Michael J. Mazzoleni

Experimental investigation of bifurcation induced bandgap reconfiguration

By applying an asymmetric on-site restoring force in a 1D chain of oscillators, we demonstrate experimentally that a morphing in the bandgap structure or passive bandgap reconfiguration can be triggered by an increase in environmental excitation amplitude. Recent studies on wave propagation have focused on new capabilities and behaviors resulting from intrinsic nonlinearities. This paper details a bistable experimental design that achieves amplitude dependent filtering through passive bandgap reconfiguration, which is triggered by a bifurcation. The system studied comprises a 1D chain of axially aligned pendulums in dimer unit cells with geometrically nonlinear nearest neighbor coupling where bistability is induced through repulsive magnets. When the bistability is asymmetric, each potential well has a different linear spectra. Though this paper uses mechanically coupled oscillators as an example, the phenomenon itself could be used in any wave propagation media where asymmetric bistability can be implemented.

Modeling Heart Rate Dynamics in Response to Changes in Exercise Intensity

This paper develops a nonlinear mathematical model to describe the heart rate response of an individual during cycling. The model is able to account for the fluctuations of an individual’s heart rate while they participate in exercise that varies in intensity. A method for estimating the model parameters using a genetic algorithm is presented and implemented, and the results show good agreement between the actual parameter values and the estimated values when tested using synthetic data.Copyright

Investigation of Rocking Semicircular and Parabolic Disk Equilibria, Stability, and Natural Frequencies

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb’s method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic cross sections, respectively. For the case of the semicircular disk, the system’s equation of motion is derived to verify Lamb’s method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.Copyright

A nonlinear model for the characterization and optimization of athletic training and performance

Summary Study aim: Mathematical models of the relationship between training and performance facilitate the design of training protocols to achieve performance goals. However, current linear models do not account for nonlinear physiological effects such as saturation and over-training. This severely limits their practical applicability, especially for optimizing training strategies. This study describes, analyzes, and applies a new nonlinear model to account for these physiological effects. Material and methods: This study considers the equilibria and step response of the nonlinear differential equation model to show its characteristics and trends, optimizes training protocols using genetic algorithms to maximize performance by applying the model under various realistic constraints, and presents a case study fitting the model to human performance data. Results: The nonlinear model captures the saturation and over-training effects; produces realistic training protocols with training progression, a high-intensity phase, and a taper; and closely fits the experimental performance data. Fitting the model parameters to subsets of the data identifies which parameters have the largest variability but reveals that the performance predictions are relatively consistent. Conclusions: These findings provide a new mathematical foundation for modeling and optimizing athletic training routines subject to an individual’s personal physiology, constraints, and performance goals.

Theoretical and Experimental Analysis of Bifurcation Induced Passive Bandgap Reconfiguration

This paper presents a theoretical analysis and experimental validation of passively reconfigurable bandgaps in a 1D chain of oscillators. Nonlinearities in the system result in a morphing of the bandgap structure when the excitation amplitude passes a certain threshold. Specifically, an asymmetric bistability is used to achieve amplitude dependent filtering through passive bandgap reconfiguration. The experimental system consists of a 1D chain of axially aligned pendulums arranged in dimer unit cells with nearest neighbor coupling. Repulsive magnets are used to induce bistability in the pendulums. Comparisons between experiments and theory show good agreement.

Investigation of wave propagation phenomena in microfabricated arrays of nonlinearly coupled oscillators

We demonstrate a MEMS platform for the investigation of energy propagation behavior in an array of nonlinearly coupled oscillators. The long-term objective is to experimentally demonstrate behaviors that have, until recently, only been theorized to occur in oscillator networks, such as passively reconfiguring bandgaps, energy localization, and chimera states. An improved fundamental understanding and of these phenomena could offer new capabilities for the prevention of catastrophic failures from shock loads, passive amplitude and frequency filters, and energy conversion systems. Here, we detail the design and fabrication of a coupled oscillator testbed, and then demonstrate transverse wave propagation along 1-D magnetically coupled oscillator arrays. Ongoing experiments seek to realize more complicated energy transfer behavior via design variations on this testbed.

Investigation of Wave Propagation Behavior in Magnetically Coupled MEMS Oscillators

This paper investigates the dynamic behavior of a 1D array of magnetically coupled MEMS oscillators. To facilitate future research and innovation, this paper details the model used to predict wave propagation behavior in the microfabricated array. The investigations model the oscillator array as a series of clamped-clamped beams that are coupled via magnetic proof masses. The contributions to system dynamics of the beam and magnetic interactions of each oscillator are theorized. Finally, the dynamic behavior for the entire array is investigated with a series of theoretical trend studies.Copyright