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https://feeds.library.caltech.edu/people/Vakakis-A-F/article.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:25:28 +0000Frequency 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.edu/records/3ve3j-aaq48Acoustic 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.edu/records/03xm9-d8719