Explorations for alternating FPU-chains with large mass
Publication date
2021-12
Authors
van der Kallen, W.L.J.
Verhulst, Ferdinand
Editors
Advisors
Supervisors
Document Type
Article
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cc_by
Abstract
We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems drastically, and a MATHEMATICA programme focused on these systems. We show explicitly high-low frequency interaction for systems with 2pn particles where 2≤p≤47 is prime and n is an arbitrary natural number. In addition we have strong arguments for interactions in arbitrary large chains.
Keywords
Alternating masses, FPU-chains, Invariant manifolds, Mode interaction, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Citation
van der Kallen, W & Verhulst, F 2021, 'Explorations for alternating FPU-chains with large mass', International Journal of Non-Linear Mechanics, vol. 137, 103809, pp. 1-9. https://doi.org/10.1016/j.ijnonlinmec.2021.103809