1,721,033 research outputs found
Nonlinear tuning of microresonators for dynamic range enhancement
No full textThis paper investigates the development of a novel framework and its implementation for the nonlinear
tuning of nano/microresonators. Using geometrically exact mechanical formulations, a nonlinear model is
obtained that governs the transverse and longitudinal dynamics of multilayer microbeams, and also takes
into account rotary inertia effects. The partial differential equations of motion are discretized,
according to the Galerkin method, after being reformulated into a mixed form. A zeroth-order shift
as well as a hardening effect are observed in the frequency response of the beam. These results are
confirmed by a higher order perturbation analysis using the method of multiple scales. An inverse
problem is then proposed for the continuation of the critical amplitude at which the transition
to nonlinear response characteristics occurs. Path following techniques are employed to explore the
dependence on the system parameters, as well as on the geometry of bilayer microbeams, of the magnitude
of the dynamic range in nano/microresonators
Nonlinear finite element-based path following of periodic solutions
No full textA computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) ?u = f(u; s; t; c) where u(s; t) is the vector collecting all state variables including the velocities/time rates, s is a space co-ordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and co-workers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f: A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures. Copyright © 2011 by ASME
Nonlinear Finite Element-based path following of periodic solutions
No full textA computational framework is proposed to path follow the periodic solutions of nonlinear spatially continuous systems and more general coupled multiphysics problems represented by systems of partial differential equations with time-dependent excitations. The set of PDEs is cast in first order differential form (in time) ?u = f(u; s; t; c) where u(s; t) is the vector collecting all state variables including the velocities/time rates, s is a space co-ordinate (here, one-dimensional systems are considered without lack of generality for the space dependence) and t denotes time. The vector field f depends, in general, not only on the classical state variables (such as positions and velocities) but also on the space gradients of the leading unknowns. The space gradients are introduced as part of the state variables. This is justified by the mathematical and computational requirements on the continuity in space up to the proper differential order of the space gradients associated with the unknown position vector field. The path following procedure employs, for the computation of the periodic solutions, only the evaluation of the vector field f. This part of the path following procedure within the proposed combined scheme was formerly implemented by Dankowicz and co-workers in a MATLAB software package called COCO. The here proposed procedure seeks to discretize the space dependence of the variables using finite elements based on Lagrangian polynomials which leads to a discrete form of the vector field f: A concurrent bifurcation analysis is carried out by calculating the eigenvalues of the monodromy matrix. A hinged-hinged nonlinear beam subject to a primary-resonance harmonic transverse load or to a parametric-resonance horizontal end displacement is considered as a case study. Some primary-resonance frequency-response curves are calculated along with their stability to assess the convergence of the discretization scheme. The frequency-response curves are shown to be in close agreement with those calculated by direct integration of the PDEs through the FE software called COMSOL Multiphysics. Besides primary-resonance direct forcing conditions, also parametric forcing causing the principal parametric resonance of the lowest two bending modes is considered through construction of the associated transition curves. The proposed approach integrates algorithms from the finite element and bifurcation domains thus enabling an accurate and effective unfolding of the bifurcation and post-bifurcation scenarios of nonautonomous PDEs with the underlying structures. Copyright © 2011 by ASME
Bifurcation analysis near the cessation of complete chatter and Shilnikov homoclinic trajectories in a pressure relief valve model
Full text linkThe student, Erika Fotsch, submitted this Thesis for approval on 2016-01-19 at 09:37.This Thesis was approved for publication on 2016-01-20 at 11:02.DSpace SAF Submission Ingestion Package generated from Vireo submission #9039 on 2016-07-07 at 13:48:04This thesis investigates bifurcations associated with periodic orbits with complete chatter, as well as bifurcations associated with homoclinic trajectories, in the dynamics of a pressure relief valve model. A combination of original numerical implementations with analytical tools found in the existing literature enables a deeper understanding of the dependence of the valve dynamics on system parameters. In particular, the transition from complete to incomplete chatter along a family of periodic orbits is explored to find a cascade of bifurcations that are then investigated further using a discrete-time approximation to the system dynamics. In addition, a toolbox that formulates a boundary value problem associated with a complete chatter sequence is developed within the computational framework of the continuation package coco. Lastly, a Shilnikov-type homoclinic bifurcation is located and the global manifold structure near this bifurcation point is explored using continuation methods applied to appropriate boundary value problems.Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2018-05-01The student, Erika Fotsch, accepted the attached license on 2016-01-19 at 09:30.Made available in DSpace on 2016-07-07T20:26:40Z (GMT). No. of bitstreams: 2
