Dynamics of a mass–spring–pendulum system with vastly different frequencies

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dc.contributor.author Sheheitli, Hiba
dc.contributor.author Rand, Richard H.
dc.date.accessioned 2017-09-28T12:50:03Z
dc.date.available 2017-09-28T12:50:03Z
dc.date.copyright 2012 en_US
dc.date.issued 2017-09-28
dc.identifier.issn 1573-269X en_US
dc.identifier.uri http://hdl.handle.net/10725/6289
dc.description.abstract We investigate the dynamics of a simple pendulum coupled to a horizontal mass–spring system. The spring is assumed to have a very large stiffness value such that the natural frequency of the mass–spring oscillator, when uncoupled from the pendulum, is an order of magnitude larger than that of the oscillations of the pendulum. The leading order dynamics of the autonomous coupled system is studied using the method of Direct Partition of Motion (DPM), in conjunction with a rescaling of fast time in a manner that is inspired by the WKB method. We particularly study the motions in which the amplitude of the motion of the harmonic oscillator is an order of magnitude smaller than that of the pendulum. In this regime, a pitchfork bifurcation of periodic orbits is found to occur for energy values larger that a critical value. The bifurcation gives rise to nonlocal periodic and quasi-periodic orbits in which the pendulum oscillates about an angle between zero and π/2 from the down right position. The bifurcating periodic orbits are nonlinear normal modes of the coupled system and correspond to fixed points of a Poincare map. An approximate expression for the value of the new fixed points of the map is obtained. These formal analytic results are confirmed by comparison with numerical integration. en_US
dc.language.iso en en_US
dc.title Dynamics of a mass–spring–pendulum system with vastly different frequencies en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SOE en_US
dc.author.idnumber 201306323 en_US
dc.author.department Industrial And Mechanical Engineering en_US
dc.description.embargo N/A en_US
dc.relation.journal Nonlinear Dynamics en_US
dc.journal.volume 70 en_US
dc.journal.issue 1 en_US
dc.article.pages 25-41 en_US
dc.keywords Coupled oscillators en_US
dc.keywords DPM en_US
dc.keywords Method of direct partition of motion en_US
dc.keywords WKB method en_US
dc.keywords Bifurcations en_US
dc.identifier.doi http://dx.doi.org/10.1007/s11071-012-0428-9 en_US
dc.identifier.ctation Sheheitli, H., & Rand, R. H. (2012). Dynamics of a mass–spring–pendulum system with vastly different frequencies. Nonlinear Dynamics, 70(1), 25-41. en_US
dc.author.email hiba.sheheitli@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://link.springer.com/content/pdf/10.1007%2Fs11071-012-0428-9.pdf en_US
dc.author.affiliation Lebanese American University en_US

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