Synchronous and non-synchronous responses of systems with multiple identical nonlinear vibration absorbers

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dc.contributor.author Issa, Jimmy S.
dc.contributor.author Shaw, Steven W.
dc.date.accessioned 2018-02-08T09:26:53Z
dc.date.available 2018-02-08T09:26:53Z
dc.date.copyright 2015 en_US
dc.identifier.issn 1095-8568 en_US
dc.identifier.uri http://hdl.handle.net/10725/7051
dc.description.abstract In this work we investigate the nonlinear dynamic response of systems composed of a primary inertia to which multiple identical vibration absorbers are attached. This problem is motivated by observations of systems of centrifugal pendulum vibration absorbers that are designed to reduce engine order torsional vibrations in rotating systems, but the results are relevant to translational systems as well. In these systems the total absorber mass is split into multiple equal masses for purposes of distribution and/or balance, and it is generally expected that the absorbers will act in unison, corresponding to a synchronous response. In order to capture nonlinear effects of the responses of the absorbers, specifically, their amplitude-dependent frequency, we consider them to possess nonlinear stiffness. The equations of motion for the system are derived and it is shown how one can uncouple the equations for the absorbers from that for the primary inertia, resulting in a system of identical resonators that are globally coupled. These symmetric equations are scaled for weak nonlinear effects, near resonant forcing, and small damping. The method of averaging is applied, from which steady-state responses and their stability are investigated. The response of systems with two, three, and four absorbers are considered in detail, demonstrating a rich variety of bifurcations of the synchronous response, resulting in responses with various levels of symmetry in which sub-groups of absorbers are mutually synchronous. It is also shown that undamped models with more than two absorbers possess a degenerate response, which is made robust by the addition of damping to the model. Design guidelines are proposed based on the nature of the system response, with the aim of minimizing the acceleration of the primary system. It is shown that the desired absorber parameters are selected so that the system achieves a stable synchronous response which does not undergo jumps via saddle-node bifurcations, nor instabilities related to the underlying symmetry of the system. en_US
dc.language.iso en en_US
dc.title Synchronous and non-synchronous responses of systems with multiple identical nonlinear vibration absorbers en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SOE en_US
dc.author.idnumber 200803943 en_US
dc.author.department Industrial And Mechanical Engineering en_US
dc.description.embargo N/A en_US
dc.relation.journal Journal of Sound and Vibration en_US
dc.journal.volume 348 en_US
dc.article.pages 105-125 en_US
dc.identifier.doi https://doi.org/10.1016/j.jsv.2015.03.021 en_US
dc.identifier.ctation Issa, J. S., & Shaw, S. W. (2015). Synchronous and non-synchronous responses of systems with multiple identical nonlinear vibration absorbers. Journal of Sound and Vibration, 348, 105-125. en_US
dc.author.email jimmy.issa@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url https://www.sciencedirect.com/science/article/pii/S0022460X15002394 en_US
dc.author.affiliation Lebanese American University en_US

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