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Bifurcation Analysis of a Microactuator Using a New Toolbox for Continuation of Hybrid System Trajectories
This paper presents the application of a newly developed computational toolbox, TC-HAT, for bifurcation analysis of systems in which continuous-in-time dynamics are interrupted by discrete-in-time events, here referred to as hybrid dynamical systems. In particular, new results pertaining to the dynamic behavior of a sample hybrid dynamical system, an impact microactuator, are obtained using this software program. Here, periodic trajectories of the actuator with single or multiple impacts per period and associated saddle-node, period-doubling, and grazing bifurcation curves are documented. The analysis confirms previous analytical results regarding the presence of co-dimension-two grazing bifurcation points from which saddle-node and period-doubling bifurcation curves emanate.W. Kang et al, Bifurcation Analysis of a Microactuator Using a New Toolbox for Continuation of Hybrid System Trajectories, Journal of Computational and Nonlinear Dynamics, 4(1), 0110091-8, 2009 (Top 10 Most Downloaded Articles – December 2008).A Dynamic Grain Flow Model for a Mass Flow Yield Sensor on a Combine
A model is developed to describe the flow of grain through a clean grain elevator system on a combine in order to facilitate accurate mass flow rate estimation. The relationship between mass flow rate and impact force described by the model depends upon machine operational characteristics, mechanical interactions of the grain and the machine geometry, and material properties of the grain. The model was designed to be adaptable to varying grain conditions, such as those influenced by moisture content, by allowing free parameters of the model to be estimated through a nonlinear regression algorithm. Simulations were performed using discrete element modeling software and data was obtained from experiments conducted on a clean grain elevator system at the University of Kentucky Combine Yield Monitor Test Facility to determine the ability of the model to accurately estimate mass flow rate. The model estimated mass flow rate with a normalized root mean squared residual (NRMSR) less than 2% for discrete element modeling simulations. For experiments involving machine components, NRMSR values were less than 3% for corn at 14% moisture, less than 3% for corn at 21% moisture, and less than 5% for corn at 26% moisture.
R. Reinke, H. Dankowicz, J. Phelan, and W. Kang, A Dynamic Grain Flow Model for a Mass Flow Yield Sensor on a Combine, Journal of Precision Agriculture, 12(5), 732-749, 2011.
Granular Layers on Vibrating Plates
Acoustic methods of land mine detection rely on the vibrations of the top plate of the mine in response to sound. For granular soil .e.g., sand., the particle size is expected to influence the mine response. This hypothesis is studied experimentally using a plate loaded with dry sand of various sizes from hundreds of microns to a few millimeters. For low values of sand mass, the plate resonance decreases with added mass and eventually reaches a minimum without particle size dependence. After the minimum, a frequency increase is observed with additional mass that includes a particle-size effect. Analytical nondissipative continuum models for granular media capture the observed particle-size dependence qualitatively but not quantitatively. In addition, a continuum-based finite element model (FEM) of a two-layer plate is used, with the sand layer replaced by an equivalent elastic layer for evaluation of the effective properties of the layer. Given a thickness of sand layer and corresponding experimental resonance, an inverse FEM problem is solved iteratively to give the effective Young’s modulus and bending stiffness that matches the experimental frequency. It is shown that a continuum elastic model must employ a thickness-dependent elastic modulus in order to match experimental values.W. Kang et al, Granular Layers on Vibrating Plates: Effective Bending Stiffness and Particle-Size Effect, Journal of the Acoustical Society of America, 121(2), 888-896, 2007.
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