Extended framework of Hamilton's principle applied to Duffing oscillation

Jinkyu Kim, Hyeonseok Lee and Jinwon Shin

Applied Mathematics and Computation, 2020, vol. 367, issue C

Abstract: The paper begins with a novel variational formulation of Duffing equation using the extended framework of Hamilton's principle (EHP). Unlike the original Hamilton's principle, this formulation properly accounts for initial conditions, and it recovers all the governing differential equations as its Euler–Lagrange equation. Thus, it serves base for the development of novel computational methods, involving finite element representation over time. For its feasibility, we provide the simplest temporal finite element method by adopting linear temporal shape functions. Numerical examples are included to verify and investigate performance of non-iterative algorithm in the developed method.

Keywords: Duffing equation; Extended framework of Hamilton's principle; Variational formulation; Temporal finite element method; Non-iterative algorithm (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307544

DOI: 10.1016/j.amc.2019.124762

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