D. Dane Quinn

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]

The Effect of Non-linear Piezoelectric Coupling on Vibration-based Energy Harvesting

Advances in electronic and consumer technology are increasing the need for smaller, more efficient energy sources. Thus vibration-based energy harvesting, the scavenging of energy from existing ambient vibration sources and its conversion to useful electrical power, is becoming an increasingly attractive alternative to traditional power sources such as batteries. Energy harvesting devices have been developed based on a number of electromechanical coupling mechanisms and their design must be optimized to produce the maximum output for given environmental conditions. While the role of non-linearities in the components has been shown to be significant in terms of the overall device efficiency, few studies have systematically investigated their influence on the system performance. In this work the role of a non-linear piezoelectric relationship is considered on the performance of a vibration-based energy harvester. Using a Poincaré-Lindstedt perturbation analysis the response of the harvesting system is approximated, including mechanical damping, stiffness non-linearities, and the above mentioned non-linear piezoelectric constitutive relationship. The predicted behavior is then compared against numerical simulations of the original system, focusing on the relationship between the power generated by the device, the ambient vibration characteristics, and the non-linearities in the system.

Cracked shaft detection and diagnostics: A literature review

Cracks in shafts have long been identified as factors limiting the safe and reliable operation of turbomachines. They can sometimes result in catastrophic failure of equipment (rotor bursts) and, more often, in costly process upsets, repairs and premature scrapping and replacement of equipment. Cracked shafts still pose a significant and real threat to equipment in spite of the great advances made in the areas of metallurgy, manufacturing and design. In the past two decades, much research and many resources have gone into developing various on-line and off-line diagnostic techniques to effectively detect cracks before they cause serious damage. Because of the enormous amount of ongoing research in this area (more than 500 technical papers have been published in English alone in the past 30 years), there is a real need to periodically condense and summarize the information. This paper reviews literature on cracked shaft detection and diagnostics published after 1990.

Effective Stiffening and Damping Enhancement of Structures With Strongly Nonlinear Local Attachments

can have on the dynamics of a primary linear structure. These local attachments can be designed to act as nonlinear energy sinks (NESs) of shock-induced energy by engaging in isolated resonance captures or resonance capture cascades with structural modes. After the introduction of the NESs, the effective stiffness and damping properties of the structure are characterized through appropriate measures, developed within this work, which are based on the energy contained within the modes of the primary structure. Three types of NESs are introduced in this work, and their effects on the stiffness and damping properties of the linear structure are studied via (local) instantaneous and (global) weightedaveraged effective stiffness and damping measures. Three different applications are considered and show that these attachments can drastically increase the effective damping properties of a two-degrees-of-freedom system and, to a lesser degree, the stiffening properties as well. An interesting finding reported herein is that the essentially nonlinear attachments can introduce significant nonlinear coupling between distinct structural modes, thus paving the way for nonlinear energy redistribution between structural modes. This feature, coupled with the well-established capacity of NESs to passively absorb and locally dissipate shock energy, can be used to create effective passive mitigation designs of structures under impulsive loads. [DOI: 10.1115/1.4005005]

Using Series-Series Iwan-Type Models for Understanding Joint Dynamics

In mechanical assemblies, the energy loss induced by joints and interfaces can account for a significant portion of the overall structural dissipation. This work considers the dynamical behavior of an elastic rod on a frictional foundation as a model for the dissipation introduced by micro-slip in mechanical joints. In a quasi-static loading limit, the deformation of the rod and hence the frictional dissipation can be solved in closed form. The resulting model is a continuum model of series arrangements of parallel Jenkins elements. For a general class of normal load distributions, the resulting energy loss per forcing cycle follows a power-law and is qualitatively similar to observed experimental findings. Finally, these results are compared with those obtained from a discrete formulation of the rod including inertial effects. For loading conditions that are consistent with mechanical joints, the numerical results from the discrete model are consistent with the closed form predictions obtained in the quasistatic limit.

Damage detection of a rotating cracked shaft using an active magnetic bearing as a force actuator - analysis and experimental verification

The active health monitoring of rotordynamic systems in the presence of breathing shaft cracks is considered in this work. The shaft is assumed to be supported by conventional bearings, and the active magnetic bearing (AMB) is used in a midshaft or outboard location as an actuator to apply specified, time-dependent forcing on the system. These forces, if properly chosen, induce a combination resonance that can be used to identify the magnitude of the time-dependent stiffness arising from the breathing mode of the shaft crack. The technique is verified experimentally on a high speed test rotor with a healthy and a cracked shaft.

