli model severely over-predicts the tip displacement and consequently the power transduction of a cantilevered piezoelectric bimorph at low length-to-width aspect ratios.

Aerodynamic Modeling of Morphing Wings Using an Extended Lifting-Line Analysis

This paper presents an extension of Weissinger’smethod and its use in analyzing morphing wings. Thismethod is shown to be ideal for preliminary analyses of these wings due to its speed and adaptability to many disparate wing geometries. It extends Prandtl’s lifting-line theory to planform wings of arbitrary curvature and chord distribution and nonideal airfoil cross sections. The problem formulation described herein leads to an integrodifferential equation for the unknown circulation distribution. It is solved using Gaussian quadrature and a sine-series representation of this distribution. In this paper, this technique is used to analyze the aerodynamics of a morphable gull-like wing. Specifically, this wing’s ability to manipulate lift-to-drag efficiency and center of pressure location is discussed.

Design Optimization of Linear and Non-Linear Cantilevered Energy Harvesters for Broadband Vibrations

In much of the vibration-based energy harvesting literature, resonant energy harvesters are designed around a single base excitation frequency, whereas many applications comprise broadband, time-varying vibrations. Since many naturally occurring vibrations are low frequency, a relatively large mass or beam length is required to resonate at the driving frequencies. This article presents a modeling and optimization procedure for designing vibration energy harvesters for maximizing power generated by vibrations recreated from real-world sources at low frequencies. It is shown that the device coupling coefficient, a significant parameter in determining the energy transduction performance, can be decoupled into terms related to the stiffness and mass distribution of the device, each of which can be optimized independently. To demonstrate the use of this design optimization procedure, measured accelerations are used to provide time-varying, broadband inputs to the energy-harvesting system. Under various size and mass constraints, optimal linear resonant harvesters are presented for human walking and automobile driving scenarios. The frequency response functions are presented alongside time histories of the power harvested using the experimental base acceleration signals. Finally, these results are compared to a non-linear device that utilizes spatially periodic magnetic excitation, a feature that is particularly suited to low-frequency, time-varying excitation.

Eigensolution of piezoelectric energy harvesters with geometric discontinuities: Analytical modeling and validation

Although cantilevered beams are the most prolific design for resonant piezoelectric energy harvesters, other topologies have been studied for their compactness or conformability to their host structures’ geometry. These more complex structures have been analyzed using custom analytical models developed from the first principles or finite-element methods to compute their eigensolutions and piezoelectric coupling effects. This article discusses the use of the transfer matrix method to derive analytical solutions to beam structures with pointwise discontinuities, bends, or lumped inertias between members or at the tip. Euler–Bernoulli beam theory is used to derive transfer matrices for the uniform beam segments, and point transfer matrices are derived to handle discontinuities in the structure between beam segments. The eigensolution of the transfer matrix is shown to produce the natural frequencies and mode shapes for these structures. Subsequently, the electromechanical coupling effects are incorporated, and the base excitation problem is considered. Parametric case studies are provided for beam structures with varying piezoelectric layer coverage and angle between members. Finally, these results are compared to finite-element solutions using COMSOL, and the modeling discrepancies are discussed. Based on the favorable comparison between these two methods, the utility and accuracy of the transfer matrix method are proven.