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Previous issue date: 2016-01-20Embargo set by: Seth Robbins for item 93061
Lift date: 2018-07-07T20:28:14Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemEmbargo set by: Seth Robbins for item 93061
Lift date: 2018-07-07T20:35:34Z
Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD systemU of I Only Restriction Lifted for Item 93061 on 2018-07-08T09:15:36Z
Analytic methods for stress analysis of two-dimensional flat anisotropic plates with notches: an overview
No full textThe anisotropy of composite plates often poses difficulties for stress field analysis in the presence of notches. The most common methods for these analyses are: (i) analytical means (AM), (ii) finite element analysis (FEA), and (iii) semi-analytical means (SAM). In industry, FEA has been especially popular for the determination of stresses in small to medium size parts but can require a considerable amount of computing power and time. For faster analyses, one can use AM. The available solutions for a given problem, however, can be quite limited. Additionally, AM implemented in commercial computer software are scarce and difficult to find. Due to this, these methods are not widespread and SAM were proposed. SAM combine the (easy) implementation of complex problems from FEA and the computational efficiency from AM to reduce the difficulty on mathematical operation and increase computational speed with respect to FEA. AM, however, are still the fastest and most accurate way to determine the stress field in a given problem. Complex problems, however, e.g., finite width plates with multiple loaded/unloaded notches, require a significant amount of mathematical involvement which quickly discourages, even seasoned, scientists, and engineers. To encourage the use of AM, this paper gives a brief review of the mathematical basis of AM followed by a historic perspective on the expansions originating from this mathematical basis. Specifically the case of a two-dimensional anisotropic plate with unloaded cut-outs subjected to in-plane static load is presented
Experimental validation of an L1 controller on a single robotic manipulator on a moving platform and a robotic cooperative network
Full text linkThis thesis reports on laboratory and in-field experimental results for a single robotic manipulator on a moving platform with unmodeled dynamics that aim to validate theoretical predictions for the dependence on control parameters of an L1 adaptive control strategy. The experiments verify expected bounds on the tracking error in terms of the bandwidth of a filter introduced in the control loop. Moreover, the results provide insight into different discretizations of the continuous-time formulation, suggesting that a partial discretization introduced by Cao and Hovakimyan is most suitable for a hardware implementation.
A second set of experimental results, obtained from an implementation of the L1 control framework for synchronization and consensus in networks of robotic manipulators, similarly validate theoretical predictions on the sensitivity to network communication delays and network topology.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-09-29 without embargo termsThe student, Andres Rodriguez Reina, accepted the attached license on 2017-04-25 at 21:11.The student, Andres Rodriguez Reina, submitted this Thesis for approval on 2017-04-25 at 21:22.This Thesis was approved for publication on 2017-04-26 at 16:38.DSpace SAF Submission Ingestion Package generated from Vireo submission #11077 on 2017-09-29 at 11:25:37Made available in DSpace on 2017-09-29T16:37:43Z (GMT). No. of bitstreams: 2
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Previous issue date: 2017-04-2
Dynamics near discontinuity events in systems with hysteresis and systems with finite state resets
No full textIn this thesis, we study the dynamics near grazing for a model of an atomic force microscope in tapping mode and a model of cell cycle mitosis. In particular, period one behavior is studied near grazing points corresponding to tangential contact with the discontinuity surface used to initiate capillary interactions in a tapping mode AFM model. Two different discontinuity mapping analysis methods are
developed and applied to this AFM model. The discontinuity mapping
analysis predicts the existence of a branch of period one solutions
emanating from the grazing point. In addition, the analysis predicts
that one eigenvalue of a suitable Poincaré map approaches minus infinity as the varied parameter approaches its grazing value.
The second, more general, method is then applied to a model of cell
cycle mitosis at two grazing points corresponding to trajectories
that have tangential contact with the discontinuity surface used to
trigger a halving of the cell mass. Again, the analysis predicts a
branch of period one solutions emanating from the grazing point, and an eigenvalue whose magnitude grows without bounds as the grazing
point is approached in parameter space.