Resonance Capture in a Three Degree-of-Freedom Mechanical System

We study the phenomena of resonance capture in a three degree-of-freedom dynamical system modeling the dynamics of an unbalanced rotor, subject to a small constant torque, supported by orthogonal, linearly elastic supports, which is constrained to move in the plane. In the physical system the resonance exists between translational motions of the frame and the angular velocity of the unbalanced rotor. These equations, valid in the neighborhood of the resonance, possess a small parameter ε which is related to the imbalance. In the limit ε → 0, the unperturbed system possesses a homoclinic orbit which separates bounded periodic motion corresponding to resonant solutions from unbounded motion which corresponds to solutions passing through the resonance. Using a generalized Melnikov integral, we characterize the splitting distance between the invariant manifolds which govern capture and escape from resonance for ε ≠ 0. It is shown that as certain slowly varying parameters evolve, the separation distance alternates sign, indicating that both capture into, and escape from resonance occur. We find that although a measurable set of initial conditions enter into a sustained resonance, as the system further evolves the orientation of the manifolds reverses and many of these captured solutions will subsequently escape.

Development, Characterization, and Design Considerations of Ni19.5Ti50.5 Pd25Pt5 High-temperature Shape Memory Alloy Helical Actuators

Shape memory alloys (SMAs) have been used in various applications since their discovery. However, their use as actuation devices in high-temperature environments has been limited due to the temperature constraints of commercially available materials. Recently, SMAs that produce good work characteristics at elevated temperatures have been developed at NASA’s Glenn Research Center. One such alloy, Ni19.5Ti50.5Pd25Pt 5, has shown repeatable strain recovery on the order of 2.5% in the presence of an externally applied stress at temperatures greater than 250°C. Based on these findings, potential applications for this alloy are being explored and further work is being done to assess the use of this alloy in various structural forms. In this article, the characterization of Ni 19.5Ti50.5Pd25Pt5 helical actuators is reported, including their mechanical responses and how variations in their responses correlate to changes in geometric parameters and training loads. Finally, implementation of previously published SMA spring design methodology in future SMA helical actuator development is considered through comparison of the observed and predicted responses.

The Dynamics of Resonant Capture

Resonant capture describes the behavior of a weakly coupled multi-degree-of-freedom system when two or more of its uncoupled frequencies become locked in resonance. Flow on the region of phase space near the resonance (the resonance manifold) involves a region bounded by a separatrix in the uncoupled (e=0) system. Capture corresponds to motions which appear to cross into the interior of the separated region for e>0. We offer two approximate methods for estimating which initial conditions lead to capture: an energy method and a perturbation method based on invariant manifold theory. These methods are applied to a model problem involving the spinup of an unbalanced rotor attached to an elastic support.

Equivalent modal damping, stiffening and energy exchanges in multi-degree-of-freedom systems with strongly nonlinear attachments

We consider the response of a linear structural system when coupled to an attachment containing strong or even essential nonlinearities. For this system, the attachment, designated as a nonlinear energy sink, is designed as a nonlinear vibration absorber, serving to dissipate energy from the structural system. Moreover, the attachment not only leads to a reduction in the total energy of the system, but also nonlinearly couples together the vibration modes of the linear structural system. When the structure is impulsively loaded, the nonlinear energy sink serves to both dissipate and redistribute energy, thus enhancing the observed structural dissipation. The effect of the nonlinear attachment on the linear primary system can be quantified in terms of equivalent measures for the damping and frequency of each mode, derived through consideration of the instantaneous energy balance in each mode. The influence of the nonlinear energy sink on the structural response is illustrated with an impulsively forced two-degree-of-freedom primary system, representing a two-story structure, with different types of nonlinear energy sink attached to the top floor. We perform optimization studies in order to design the nonlinear energy sink for optimal shock mitigation of the primary system. The proposed methodology is based only on measured time series without resorting to frequency analysis. As such, it is valid for strongly nonlinear systems as well as for systems with nonsmooth nonlinearities, and is suited to both simulated and experimental results. Finally, an experimental validation of the enhanced dissipation introduced by the nonlinear energy sink is provided, and the experimental response is compared against numerical simulation of the corresponding analytical model to illustrate the effectiveness of the nonlinear energy sink design. Thus, we analytically predict and experimentally verify the efficacy of the nonlinear energy sink to significantly reduce the response of the two degree-of-freedom system subject to shock excitation.