Abstract
A one-dimensional nonlinear elastic chain, known as Fermi–Pasta–Ulam system, is analyzed in the static field. The chain is made of elements admitting a quartic potential, with softening nonlinear behavior. When the chain is subject to pure tension, it exhibits a multi-degenerate hill-top bifurcation, from which several softening branches bifurcate. On each path, the springs either behave softening or hardening, in all the possible combinations, making the response non-unique. Both exact and asymptotic solutions are pursued, and the multitude of the bifurcated paths is illustrated by bifurcation diagrams. A proof of their instability is given. The role of the imperfections is commented, either in modifying the equilibrium paths and in unfolding the degenerate bifurcation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
