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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 15 Apr 2024 16:08:58 +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.eduhttps://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.eduhttps://authors.library.caltech.edu/records/a6nv3-2a486Frequency bands of strongly nonlinear homogeneous granular systems
https://resolver.caltech.edu/CaltechAUTHORS:20130826-112439730
Authors: {'items': [{'id': 'Lydon-J', 'name': {'family': 'Lydon', 'given': 'Joseph'}}, {'id': 'Jayaprakash-K-R', 'name': {'family': 'Jayaprakash', 'given': 'K. R.'}}, {'id': 'Ngo-Duc', 'name': {'family': 'Ngo', 'given': 'Duc'}}, {'id': 'Starosvetsky-Y', 'name': {'family': 'Starosvetsky', 'given': 'Yuli'}}, {'id': 'Vakakis-A-F', 'name': {'family': 'Vakakis', 'given': 'Alexander F.'}}, {'id': 'Daraio-C', 'name': {'family': 'Daraio', 'given': 'Chiara'}, 'orcid': '0000-0001-5296-4440'}]}
Year: 2013
DOI: 10.1103/PhysRevE.88.012206
Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [ Jayaprakash, Starosvetsky, Vakakis, Peeters and Kerschen Nonlinear Dyn. 63 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/3ve3j-aaq48Non-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.eduhttps://authors.library.caltech.edu/records/dn7be-cp618Acoustic Non-Reciprocity in Lattices With Nonlinearity, Internal Hierarchy, and Asymmetry: Computational Study
https://resolver.caltech.edu/CaltechAUTHORS:20190802-154910921
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': 'Li-Shuangbao', 'name': {'family': 'Li', 'given': 'Shuangbao'}}, {'id': 'Vakakis-A-F', 'name': {'family': 'Vakakis', 'given': 'Alexander'}}, {'id': 'Leamy-M-J', 'name': {'family': 'Leamy', 'given': 'Michael J.'}}]}
Year: 2019
DOI: 10.1115/1.4043783
Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/03xm9-d8719