Wave-based analysis of jointed elastic bars: stability of nonlinear solutions

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dc.citation.journalTitleNonlinear Dynamics
dc.contributor.authorBalaji, Nidish Narayanaa
dc.contributor.authorBrake, Matthew R.W.
dc.contributor.authorLeamy, Michael J.
dc.date.accessioned2022-12-13T20:58:46Z
dc.date.available2022-12-13T20:58:46Z
dc.date.issued2022
dc.description.abstractIn this paper we develop two new approaches for directly assessing stability of nonlinear wave-based solutions, with application to jointed elastic bars. In the first stability approach, we strain a stiffness parameter and construct analytical stability boundaries using a wave-based method. Not only does this accurately determine stability of the periodic solutions found in the example case of two bars connected by a nonlinear joint, but it directly governs the response and stability of parametrically forced continuous systems without resorting to discretization, a new development in of itself. In the second stability approach, we pose a perturbation eigenproblem residue (PER) and show that changes in the sign of the PER locate critical points where stability changes from stable to unstable, and vice-versa. Lastly, we discuss follow-on research using the developed stability approaches. In particular, we identify an opportunity to study stability around internal resonance, and then identify a need to further develop and interpret the PER approach to directly predict stability.
dc.identifier.citationBalaji, Nidish Narayanaa, Brake, Matthew R.W. and Leamy, Michael J.. "Wave-based analysis of jointed elastic bars: stability of nonlinear solutions." <i>Nonlinear Dynamics,</i> (2022) Springer Nature: https://doi.org/10.1007/s11071-022-07969-4.
dc.identifier.doihttps://doi.org/10.1007/s11071-022-07969-4
dc.identifier.urihttps://hdl.handle.net/1911/114139
dc.language.isoeng
dc.publisherSpringer Nature
dc.rightsThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer Nature.
dc.titleWave-based analysis of jointed elastic bars: stability of nonlinear solutions
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpost-print
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