Sustained High-Frequency Dynamic Instability of a Nonlinear System of Coupled Oscillators Forced by Single or Repeated Impulses: Theoretical and Experimental Results

This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and kinematics. It has been found that under specific impulse excitations the transient damped dynamics of this system tracks a high-frequency impulsive orbit manifold (IOM) in the frequency-energy plane. The IOM extends over finite frequency and energy ranges, consisting of a countable infinity of periodic orbits and an uncountable infinity of quasi-periodic orbits of the underlying Hamiltonian system and being initially at rest and subjected to an impulsive force on the linear oscillator. The damped nonresonant dynamics tracking the IOM then resembles continuous resonance scattering; in effect, quickly transitioning between multiple resonance captures over finite frequency and energy ranges. Dynamic instability arises at bifurcation points along this damped transition, causing bursts in the response of the nonlinear light oscillator, which resemble self-excited resonances. It is shown that for an appropriate parameter design the system remains in a state of sustained high-frequency dynamic instability under the action of repeated impulses. In turn, this sustained instability results in strong energy transfers from the directly excited oscillator to the lightweight nonlinear attachment; a feature that can be employed in energy harvesting applications. The theoretical predictions are confirmed by experimental results.National Science Foundation (U.S.) (Grant CMMI-1100722

The slow-flow method of identification in nonlinear structural dynamics

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flowmodel identification method, which is demonstrated using numerical examples

PASSIVE SUPPRESSION OF AEROELASTIC INSTABILITIES OF IN-FLOW WINGS BY TARGETED ENERGY TRANSFERS TO LIGHTWEIGHT ESSENTIALLY NONLINEAR ATTACHMENTS

Theoretical and experimental suppression of aeroelastic instabilities by means of broadband passive targeted energy transfers has been recently studied. A single-degree-offreedom (SDOF) nonlinear energy sink (NES) was coupled to a 2-DOF rigid wing modeled in the low-speed, subsonic regime with quasi-steady aerodynamic theory. The nonlinear attachment was designed and optimized to suppress the critical nonlinear modal energy exchanges between the flow and the (pitch and heave) wing modes, thus suppressing the (transient) triggering mechanism of aeroelastic instability. We performed bifurcation analysis to find regions of robust passive aeroelastic suppression in parameter space. Then, we employed multi-degreeof-freedom nonlinear energy sinks (MDOF NESs) to improve robustness of the aeroelastic instability suppression. Bifurcation analysis by a numerical continuation technique demonstrated that controlling the occurrence of a limit point cycle (LPC or saddle-node) bifurcation point above a Hopf bifurcation point is crucial to enhancing suppression robustness. MDOF NESs not only can enhance robustness of suppression against even strong gust-like disturbances, but they require lower NES mass compared to SDOF NES designs. The validity of the theoretical findings was proven by a series of wind tunnel experiments

Empirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems

peer reviewedA relationship between IntrinsicMode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a nonlinear dynamical system has been exploited in the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems are identified from experimental data. Both the slow flows and IMFs provide the means to expand a general multicomponent signal in terms of a series of simpler, dominant, monocomponent signals. The slow flows are obtained analytically, for example through application of the method of complexification and averaging (CxA), which transforms the equations of motion into a set of approximate equations in amplitude and phase for each modeled frequency component. In contrast, the EMD characterizes a signal through the envelope and phase of its elemental components, the IMFs. Thus, between nonlinear transitions, the equations derived using the CxA method govern the amplitude and phase of the modeled IMFs. Application of SFMI has, until now, been limited to low-dimensional systems subjected to impulsive excitation. Herein, the method is extended to identification of a planar rigid airfoi

Pediatric functional magnetic resonance neuroimaging: tactics for encouraging task compliance

<p>Abstract</p> <p>Background</p> <p>Neuroimaging technology has afforded advances in our understanding of normal and pathological brain function and development in children and adolescents. However, noncompliance involving the inability to remain in the magnetic resonance imaging (MRI) scanner to complete tasks is one common and significant problem. Task noncompliance is an especially significant problem in pediatric functional magnetic resonance imaging (fMRI) research because increases in noncompliance produces a greater risk that a study sample will not be representative of the study population.</p> <p>Method</p> <p>In this preliminary investigation, we describe the development and application of an approach for increasing the number of fMRI tasks children complete during neuroimaging. Twenty-eight healthy children ages 9-13 years participated. Generalization of the approach was examined in additional fMRI and event-related potential investigations with children at risk for depression, children with anxiety and children with depression (N = 120). Essential features of the approach include a preference assessment for identifying multiple individualized rewards, increasing reinforcement rates during imaging by pairing tasks with chosen rewards and presenting a visual 'road map' listing tasks, rewards and current progress.</p> <p>Results</p> <p>Our results showing a higher percentage of fMRI task completion by healthy children provides proof of concept data for the recommended tactics. Additional support was provided by results showing our approach generalized to several additional fMRI and event-related potential investigations and clinical populations.</p> <p>Discussion</p> <p>We proposed that some forms of task noncompliance may emerge from less than optimal reward protocols. While our findings may not directly support the effectiveness of the multiple reward compliance protocol, increased attention to how rewards are selected and delivered may aid cooperation with completing fMRI tasks</p> <p>Conclusion</p> <p>The proposed approach contributes to the pediatric neuroimaging literature by providing a useful way to conceptualize and measure task noncompliance and by providing simple cost effective tactics for improving the effectiveness of common reward-based protocols.</p

Host movement dominates the predicted effects of climate change on parasite transmission between wild and domestic mountain ungulates

Climate change is shifting the transmission of parasites, which is determined by host density, ambient temperature and moisture. These shifts can lead to increased pressure from parasites, in wild and domestic animals, and can impact the effectiveness of parasite control strategies. Understanding the interactive effects of climate on host movement and parasite life histories will enable targeted parasite management, to ensure livestock productivity and avoid additional stress on wildlife populations. To assess complex outcomes under climate change, we applied a gastrointestinal nematode transmission model to a montane wildlife–livestock system, based on host movement and changes in abiotic factors due to elevation, comparing projected climate change scenarios with the historic climate. The wildlife host, Alpine ibex (Capra ibex ibex), undergoes seasonal elevational migration, and livestock are grazed during the summer for eight weeks. Total parasite infection pressure was more sensitive to host movement than to the direct effect of climatic conditions on parasite availability. Extended livestock grazing is predicted to increase parasite exposure for wildlife. These results demonstrate that movement of different host species should be considered when predicting the effects of climate change on parasite transmission, and can inform decisions to support wildlife and livestock health.<br/

Library Design in Combinatorial Chemistry by Monte Carlo Methods

Strategies for searching the space of variables in combinatorial chemistry experiments are presented, and a random energy model of combinatorial chemistry experiments is introduced. The search strategies, derived by analogy with the computer modeling technique of Monte Carlo, effectively search the variable space even in combinatorial chemistry experiments of modest size. Efficient implementations of the library design and redesign strategies are feasible with current experimental capabilities.Comment: 5 pages, 3 figure

Toward a fundamental understanding of the HHT in nonlinear structural dynamics

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flow model identification method, which is demonstrated using numerical examples

Suppression Aeroelastic Instability Using Broadband Passive Targeted Energy Transfers, Part 1: Theory

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76103/1/AIAA-24062-636.pd