Book Section records
https://feeds.library.caltech.edu/people/Vakakis-A-F/book_section.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:25:28 +0000Chaotic motions in the dynamics of a hopping robot
https://resolver.caltech.edu/CaltechAUTHORS:20190611-155909131
Authors: {'items': [{'id': 'Vakakis-A-F', 'name': {'family': 'Vakakis', 'given': 'A. F.'}}, {'id': 'Burdick-J-W', 'name': {'family': 'Burdick', 'given': 'J. W.'}}]}
Year: 1990
DOI: 10.1109/ROBOT.1990.126212
Discrete dynamical systems theory is applied to the dynamic stability analysis of a simplified hopping robot. A Poincare return map is developed to capture the system dynamics behavior, and two basic nondimensional parameters which influence the systems dynamics are identified. The hopping behavior of the system is investigated by constructing the bifurcation diagrams of the Poincare return map with respect to these parameters. The bifurcation diagrams show a period-doubling cascade leading to a regime of chaotic behavior, where a strange attractor is developed. One feature of the dynamics is that the strange attractor can be controlled and eliminated by tuning an appropriate parameter corresponding to the duration of applied hopping thrust. Physically, the collapse of the strange attractor leads to globally stable uniform hopping motion.https://authors.library.caltech.edu/records/jrggc-5es35On the periodic motions of simple hopping robots
https://resolver.caltech.edu/CaltechAUTHORS:20190611-105732075
Authors: {'items': [{'id': "M'Closkey-R-T", 'name': {'family': "M'Closkey", 'given': 'R. T.'}}, {'id': 'Burdick-J-W', 'name': {'family': 'Burdick', 'given': 'J. W.'}}, {'id': 'Vakakis-A-F', 'name': {'family': 'Vakakis', 'given': 'A. F.'}}]}
Year: 1990
DOI: 10.1109/ICSMC.1990.142225
Discrete dynamical systems theory is applied to the analysis of simplified hopping robot models. A one-dimensional vertical hopping model that captures both the vertical hopping dynamics and nonlinear control algorithm is reviewed. A more complicated two-dimensional model that includes both forward and vertical hopping dynamics and a foot placement algorithm is presented. These systems are analyzed using a Poincare return map and hopping behavior is investigated by constructing the return map bifurcation diagrams with respect to system parameters. The diagrams show period doubling leading to chaotic behavior. Using the vertical model results as a guide, dynamic behaviour of the planar hopping system is interpreted.https://authors.library.caltech.edu/records/a6nv3-2a486Non-Reciprocity in Structures With Nonlinear Internal Hierarchy and Asymmetry
https://resolver.caltech.edu/CaltechAUTHORS:20180215-140456213
Authors: {'items': [{'id': 'Fronk-M-D', 'name': {'family': 'Fronk', 'given': 'Matthew D.'}}, {'id': 'Tawfick-S', 'name': {'family': 'Tawfick', 'given': 'Sameh'}}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}, {'id': 'Vakakis-A-F', 'name': {'family': 'Vakakis', 'given': 'Alexander F.'}}, {'id': 'Leamy-M-J', 'name': {'family': 'Leamy', 'given': 'Michael J.'}}]}
Year: 2017
DOI: 10.1115/DETC2017-67965
Acoustic reciprocity is a property of linear, time invariant systems in which the locations of the source of a forcing and the received signal can be interchanged with no change in the measured response. This work investigates the breaking of acoustic reciprocity using a hierarchical structure consisting of internally-scaled masses coupled with cubically nonlinear springs. Using both direct results and variable transformations of numerical simulations, energy transmission is shown to occur in the direction of decreasing scale but not vice versa, constituting the breaking of acoustic reciprocity locally. When a linear spring connects the smallest scale of such a structure to the largest scale of another identical structure, an asymmetrical lattice is formed. Because of the scale mixing and transient resonance capture that occurs within each unit cell, it is demonstrated through further numerical experiments that energy transmission occurs primarily in the direction associated with the nonlinear coupling from the large to the small scale, thus signifying the breaking of reciprocity globally. This nonlinear hierarchical structure exhibits strong amplitude-dependency in which reciprocity-breaking is associated with specific ranges of excitation amplitudes for both impulse and harmonic forcing.https://authors.library.caltech.edu/records/dn7be-cp618