In the case of both the AFM model and the cell cycle model, predictions produced using the discontinuity mapping analysis are shown to agree
with results produced using numerical continuation. In addition, we remark on the limitations of the discontinuity mapping analysis and provide suggestions for future work. Specifically, we identify a family
of attractors that exist for the AFM model and that warrant further investigation.Item withdrawn by Alexis Thompson ([email protected]) on 2010-06-17T15:51:19Z
Item was in collections:
University of Illinois Theses & Dissertations (ID: 1)
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Mathematical model for improved mass flow estimation in the feeder housing of a forage harvester
Full text linkFor the implementation of precision agriculture practices, accurate yield maps are needed. These yield maps depend on accurate mass flow measurements made during harvest, measurements that are difficult to make because of variability in yield and crop conditions within each field. One way to estimate mass flow rate in a self-propelled forage harvester is to measure the displacement of feed rollers as material enters the machine. In this work, a mathematical model that captures the interaction between the feed rollers and the incoming material was developed to improve the accuracy of the mass flow estimation. The model was developed based on physical principles, various material compaction models, and discrete element method simulations. When tested with experimental data, the model performed better than the current sensor system for some parameter sets, and as well as the current sensor system for others. Because of the mathematical complexity of the full dynamic model, and in order to reduce computation time, a reduced order quasi-static polynomial model was developed to approximate the relationship between feed roller displacement and mass flow rate. Finally, the perturbation induced learning technique was investigated as a method to real-time calibration of model parameters.Item withdrawn by Mark Zulauf ([email protected]) on 2012-03-19T14:37:37Z
Item was in collections:
University of Illinois Theses & Dissertations (ID: 1)
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license.txt: 4058 bytes, checksum: c4c591217a15981343821e41306fe1d9 (MD5)Item marked as restricted to the 'Administrator' Group (id=1) by William Ingram ([email protected]) on 2012-06-27T21:32:52Z
Item is restricted until 2014-06-27T21:32:23ZItem reinstated by Sarah Shreeves ([email protected]) on 2014-06-28T10:00:29Z
Item was in collections:
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Dissertations and Theses - Mechanical Science and Engineering (ID: 675)
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Robust design optimization with dynamic constraints using numerical continuation
Full text linkThis thesis develops a framework for performing robust design optimization of objective functions constrained by differential, algebraic, and integral constraints. A successive parameter continuation method combined with polynomial chaos expansions is used to locate stationary points. The use of such an expansion provides the benefit of being able to directly drive the mean and variance of a given response function (or an objective function that uses them) during continuation. A toolbox capable of constructing polynomial chaos expansions for system response functions evaluated on boundary value problems has been developed for this work. Its use is demonstrated and results are compared to analytically derived solutions of a linear, harmonically forced oscillator. The robust design optimization method is then applied a harmonically forced nonlinear oscillator.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-08-22 without embargo termsThe student, Jesse Anderson, accepted the attached license on 2018-12-10 at 18:54.The student, Jesse Anderson, submitted this Thesis for approval on 2018-12-10 at 19:15.This Thesis was approved for publication on 2019-01-02 at 11:02.DSpace SAF Submission Ingestion Package generated from Vireo submission #13280 on 2019-08-22 at 14:38:34Made available in DSpace on 2019-08-23T19:51:20Z (GMT). No. of bitstreams: 2
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Previous issue date: 2019-01-0
A study of chatter-induced loss of mechanical contact
Full text linkThis thesis concerns a recently discovered paradox in rigid body mechanics called reverse chatter, in which friction can cause the problem of two rigid bodies in sustained contact to admit multiple solutions. In particular, when the point of contact between the two bodies comes to rest, under certain conditions the rigid body model-coupled with Amontons-Coulomb friction and Stronge's energetic impact termination condition-allows for sustained stick, as well as an infinite number of other trajectories, each involving an infinite number of impacts in finite time. A similar mechanism can occur between two bodies with a compliant contact model, though in this case there are only finitely many impacts. The purpose of the present work is to call attention to this reverse chatter phenomenon, and to explore it in greater depth. In particular, we investigate what becomes of reverse chatter under alternative impact termination conditions to that of Stronge, namely those of Newton and Poisson. We begin by establishing, for the first time to our knowledge, that Poisson's impact termination condition is energetically consistent (i.e., it cannot generate energy during a frictional impact). We then show that reverse chatter is possible under Poisson's impact termination condition, but not under Newton's, thus establishing that, while the possibility of reverse chatter is sensitive to the impact termination condition used, it is not simply an artifact of Stronge's hypothesis. Additionally, we consider what becomes of chatter in the presence of an external control scheme which attempts to keep two bodies in sustained contact. We find that chatter-like behavior is still possible, and can lead to a loss of contact followed by a sequence of impacts qualitatively similar to that observed when chalk hops on a chalkboard. It is argued that reverse chatter may be responsible for this and similar phenomena. Furthermore, the present results suggest that reverse chatter occurs under easily achievable laboratory conditions, setting the stage for reverse chatter to be studied experimentally in the future.Item withdrawn by Alexis Thompson ([email protected]) on 2013-07-09T15:07:37Z
Item was in collections:
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