Mohammed F. Daqaq

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

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. [DOI: 10.1115/1.4026278]

A scalable concept for micropower generation using flow-induced self-excited oscillations

Inspired by music-playing harmonicas that create tones via oscillations of reeds when subjected to air blow, this paper entails a concept for microwind power generation using flow-induced self-excited oscillations of a piezoelectric beam embedded within a cavity. Specifically, when the volumetric flow rate of air past the beam exceeds a certain threshold, the energy pumped into the structure via nonlinear pressure forces offsets the system’s intrinsic damping setting the beam into self-sustained limit-cycle oscillations. The vibratory energy is then converted into electricity through principles of piezoelectricity. Experimental and theoretical results are presented demonstrating the feasibility of the proposed concept.

Investigation of Power Harvesting via Parametric Excitations

This article presents an analytical and experimental investigation of energy harvesting via parametrically excited cantilever beams. To that end, we consider a lumped-parameter non-linear model that describes the first-mode dynamics of a parametrically excited cantilever-type harvester. The model accounts for the beams geometric and inertia non-linearities as well as non-linearities representing air drag. Using the method of multiple scales, we obtain approximate analytical expressions describing the beam response, voltage drop across a purely resistive load, and output power in the vicinity of the first principle parametric resonance. Using these expressions, we study the effect of the electromechanical coupling and load resistance on the output power. We show that these parameters play an imperative role in determining the magnitude of the output power and characterizing the broad-band properties of the harvester. Specifically, we show that the region of parametric instability wherein energy can be harvested shrinks as the coupling coefficient increases. Furthermore, we show that there exists a coupling coefficient beyond which the peak power decreases. We also demonstrate that there is a critical excitation level below which no energy can be harvested. The amplitude of this critical excitation increases with the coupling coefficient and is maximized for a given load resistance. Theoretical findings that were compared to experimental results show good agreement and reflect the general trends.

Modeling, Nonlinear Dynamics, and Identification of a Piezoelectrically Actuated Microcantilever Sensor

Nanomechanical cantilever sensors (NMCSs) have recently emerged as an effective means for label-free chemical and biological species detection. They operate through the adsorption of species on the functionalized surface of mechanical cantilevers. Through this functionalization, molecular recognition is directly transduced into a micromechanical response. In order to effectively utilize these sensors in practice and correctly relate the micromechanical response to the associated adsorbed species, the chief technical issues related to modeling must be resolved. Along these lines, this paper presents a general nonlinear-comprehensive modeling framework for piezoelectrically actuated microcantilevers and validates it experimentally. The proposed model considers both longitudinal and flexural vibrations and their coupling in addition to the ever-present geometric and material nonlinearities. Utilizing Euler-Bernoulli beam theory and employing the inextensibility conditions, the coupled longitudinal-flexural equations of motion are reduced to one nonlinear partial differential equation describing the flexural vibrations of the sensor. Using a Galerkian expansion, the resulting equation is discretized into a set of nonlinear ordinary differential equations. The method of multiple scales is then implemented to analytically construct the nonlinear response of the sensor near the first modal frequency (primary resonance of the first vibration mode). These solutions are compared to experimental results demonstrating that the sensor exhibits a softening-type nonlinear response. Such behavior can be attributed to the presence of quadratic material nonlinearities in the piezoelectric layer. This observation is critical, as it suggests that unlike macrocantilevers where the geometric hardening nonlinearities dominate the response behavior, material nonlinearities dominate the response of microcantilevers yielding a softening-type response. This behavior should be accounted for when designing and employing such sensors for practical applications.

Energy harvesting in the super-harmonic frequency region of a twin-well oscillator

Nonlinear dynamical systems exhibit super-harmonic resonances that can activate large-amplitude motions at fraction integers of the fundamental frequency of the system. Such resonances offer a unique and untapped opportunity for harnessing vibratory energy from excitation sources with low-frequency components. To that end, this paper exploits the super-harmonic frequency bands of a nonlinear twin-well (bi-stable) oscillator for harvesting energy from low-frequency excitations. Theoretical and experimental studies are performed on an axially loaded clamped-clamped piezoelectric beam harvester with bi-stable potential characteristics. Voltage- and power-frequency bifurcation maps are generated near the super-harmonic resonance of order two. It is shown that, for certain base acceleration levels, the harvester can exhibit responses that are favorable for energy harvesting. These include a unique branch of large-orbit periodic inter-well oscillations, coexisting branches of large-orbit solutions, and a bandwidth of frequencies where a unique chaotic attractor exists. In these frequency regions, the harvester can produce power levels at half its fundamental frequency that are comparable to those obtained near the fundamental frequency.

Investigation of concurrent energy harvesting from ambient vibrations and wind using a single piezoelectric generator

In this letter, a single vibratory energy harvester integrated with an airfoil is proposed to concurrently harness energy from ambient vibrations and wind. In terms of its transduction capabilities and power density, the integrated device is shown to have a superior performance under the combined loading when compared to utilizing two separate devices to harvest energy independently from the two available energy sources. Even below its flutter speed, the proposed device was able to provide 2.5 times the power obtained using two separate harvesters.

A Graphical Approach to Input-Shaping Control Design for Container Cranes With Hoist

A traditional input-shaping technique is adapted to control transfer maneuvers on quay-side container cranes. The controller is developed using an accurate two-dimensional four-bar-mechanism model of a container crane and accounts for maneuvers that involve large hoisting operations. A graphical representation of the phase plane of the payload oscillations is used to derive mathematical constraints to compute the switching times of a double-step acceleration profile that results in minimal transient and residual oscillations. In contrast with single-step shaped acceleration profiles which are very sensitive to frequency approximations, the proposed double-step profile is less sensitive to small variations in the frequency even for large trolley accelerations

Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations

This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are presented to characterize the response behavior under the combined loading.

Pendulation Reduction on Small Ship-Mounted Telescopic Cranes

Small ship-mounted telescopic cranes are used to load and unload cargo of limited size and weight. The wave-induced motions of the crane ship can cause large pendulations of the hoisted payload bringing the transfer operations to a complete halt. The small size of such a crane, combined with its limited maneu-verability, compared to the relatively larger motion of the host ship, poses a serious control challenge. In this work, a nonlinear control system is introduced which reduces pendulations on these cranes to the point where the transfer operations do not pose a dangerous working environment. Delayed position-feedback technique is used to reduce the payload pendulations. The presented control system uses the slewing, luffing, and telescopic degrees of freedom of the crane to drive the horizontal position of the boom tip. The saturation problem arising from the limited speed and motion of the crane actuators is another issue addressed by this control technique. To demonstrate the performance of the developed control system, numerical simulations are performed on a nonlinear three-dimensional mathematical model of the telescopic crane mounted on the USNS WATERS. The crane has four degrees of freedom: hoisting, slewing, luffing, and extension of the telescopic boom. In addition to its limited maneuverability, nonlinear hydraulic actuators are used for the luffing and extensional degrees of freedom.

On the optimal performance and universal design curves of galloping energy harvesters

In this letter, we establish a universal relationship between a dimensionless version of the output power and the flow speed for galloping energy harvesters. This relationship yields a unique curve, which is only sensitive to the aerodynamic properties of the bluff body, but is, otherwise, invariant under any changes in the mechanical and electrical design parameters of the harvester. The curve permits a simple and direct comparative analysis of the energy harvesting performance of different bluff bodies so long that the other design parameters are kept constant. The universal curve is also shown to facilitate the optimization analysis, thereby providing significant insight into the optimal performance conditions.